Answer:
Given
[tex]f(m+n)=f(m)f(n)[/tex]
If we assume
[tex]f(x)=ae^{x}\\\\f(m+n)=ae^{m+n}\\\\\therefore f(m+n)=ae^{m}\times ae^{n}(\because x^{a+b}=x^{a}\times x^{b})\\\\\Rightarrow f(m+n)=f(m)\times f(n)[/tex]
Similarly
We can generalise the result for
[tex]f(x)=am^{x }[/tex] where a,m are real numbers
2)
[tex]f(m\cdot n)=f(m)+f(n)\\\\let\\f(x)=log(x)\\\therefore f(mn)=log(mn)=log(m)+log(n)\\\\\therefore f(mn)=f(m)+f(n)[/tex]
QUESTION 7 10 points Save Answer You are spinning a 025 kg mass over your head at the end of a 0 5 m string lif you let go of the string the mass wil sail ofof a tangent at 2 mis What isthe angular momenturm of the spining mass belore You are spinning a 0 25 kg mass over your head at the release? Because angular momentum is always conserved, where does the angular momentum go atter release? QUESTION 8 10 points Save Answer
Answer:
angular moment is 0.25 kg.m²/s
Step-by-step explanation:
given data in question
mass (m) = 0.25 kg
length of string i.e. radius (r) = 0.5 m
velocity = 2 m/s
to find out
angular momentum before mass release
solution
we know angular moment formula i.e.
angular moment = mass × velocity × radius ................1
put the value mass velocity and radius in equation 1 we get angular moment i.e.
angular moment = mass × velocity × radius
angular moment = 0.25 × 2 × 0.5
angular moment = 0.25
so the angular moment is 0.25 kg.m²/s before release and 0.25 kg.m²/s after release because angular momentum is always conserved
The question deals with angular momentum and its conservation in rotational motion. The angular momentum before the mass is released remains constant and is carried by the mass upon release. Supplementary problems discuss changes in angular momentum and the effects of pulling in a spinning mass on its rotational dynamics.
The question regards the concept of angular momentum in classical mechanics, specifically within the realm of rotational motion. Angular momentum, denoted by L, is a physical quantity that represents the rotational inertia of a spinning object multiplied by its angular velocity, and it's given by the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.
For the case where a mass is spinning over your head and then released, the angular momentum just before the release is conserved. This means that if we calculate the angular momentum while the mass is attached to the string and spinning, the same amount of angular momentum will be present in the mass's linear motion after it is released along the tangent. If we assume that the mass travels in a circular path while attached to the string, the angular momentum can be related to the linear momentum by L = mvr, where m is the mass, v is the linear velocity just before release, and r is the radius of the circular path.
Upon release, because angular momentum is conserved, the mass carries this angular momentum into its linear motion, causing it to move off on a tangent at a velocity that reflects this conservation. If there are no external torques acting on the system, the angular momentum will not change; therefore, it 'moves' with the mass as linear momentum.
Regarding the supplementary problems provided, when angular velocity is increased, the tendency for a spinning object is to move outward due to centrifugal force. Consequently, the string's angle with respect to the vertical will increase. To calculate the initial and final angular momenta, one would use the same conservation principle, taking into account the changes in angular velocity and the moment of inertia. A scenario where the rod spins fast enough to make the ball horizontal suggests an infinitely large angular velocity, which is not practically achievable. Therefore, the ball cannot be truly horizontal as it would require an infinite amount of energy.
Concerning the rock on a string example, as you pull the string in and reduce the radius, the angular momentum remains constant assuming no external torques are acting on the system. This leads to an increase in the angular velocity since L = Iω and I decreases with a smaller radius (I for a point mass is mr²). The increased speed will result in a shorter time required for one revolution (higher frequency of rotation) and a greater centripetal acceleration. The string is under more tension as a result of the increased centripetal force, which might lead to it breaking.
For the collision problem with the spinner and the rod spinning at different rates, conservation of energy or momentum principles would be employed to find the corresponding change in angular velocity. The initial and final angular momenta or energies are equated, considering that all the energy transferred is mechanical and that the rotational inertia of the spinner is required to calculate the angular velocity post-collision.
Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated list. x =
Answer:
[tex]x=-2,0,3[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=15x^3-15x^2-90x[/tex]. We are asked to find the zeros of our given function.
To find the zeros of our given function, we will equate our given function by 0 as shown below:
[tex]15x^3-15x^2-90x=0[/tex]
Now, we will factor our equation. We can see that all terms of our equation a common factor that is [tex]15x[/tex].
Upon factoring out [tex]15x[/tex], we will get:
[tex]15x(x^2-x-6)=0[/tex]
Now, we will split the middle term of our equation into parts, whose sum is [tex]-1[/tex] and whose product is [tex]-6[/tex]. We know such two numbers are [tex]-3\text{ and }2[/tex].
[tex]15x(x^2-3x+2x-6)=0[/tex]
[tex]15x((x^2-3x)+(2x-6))=0[/tex]
[tex]15x(x(x-3)+2(x-3))=0[/tex]
[tex]15x(x-3)(x+2)=0[/tex]
Now, we will use zero product property to find the zeros of our given function.
[tex]15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0[/tex]
[tex]15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0[/tex]
[tex]\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0[/tex]
[tex]x=0\text{ (or) }x=3\text{ (or) }x=-2[/tex]
Therefore, the zeros of our given function are [tex]x=-2,0,3[/tex].
Use Laplace transforms to solve the following initial value problem: x"+8x'+15x = 0; x(0) = 2, x'(0) = -3 PLEASE SHOW ALL WORK, OR RISK LOSING ALL POINTS!!!! x')=sX (s) - x(0) x"(t) = sº X(s) - sx(0) - x'(0)
Taking the transform of both sides gives
[tex]\mathcal L_s\{x''+8x'+15x\}=0[/tex]
[tex](s^2X(s)-sx(0)-x'(0))+8(sX(s)-x(0))+15X(s)=0[/tex]
where [tex]X(s)[/tex] denotes the Laplace transform of [tex]x(t)[/tex], [tex]\mathcal L_s\{x(t)\}[/tex]. Solve for [tex]X(s)[/tex] to get
[tex](s^2+8s+15)X(s)=2s+13[/tex]
[tex]X(s)=\dfrac{2s+13}{s^2+8s+15}=\dfrac{2s+13}{(s+3)(s+5)}[/tex]
Split the right side into partial fractions:
[tex]\dfrac{2s+13}{(s+3)(s+5)}=\dfrac a{s+3}+\dfrac b{s+5}[/tex]
[tex]2s+13=a(s+5)+b(s+3)[/tex]
If [tex]s=-3[/tex], then [tex]7=2a\implies a=\dfrac72[/tex]; if [tex]s=-5[/tex], then [tex]3=-2b\implies b=-\dfrac32[/tex]. So
[tex]X(s)=\dfrac72\dfrac1{s+3}-\dfrac32\dfrac1{s+5}[/tex]
Finally, take the inverse transform of both sides to solve for [tex]x(t)[/tex]:
[tex]x(t)=\dfrac72e^{-5t}-\dfrac32e^{-3t}[/tex]
The initial value problem is a second-order homogeneous differential equation that can be solved using the Laplace Transform. After substituting the initial conditions and simplifying the equation, one can decompose the equation using partial fraction decomposition and finally find the solution in the time domain.
Explanation:Your given initial value problem is a second-order homogeneous differential equation. You should use the Laplace Transform to solve it. The Laplace transform of this equation is: L{x''(t) + 8x'(t) + 15x(t)} = 0 which simplifies to s²X(s) - sx(0) - x'(0) + 8[sX(s) - x(0)] + 15X(s) = 0. Substituting the initial conditions x(0) = 2 and x'(0) = -3, we get s²X(s) - 2s - (-3) + 8[sX(s) - 2] + 15X(s) = 0, then simplify to (s² + 8s + 15)X(s) = 2s + 3.
The roots of the quadratic equation s² + 8s + 15 = 0 are -5 and -3. So, the solution of the equation X(s) = (2s + 3) / (s² + 8s + 15) can be solved by using partial fraction decomposition. Therefore, the solution in the time domain would be x(t) = 2e⁻³ᵗ - e⁻⁵ᵗ.
Learn more about Laplace Transform here:https://brainly.com/question/31481915
#SPJ11
If there are 1.338 trillion barrels of oil in proven reserves and oil consumption is 82.78 million barrels per day, what is the maximum number of years current proven supply of oil runs out, if consumption does not decrease?
Answer:
Oil supply will run out in 44.283 years.
Step-by-step explanation:
There are 1.338 trillion barrels of oil in proven reserves.
If oil consumption is 82.78 million barrels per day then we have to calculate the number of years in which supply of oil runs out.
In this sum we will convert 1.338 million barrels of oil into million barrels first then apply unitary method to calculate the time in which oil supply runs out.
Since 1 trillion = [tex]10^{6}[/tex] million
Therefore, 1.338 trillion = 1.338×[tex]10^{6}[/tex] million
∵ 82.78 million barrels oil is the consumption of = 1 day
∴ 1 million barrels oil is the consumption of = [tex]\frac{1}{82.78}[/tex] day
∴ 1.338×[tex]10^{6}[/tex] barrels will be consumed in = [tex]\frac{1.338(10^{6})}{82.78}[/tex] days
= 16163.3245 days
≈ [tex]\frac{16163.3245}{365}[/tex] years
≈ 44.283 years
Therefore, oil supply will run out in 44.283 years
1 inch = 2.54 centimeters
800 centimeters= _______ inches
please round to nearest tenth please
I have been getting wrong answers
Answer:
It should be 314.9
Step-by-step explanation:
In every centimeter, there are about .3937 inches
So if you multiple .3937 by 800 and round to the nearest tenth, you get that answer
Which quantity is proportional to 20⁄5? Check all that are true. 100⁄25 10⁄2 60⁄15 40⁄2 4⁄1
Answer:
100⁄25 60⁄15 4⁄1
Step-by-step explanation:
20/5 = 4
We need to see what equals 4
100⁄25 = 4
10⁄2=5
60⁄15=4
40⁄2=20
4⁄1=4
When a company produces 10 items, it charges a price of $65 per product. When it produces 20 items, it charges a price of $60 per product. The cost to produce 10 items is $650, and the cost to produce 20 items is $1050. Based on this information, find the following:
price function
cost function
revenue function
profit function
break even points ,
maximum profit
number of products to produce maximum profit
Answer:
price function: p = 70-q/2 . . . . price per itemcost function: c = 40q +250 . . . . cost of q itemsrevenue function: r = q/2(140 -q) . . . . revenue from q itemsprofit function: P = 1/2(50-q)(q-10) . . . . profit from q itemsbreak even points: (p, q) = (65, 10), (45, 50)maximum profit: $200quantity for maximum profit: 30Step-by-step explanation:
For these we have to assume the price and cost functions are linear.
Let p, c, r, P, q represent price, cost, revenue, Profit, and quantity (of items), respectively. The 2-point form of the equation for a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Price Function
Using the two-point form for price, we get ...
p = (60 -65)/(20 -10)(q -10) +65 = -5/10(q -10) +65
p = (-1/2)q +70 . . . . price per item
Cost Function
Using the two-point form for cost, we get ...
c = (1050 -650)/(20 -10)(q -10) +650 = 40(q -10) +650
c = 40q +250 . . . . cost for q items
Revenue Function
Revenue is the product of price and quantity:
r(q) = qp
r(q) = (1/2)q(140 -q) . . . . revenue from sale of q items
Profit Function
Profit is the difference between revenue and cost.
P(q) = r(q) -c = 1/2q(140 -q) -(40q +250)
P(q) = -1/2q^2 +30q -250
P(q) = (-1/2)(q -10)(q -50) . . . . factored form
Break-Even Points
The profit function will be zero when its factors are zero, at q=10 and q=50. The price function tells us the corresponding prices are $65 and $45 per item, respectively.
Maximum Profit
The profit function is a maximum at the quantity halfway between the break-even points. There, q = (10+50)/2 = 30, and P(30) is ...
P(30) = -1/2(30-10)(30-50) = 1/2(20^2) = 200 . . . . dollars
Quantity for Maximum Profit
This was found to be 30 in the previous section.
If you are selecting courses for next semester and you have 4 options to fill your science requirement, 2 options to fill your diversity requirement, 5 options to fill your English requirement and 4 options to fill your math requirement, use the fundamental counting principal or slot diagram to find out how many possible outcomes do you have for schedules.
Answer: 160
Step-by-step explanation:
Given : The options to fill science requirement =4
The options to fill diversity requirement =2
The options to fill English requirement =5
The options to fill math requirement = 4
The Fundamental Counting Principle say that the number of total outcomes is equal to the product of the number of ways of all the events occur in the problem.
Using Fundamental Counting Principle, we have the total number of possible outcomes for the given situation :-
[tex]4\times2\times5\times4=160[/tex]
Hence, the total number of possible outcomes = 160
The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Draw the triangle with vertices A(1, 1), B(4, 3), C(1, 7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)
Answer:
see below
Step-by-step explanation:
Filling the given numbers into the given formulas, you have ...
Line AB:
x = 1 +(4-1)t, y = 1 +(3-1)t
x = 1+3t, y = 1+2t . . . . . . simplify
Line BC:
x = 4 +(1-4)t, y = 3 +(7-3)t
x = 4 -3t, y = 3 +4t . . . . . simplify
Line AC:
x = 1 +(1-1)t, y = 1 +(7-1)t
x = 1, y = 1+6t . . . . . . . . . .simplify
b. Suppose 20% of all balls produced by a particular manufacturer are less than 1.680 inches in diameter, and assume that the number of such balls, x, in a sample of two dozen balls can be adequately characterized by a binomial probability distribution. Find the mean and standard deviation of the binomial distribution.
Answer: Mean = 4.8
Standard deviation = 1.96
Step-by-step explanation:
The mean and standard deviation of the binomial distribution is given by :-
[tex]\mu=np\\\sigma=\sqrt{np(1-p)}[/tex], where n is the total number of trials , p is the the probability of success.
Given : The probability that the produced by a particular manufacturer are less than 1.680 inches in diameter = 20%=0.2
Sample size : n=24 [since 1 dozen = 12]
Now, the mean and standard deviation of the binomial distribution is given by :-
[tex]\mu=24\times0.2=4.8\\\\\sigma=\sqrt{24(0.2)(1-0.2)}\\\\=1.95959179423\approx1.96[/tex]
The mean of the binomial distribution for the balls less than 1.680 inches in diameter is 4.8, and the standard deviation is approximately 1.96.
Explanation:To find the mean and standard deviation for a binomial probability distribution where 20% of all balls are less than 1.680 inches in diameter from a sample of two dozen (24) balls, we use the formulas for a binomial distribution. The mean (μ) of a binomial distribution is calculated as μ = n * p, where n is the number of trials and p is the probability of success on a single trial. In this case, n = 24 and p = 0.20.
The mean is μ = 24 * 0.20 = 4.8.
To calculate the standard deviation (σ), we use the formula σ = √(n * p * (1 - p)), where (1 - p) is the probability of failure. The standard deviation is σ = √(24 * 0.20 * 0.80) = √(3.84) ≈ 1.96.
In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 95% confident that your sample mean is within 12 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 213 min. What is a major obstacle to getting a good estimate of the population mean? Use technology to find the estimated minimum required sample size. The minimum sample size required is 1211 computer users. (Round up to the nearest whole number.) What is a major obstacle to getting a good estimate of the population mean?
PLEASE HELP!!
Demonstrate your understanding of how to solve exponential equations by rewriting the base. Solve the problem below fully and explain all the steps...
25^3k = 625
To solve the equation [tex]25^3^k[/tex] = 625, rewrite the base as a power of 5 and use the exponentiation rule. Simplify the equation and equate the exponents to solve for k.
Explanation:To solve the exponential equation 253k = 625, we need to rewrite the base of 25 as a power of 5. Since 25 = 52, we can rewrite the equation as (52)3k = 625.
Using the rule (ab)c = ab × c, we can simplify the equation to 52 × 3k = 625.
Now, we can rewrite 625 as a power of 5 by realizing that 625 = 54. Therefore, we have 52 × 3k = 54.
Since the bases are the same, we can equate the exponents and solve for k:
2 × 3k = 4
6k = 4
k = 4/6
k = 2/3
Learn more about Exponential equations here:https://brainly.com/question/32034918
#SPJ3
To solve the exponential equation 25^3k = 625, rewrite the base 25 as a power of 5. Simplify the equation and set the exponents equal to each other to solve for k.
Explanation:To solve the exponential equation 253k = 625, we can rewrite the base 25 as a power of 5, since 52 = 25. So, the equation becomes (52)3k = 625. Using the rule of exponents (am)n = amn , we can simplify it to 56k = 625.
Next, we can rewrite 625 as a power of 5: 625 = 54. So, the equation becomes 56k = 54.
Since the bases are the same, we can set the exponents equal to each other: 6k = 4. Solving for k, we divide both sides by 6 to get k = 4/6 = 2/3.
Learn more about Exponential equations here:https://brainly.com/question/11672641
#SPJ6
Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.5 in. and a standard deviation of 0.9 in. Find Upper P 99. That is, find the hip breadth for men that separates the smallest 99% from the largest 1%.
Answer:
16.59 inches
Step-by-step explanation:
Mean value = u = 14.5 inches
Standard deviation = [tex]\sigma[/tex] = 0.9 in
We need to find the 99th percentile of the given distribution. This can be done by first finding the z value associated with 99th percentile and then using that value to calculate the exact value of hip breadth that lies at 99th percentile
From the z-table, the 99th percentile value is at a z-value of:
z = 2.326
This means 99% of the z-scores are below this value. Now we need to find the equivalent hip breadth for this z-score
The formula to calculate the z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
where, x is the hip breadth which is equivalent to this z-score.
Substituting the values we have:
[tex]2.326=\frac{x-14.5}{0.9}\\\\ 2.0934=x-14.5\\\\ x=16.5934[/tex]
Rounded to 2 decimal places, engineers should design the seats which can fit the hip breadth of upto 16.59 inches to accommodate the 99% of all males.
To find the hip breadth for men that separates the smallest 99% from the largest 1%, we can use the z-score formula and the standard normal distribution table. The hip breadth that separates the smallest 99% is approximately 16.197 inches.
Explanation:To find the hip breadth for men that separates the smallest 99% from the largest 1%, we need to determine the z-score corresponding to a 99% percentile. Firstly, we will calculate the z-score using the formula: z = (x - μ) / σ, where x is the hip breadth, μ is the mean (14.5 in.), and σ is the standard deviation (0.9 in.). Secondly, we use the standard normal distribution table or a z-score calculator to find the z-score that corresponds to a 99% percentile. Finally, we can solve for x using the formula: x = z * σ + μ.
Substituting the values, we have z = (x - 14.5) / 0.9. From the standard normal distribution table, the z-score that corresponds to a 99% percentile is approximately 2.33.
Plugging the values into the equation, we get 2.33 = (x - 14.5) / 0.9. Solving for x gives us x = 2.33 * 0.9 + 14.5 = 16.197 in.
Learn more about Z-Score for Normal Distribution here:https://brainly.com/question/31322979
#SPJ
Proponents of rational expectations theory argued that, in the most extreme case, if policymakers are credibly committed to reducing inflation and rational people understand that commitment and quickly lower their inflation expectations, the sacrifice ratio could be as small as A. 5. B. 4. C. 1. D. 0.
Answer:
The answer is zero or option D.
Step-by-step explanation:
Proponents of rational expectations theory argued that, in the most extreme case, if policymakers are credibly committed to reducing inflation and rational people understand that commitment, and quickly lower their inflation expectations, the sacrifice ratio could be as small as 0.
roduction records indicate that 2.8% of the light bulbs produced in a facility are defective. A random sample of 30 light bulbs was selected. a. Use the binomial distribution to determine the probability that fewer than three defective bulbs are found.
Answer: Our required probability is 0.947.
Step-by-step explanation:
Since we have given that
Number of light bulbs selected = 30
Probability that the light bulb produced in a facility are defective = 2.8% = 0.028
We need to find the probability that fewer than 3 defective bulbs are found.
We will use "Binomial distribution":
n = 30, p = 0.028
so, P(X>3)=P(X=0)+P(X=1)+P(X=2)
So, it becomes,
[tex]P(X=0)=(1-0.0.28)^{30}=0.426[/tex]
and
[tex]P(X=1)=^{30}C_1(0.028)(0.972)^{29}=0.368\\\\P(X=2)=^{30}C_2(0.028)^2(0.972)^28=0.153[/tex]
So, the probability that fewer than three defective bulbs are defective is given by
[tex]0.426+0.368+0.153\\\\=0.947[/tex]
The function g is defined below.
Find all values of x that are NOT in the domain of g .
If there is more than one value, separate them with commas.
g(x) = x - 3 / x^2 - x -6
The answer is:
The only value of "x" that ARE NOT in the domain of the function g, are -2 and 3.
Restriction: {-2,3}
Why?Since we are working with a quotient (or division), we must remember that the only restriction for this kind of functions are the values that make the denominator equal to 0, so, the domain of the function will include all the values of "x" that are different than the zeroes or roots of the denominator.
We have the function:
[tex]h(x)=\frac{x-3}{x^2-x-6}[/tex]
Where its denominator is :
[tex]x^2-x-6[/tex]
Now, finding the roots or zeroes of the expression, by factoring, we have:
We need to find two numbers which product is equal to -6 and its addition is equal to -1, these numbers are -3 and 2, we have:
[tex]-3*2=-6\\-3+2=-1[/tex]
So, the factorized form of the expression will be:
[tex](x-3)*(x+2)[/tex]
We have that the expression will be equal to 0 if "x" is equal to "-2" and "3", so, the values that are not in the domain of g are: -2,3.
Hence, we have:
Restriction: {-2,3}
Domain: (-∞,-2)U(-2,3)U(3,∞)
Have a nice day!
To find the values of x that are not in the domain of the function g(x), we need to identify any values for x that would make the function undefined. The function g(x) = (x - 3) / (x^2 - x - 6) becomes undefined when the denominator is equal to zero, since division by zero is not allowed.
Thus, we need to find the values of x that make the denominator x^2 - x - 6 equal to zero. To do this, we'll solve the quadratic equation:
x^2 - x - 6 = 0
To solve this quadratic equation, we can factor the quadratic expression, or use the quadratic formula. We'll try factoring first:
x^2 - x - 6 = (x - 3)(x + 2)
Set each factor equal to zero and solve for x:
x - 3 = 0 --> x = 3
x + 2 = 0 --> x = -2
So, the values of x that are not in the domain of g(x) are -2 and 3, because these are the values that make the denominator equal to zero. Hence, g(x) is undefined at x = -2 and x = 3.
Therefore, the values that are NOT in the domain of g are:
-2, 3
The maker of an automobile advertises that it takes 12 seconds to accelerate from 20 kilometers per hour to 65 kilometers per hour. Assuming constant acceleration, compute the acceleration in meters per second per second. Round your answer to three decimal places.
Answer:
The acceleration is 1.0416 m/[tex]s^{2}[/tex]
Step-by-step explanation:
In order to solve this problem we first need to know the formula for acceleration which is the following.
[tex]acceleration = \frac{final.velocity - initial.velocity}{final.time - initial.time}[/tex]
Since the time acceleration is calculated as [tex]m/s^{2}[/tex] we need to convert the km/h into m/s. Since 1km = 1000m and 1 hour = 3600 seconds, then
[tex]\frac{20*1000 }{3600s} = \frac{20,000m}{3600s} = \frac{20m}{3.6s}[/tex]
**Dividing numerator and denominator by 1000 to simplify**
[tex]\frac{65*1000 }{3600s} = \frac{65,000m}{3600s} = \frac{65m}{3.6s}[/tex]
**Dividing numerator and denominator by 1000 to simplify**
Now we can plug in the values into the acceleration formula to calculate the acceleration.
[tex]acceleration = \frac{\frac{65m}{3.6s}-\frac{20m}{3.6s} }{12s-0s}[/tex]
[tex]acceleration = \frac{\frac{45m}{3.6s}}{12s}[/tex]
[tex]acceleration = \frac{\frac{12.5m}{s}}{12s}[/tex]
[tex]acceleration = \frac{\frac{1.0416m}{s}}{s}[/tex]
Finally we can see that the acceleration is 1.0416 m/[tex]s^{2}[/tex]
In order to find the acceleration, we first need to convert the speed from km/h to m/s. Then we use the formula for acceleration which is the change in velocity divided by the change in time. The final acceleration is approximately 1.042 m/s².
Explanation:The subject of the question pertains to the concept of acceleration in Physics. Acceleration, measured in meters per second per second (m/s²), is the rate at which an object changes its velocity. To determine this, we first have to convert the velocities from kilometers per hour (km/h) to meters per second (m/s). We know that 1 km = 1,000 m and 1 hour = 3,600 s. Therefore:
20 km/h = 20,000 m/3,600 s = 5.56 m/s65 km/h = 65,000 m/3,600 s = 18.06 m/sNext we use the formula for acceleration: a = Δv / Δt. The change in velocity (Δv) is the final velocity minus the initial velocity. Thus, Δv = 18.06 m/s - 5.56 m/s = 12.5 m/s. The change in time (Δt) is given as 12 seconds.
Substituting these values into the formula, we get: a = Δv / Δt = 12.5 m/s ÷ 12 s = 1.042 m/s². Therefore, the car's acceleration, assuming it's constant, is approximately 1.042 m/s².
Learn more about Acceleration here:https://brainly.com/question/12550364
#SPJ11
a computer sells for$995. which is markedup 35% Whats the cost of computer
Answer:
$1343.25
Step-by-step explanation:
995*1.35=1343.25
Find the derivative of the following functions: a. f(x) = (x^3 + 5)^1/4 - 15e^x^3 b. f(x) = (x - 3)^2 (x - 5)/(x - 4)^2(x^2 + 3)^5
Answer:
Step-by-step explanation:
Given function is
(a)F(x)=[tex]\left ( x^{3}+5\right )^{0.25}-15e^{x^{3}}[/tex]
[tex]F^{'}\left ( x\right )[/tex]=[tex]0.25\left ( x^{3}+5\right )^{-0.75}\frac{\mathrm{d} x^{3}}{\mathrm{d} x}-15e^{x^{3}}\frac{\mathrm{d} x^{3}}{\mathrm{d} x}[/tex]
[tex]F^{'}\left ( x\right )=0.25\left ( x^{3}+5\right )^{-0.75}\times 3x^{2}-15e^{x^{3}}\times \left ( 3x^{2}\right )[/tex]
(b)F(x)=[tex]\frac{\left ( x-3\right )^2\left ( x-5\right )}{\left ( x-4\right )^2\left ( x^{2}+3\right )^5}[/tex]
[tex]F^{'}\left ( x\right )[/tex]=[tex]\frac{\left [ 2\left ( x-3\right )\right \left ( x-5\right )+\left ( x-3\right )^2]\left [ \left ( x-4\right )^2\left ( x^2+3\right )^5\right ]-\left [ 2\left ( x-4\right )^{3}\left ( x^2+3\right )^5+5\left ( x^2+3\right )^4\left ( 2x\right )\left ( x-4\right )^2\right ]\left [ \left ( x-3\right )^2\left ( x-5\right )\right ]}{\left [\left ( x-4\right )^2\left ( x^2+3\right )^5\right ]^2}[/tex]
Let A and B are n x n matrices from which A is invertible. Suppose AB is singular. What conclusion can be made about the invertibility of B?
Answer: Matrix B is non- invertible.
Step-by-step explanation:
A matrix is said to be be singular is its determinant is zero,
We know that if a matrix is singular then it is not invertible. (1)
Or if a matrix is invertible then it should be non-singular matrix. (2)
Given : A and B are n x n matrices from which A is invertible.
Then A must be non-singular matrix. ( from 2 )
If AB is singular.
Then either A is singular or B is singular but A is a non-singular matrix.
Then , matrix B should be a singular matrix. ( from 2 )
So Matrix B is non- invertible. ( from 1 )
The position of a particle along a straight line is given by s = (1.5t 3 - 13.5t 2 + 22.5t) ft, where t is in seconds. Determine the position of the particle when t = 6 s and the total distance it travels during the 6-s time interval. Hint: Plot the path to determine the total distance traveled.
The position of the particle when t equals 6 is equal to -27 feet.
The total distance this particle travels during the 6-s time interval is equal to 69 feet.
Based on the information provided above, we can logically deduce the following polynomial function that models the position of a particle along a straight line;
[tex]s = 1.5t^3 - 13.5t^2 + 22.5t[/tex]
In order to determine the position of the particle when t is equal to 6, we would substitute 6 for t in the polynomial function as follows;
[tex]s(6) = 1.5(6)^3 - 13.5(6)^2 + 22.5(6)[/tex]
s(6) = 324 - 486 + 135
s(6) = -27 feet.
In order to determine the total distance this particle travels during the 6-s time interval, we would have to plot a graph of the velocity of the particle. Also, the velocity of the particle can be determined by taking the first derivative of the position with respect to time;
[tex]s = 1.5t^3 - 13.5t^2 + 22.5t\\\\s' = 4.5t^2 - 27t + 22.5[/tex]
Based on the graph, the particle changes directions at t equal 1 seconds and again t equal 5 seconds. Hence, the velocity of the particle drops to zero at these positions.
In this context, we would find the distance between these intervals;
Distance (0 ≤ t ≤ 1) = 10.5 - 0 = 10.5 feet.
Distance (1 ≤ t ≤ 5) = 10.5 - (-37.5) = 48 feet.
Distance (5 ≤ t ≤ 6) = -27 - (-37.5) = 10.5 feet.
For the total distance, we have;
Total distance = 10.5 + 48 + 10.5
Total distance = 69 feet.
Complete Question:
The position of a particle along a straight line is given by [tex]s = 1.5t^3 - 13.5t^2 + 22.5t[/tex] ft, where t is in seconds. Determine the position of the particle when t = 6 s and the total distance it travels during the 6-s time interval. Hint: Plot the path to determine the total distance traveled.
Use Archimedes exhaustion method to estimate pi accurate to two decimal places
Step-by-step Answer:
Calculating Pi using Archimedes method of polygons.
We know that the definition of pi is the ratio of circumference of a circle divided by the diameter. Starting with Pythagorean Theorem, and proposition 3 of Euclid’s Elements, Archimedes was able to approximate pi to any precision arithmetically, without further resort to geometry!
He figured that the perimeter of any regular polygon (all sides and vertex angles equal) is an approximation to a circle. More sides will make closer approximations.
Starting with a hexagon, he bisects the central angles to make polygons 12-, 24-, 48- and 96-sides, whose perimeters approaches that of a circle, and hence the approximation to pi since the diameter remains known and constant.
Proposition 3 is also commonly referred to as the angle bisector theorem, which states that in a triangle, an angle bisector subdivides the opposite sides in the ratio of the two remaining sides.
Please refer to the attached image for the nomenclature of the geometry.
The accompanying diagram shows that the perimeter of a hexagon is 12 times the length of AB, or 12*(1.0/2) = 6. With the diameter equal to 2*1.0 = 2, the approximation to pi is 6/2=3.0.
Pi(6) = 3.0
If we divide the central angle by two, we end up with a 12-sided polygon (dodecagon), with the half central angle of 15 degrees (triangle A’BC). To calculate the new perimeter, we need to calculate the length A’B, which is given by the angle-bisector theorem as
A’B / A’A = BC / AC
All other sides are known in terms of A’B
A’B / (0.5-A’B) = sqrt(3)/2 / 1
Solve for A’B by cross-multiplication and solving for A’B, we get
A’B = sqrt(3)/(2sqrt(3)+4) = 0.2320508 (to 7 decimals)
At the same time, the radius has been reduced to
A’C = sqrt(A’B^2+BC^2) = 0.896575
That brings the approximation of pi as 12*A’B/A’C
P(12) = 3.1058285 (7 decimals)
Continuing bisecting, now using a polygon of 24 sides, we only have to replace
AB by A’B, AC by A’C, and 12 by 24 to get
Pi(24) = 3.132629 (7 decimals)
Repeating again for a polygon of 48 sides,
Pi(48) = 3.1393502
Pi(96) = 3.1410320
Pi(192) = 3.1414525
Pi(384) = 3.1415576
Etc.
The accurate value of pi to 10 digits is 3.1415926536
And we conclude that Pi(48) is the first approximation the provides 2 decimal places of accuracy.
Note: What was calculated was actually the lower bound value of pi.
We can obtain the upper bound value of pi using the length of BC as the radius, which gives the upper bound. The average of the two bounds for a 384-sided polygon gives P_mean(384) = 3.1416102, which is accurate to 2 units in the 5th decimal place.
The Archimedes exhaustion method is a geometric approach to estimate the value of pi. By inscribing and circumscribing regular polygons within and around a circle, Archimedes determined lower and upper bounds for the value of pi.
As the number of sides for the polygons increased, the approximation of pi became more accurate. With a 96-sided polygon, Archimedes found that pi was greater than 3.1408 and less than 3.1429. By taking the average of these bounds, a more precise estimation of pi accurate to two decimal places is achieved.
Thus, using the Archimedes exhaustion method, we can estimate pi to be approximately 3.14, making it precise to two decimal places.
To know more about Archimedes visit:
https://brainly.com/question/31950755
#SPJ2
The distance between major cracks in a highway follows an exponential distribution with a mean of 13 miles. What is the standard deviation of the distance between two major cracks? Please enter the answer to 2 decimal places.
Answer:
σ = 13 miles
Step-by-step explanation:
Let us consider X continuous random variable and λ be the parameter of exponential density function.
where E(x) = [tex]\frac{1}{\lambda}[/tex]
where E(x) = is expected value=13
we have to find λ=[tex]\frac{1}{E(x)}[/tex]
λ=[tex]\frac{1}{13}[/tex]
λ=0.076
standard deviation = V(X) = σ = [tex]\frac{1}{\lambda}[/tex]
now , σ = [tex]\frac{1}{0.076}[/tex]
σ = 13 miles is the distance between the two major crack.
Final answer:
The standard deviation of the distance between two major cracks in a highway, which follows an exponential distribution with a mean of 13 miles, is 13 miles.
Explanation:
The question asks for the standard deviation of the distance between two major cracks in a highway, given that this distance follows an exponential distribution with a mean of 13 miles.
In an exponential distribution, the mean (μ) and standard deviation (σ) are equal.
Therefore, the standard deviation of the distance between two major cracks is also 13 miles.
The average of 1/5 and other two numbers out of which one is the half of the other is 1/4. The smallest fraction out of unknowns is:
a) 1/6 b) 11/60 c) 1 1/30 d) 1/2 e) 9/20
Answer:
The smallest fraction is b 11/60
To find the smallest of the unknown fractions given that their average with 1/5 is 1/4, we denoted the smallest fraction as x, leading to a simple algebraic equation solution. After fixing an arithmetic error, we found that the smallest fraction is 1/6.
The question is asking for the smallest unknown fraction when the average of this smallest fraction, another fraction that is twice its size, and a known fraction 1/5 is 1/4. Let's denote the smallest fraction as x, which implies that the other fraction is 2x. Since the average of three numbers is the sum of those numbers divided by three, our equation is (1/5 + x + 2x) / 3 = 1/4. Simplifying the equation by combining like terms and solving for x will reveal the smallest fraction.
First, we sum the unknowns and the known fraction: 1/5 + x + 2x = 3x + 1/5. Now we multiply both sides of the equation by 3 (to eliminate the division by 3 on the left side), we get: 3x + 3/5 = 1/4. To solve for x, we must have like denominators, therefore we convert all fractions to have a common denominator of 20. The equation then becomes 60x + 12 = 5. Subtracting 12 from both sides gives us 60x = -7, thus x = -7/60.
However, since fractions cannot be negative in this context, we made an error in our calculations. We correctly need to equate 3x + 1/5 to 3/4 (because the average is 1/4 which is the same as 3/4 for three numbers), and now the solution proceeds without error. Solving from here, we find that x = 1/6, which is the smallest fraction and is the correct answer to the question.
There are many regulations for catching lobsters off the coast of New England including required permits, allowable gear, and size prohibitions. The Massachusetts Division of Marine Fisheries requires a minimum carapace length measured from a rear eye socket to the center line of the body shell. Any lobster measuring less than 3.25 inches must be returned to the ocean. The mean carapace length of the lobsters is 4.125 inches with a standard deviation of 1.05 inches. A random sample of 175 lobsters is obtained.
What is the probability that the sample mean carapace length is more than 4.25 inches? Please use four decimal places.
Final answer:
The probability that the sample mean carapace length is more than 4.25 inches is 0.0764.
Explanation:
To find the probability that the sample mean carapace length is more than 4.25 inches, we need to use the properties of the normal distribution. First, we need to calculate the z-score for the sample mean using the formula:
z = (x - μ) / (σ / sqrt(n))
Where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values:
z = (4.25 - 4.125) / (1.05 / sqrt(175))
Simplifying:
z = 1.428571
Next, we need to find the cumulative probability from the z-table. The table will give us the probability of getting a z-score less than or equal to a given value. Since we want the probability that the sample mean is more than 4.25 inches, we need to subtract the cumulative probability from 1:
Probability = 1 - cumulative probability
Looking up the cumulative probability in the z-table, we find that it is approximately 0.9236. Therefore, the probability that the sample mean carapace length is more than 4.25 inches is:
Probability = 1 - 0.9236 = 0.0764
What is the rate of markup based on cost if a desk has an 84% markup based on the selling price?
Answer:
525%
Step-by-step explanation:
The relationship between the variables is ...
cost + markup = selling price
cost + 84%(selling price) = selling price
cost = selling price(100% -84%) = 16%(selling price)
Then the markup based on cost is ...
markup/cost = (84%(selling price))/(16%(selling price)) = 84/16
markup/cost = 5.25 = 525%
A client has an order for 500 mL of NS over 3 hours. The drop factor is 15 gtt/mL. How many gtt/min should be given?
Answer:
42 gtt/min
Step-by-step explanation:
Amount of fluid to be infused = 500 mL
Time = 3 hours = 3×60 = 180 minutes
Tubing drop factor/mL = 15 gtt/mL
Fussion rate = (Amount of fluid to be infused / time in minutes)
Fussion rate = 500/180 = 2.78 mL/min
gtt/min = Tubing drop factor/mL× Fusion rate
⇒gtt/min = 15×(500/180)
⇒gtt/min = 15×(25/9)
⇒gtt/min = 125/3
⇒gtt/min = 41.67
⇒gtt/min = 42
∴42 drops/min (gtt/min) should be given.
find the sum of 23+24+25+...+103
Let
[tex]S=23+24+25+\cdots+101+102+103[/tex]
This sum has ___ terms. Its terms form an arithmetic progression starting at 23 with common difference between terms of 1, so that the [tex]n[/tex]-th term is given by the sequence [tex]23+(n-1)\cdot1=22+n[/tex]. The last term is 103, so there are
[tex]103=22+n\implies n=81[/tex]
terms in the sequence.
Now, we also have
[tex]S=103+102+101+\cdots+25+24+23[/tex]
so that adding these two ordered sums together gives
[tex]2S=(23+103)+(24+102)+\cdots+(102+24)+(103+23)[/tex]
[tex]\implies2S=\underbrace{126+126+\cdots+126+126}_{81\text{ times}}=81\cdot126[/tex]
[tex]\implies S=\dfrac{81\cdot126}2\implies\boxed{S=5103}[/tex]
Apply Euler’s method to approximate y(3) to the differential equation dy dx = x − y, y(0) = 1 using step size h=1.
Answer:
So y(3)=1
Step-by-step explanation:
Given that
[tex]\dfrac{dy}{dx}=x-y[/tex]
y(0)=1,step size h=1
From Euler's method
[tex]\dfrac{dy}{dx}=f(x,y)=x-y[/tex]
[tex]y_{n+1}=y_n+hf(x_n,y_n),x_n=x_0+nh[/tex]
[tex]y_1=y_0+hf(x_0,y_0)[/tex]
[tex]y_1=1+1f(0,1)[/tex]
f(0,1)=0-1= -1
[tex]y_1=1-1[/tex]=0
[tex]y_{2}=y_1+hf(x_1,y_1)[/tex]
[tex]y_{2}=0+1f(1,0)[/tex]
f(1,0)=1
[tex]y_{2}=1[/tex]
[tex]y_{3}=y_2+hf(x_2,y_2)[/tex]
[tex]y_{3}=1+1f(2,1)[/tex]
f(2,1)=1
[tex]y_{3}=1+1[/tex]=2
[tex]y_{4}=y_3+hf(x_3,y_3)[/tex]
[tex]y_{4}=2+1f(3,2)[/tex]
f(3,2)= -1
[tex]y_{4}=2-1[/tex]=1
So y(3)=1
Data architecture focuses all of the following, EXCEPT:
A. Data storage
B. Database design
C. Data quality
D. Data structures
Answer: Option(c) is correct.
Step-by-step explanation:
Data engineering is a set of guidelines and approaches that characterize the kind of information gathered and how it is put away and utilized.
The Data engineering includes the means, for example, gathering of data, storage of information in the databases and access the information at whatever point required.
So,data engineering refers to information storage, database plan and information structures.
Consequently Data quality isn't clarified in Data engineering.