If f(x)= sin^−1 (x), then what is the value of f'(sqrt 3/ 2) in simplest form?
Answers
Answer:
2
Step-by-step explanation:
We can use the formula for the derivative of the arcsin function:
f'(x) = 1/√(1 -x²)
Filling in x=(√3)/2, we get ...
f'((√3)/2) = 1/√(1 -3/4) = 1/(1/2)
f'((√3)/2) = 2
To find the value of f'(√3/2) for f(x) = sin⁻¹(x), we can use the chain rule and substitute the given value into the derivative expression.
Explanation:To find the derivative of f(x) = sin⁻¹(x), we can use the chain rule. Let's denote u = x, then y = sin⁻¹(u). Taking the derivative of y with respect to u, we get dy/du = 1/√(1 - u²). Now, substituting u = √3/2, we can find the value of f'(√3/2) in simplest form.
Substituting u = √3/2 into the derivative, we have dy/du = 1/√(1 - (√3/2)²) = 1/√(1 - 3/4) = 1/√(1/4) = 1/√1/4 = 1/(1/2) = 2.
Therefore, the value of f'(√3/2) is 2.
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Related Questions
Find the cotangent of both angle A and angle B.
Thank you!
Answers
Answer: tangent of A = 2.4
Cotangent of B = 0.4167
Step-by-step explanation:
Answer:
[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A[/tex]
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Find all solutions in the integers of the equation ||x−3|−5| = 10, where the bars indicate absolute value.
Answers
Answer:
x = 18 or x = -12.
Step-by-step explanation:
||x-3|-5| = 10 only if |x-3|-5 = 10 or |x-3|-5 = -10, i.e., if |x-3|=15 or |x-3|=-5; but |x-3| cannot be equal to -5, because |x-3| should be a non-negative value. Therefore, the first equation is true only if |x-3|=15. |x-3| = 15 only if x-3 = 15 or x-3 = -15, i.e., x = 18 or x = -12. We can verify this in the following way: ||18-3|-5|=||15|-5|=|10|=10 and ||-12-3|-5|=||-15|-5|=|15-5|=|10|=10. This verify that our solution is correct.
Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 1 mi, 9 mi, 10 mi B. 8 mi, 9 mi, 2 mi C. 1 mi, 9 mi, 11 mi D. 8 mi, 9 mi, 17 mi
Answers
Answer:
Option B. 8 mi, 9 mi, 2 mi
Step-by-step explanation:
The option A doesn't have a set of numbers which could be the lengths of the sides of a triangle. The numbers 1,9,10 mean that the longest side is exactly the sum of the others. The only possible way is they lie in the same line, no triangle is formed
Option C gives the numbers 1,9,11. It's impossible to have a side of 11 when you have the sum of the others less than 11. The maximum extension of the other sides (forming a line) won't be enough to reach the length of 11
Option D is also infeasible for the same reason as the option A. The three lines must be aligned to be connected in its extremes
Option B is the only one who can provide a set of possible lengths of a triangle since the sum of the shortest sides is greater than the third. If we open wide enough the angle between the 2 mi side and the 8 mi side, we would eventually connect the 9 mi side and form a triangle
A flag post 10 meters long is fixed on top of a tower. From a point on horizontal ground, the angles of elevation of the top and bottom of the flag post are 40 degrees and 33 degrees respectively. Calculate:
a) The height of the tower
b) The shortest distance from the point on the ground to the top of the flag post
Answers
Answer:
Tan33=x/y
y= x/Tan33
Tan40=(10+x)/y
y= (10+x)/Tan40
Therefore
x/Tan33 = (10+x)/Tan40
xTan40-xTan33 =10Tan33
x= 10Tan33/(Tan40-Tan33)
x=34.2m
Step-by-step explanation:
Which is proportional to ¾?
5/6
6/8
6/7
8/9
Answers
Answer:
6:8
Step-by-step explanation:
50 points
Kanna has 2 red pens, 4 black pens, 3 blue pens, 1 purple pen. What is the chance Kanna pulls one of her black pens. Write you answer in a fraction and percentage.
[Note:False answers will be reported]
Answers
Answer:
4 out of 10 or 4/10 is my answer
Answer:
The fraction will be 4/10, or 2/5.
The percentage will be 40%.
Step-by-step explanation:
The fraction and percentage will be the number of black pens divided by the total number of pens.
We can find the total number of pens by adding all the pens in each color together.
2 + 4 + 3 + 1 = 10
The total number of pens is 10. The number of black pens is 4.
The fraction will be 4/10, or 2/5.
The percentage will be 40%.
I hope this helps. Happy studying. :)
Find the missing side length
Answers
Answer:
Step-by-step explanation:
The triangle given is aright angle triangle. This is because one if its angles is 90 degrees. The other two angles add up to give 180 degrees. Looking at the right angle triangle, taking the 8 degree angle as the reference angle, the length of the adjacent side is 82, the length of the opposite side is t. Applying trigonometric ratio,
Tan # = opposite side / adjacent side.
# = 8 degrees
Tan 8 = t/82
t = 82 tan8
t = 82 × 0.1405
t = 11.521
A farmer needs to fence in a rectangular plot of land, and he has 200 meters of fence to work with. He is going to construct the plot next to a river, so he will only have to use fence for three sides of the plot. Find the dimensions that will allow the farmer to maximize the area of the plot.
Answers
Answer:
the farmer will need to have 2 pieces of 50 m and one of 100m to maximise the area ( Maximum area=5000 m²)
Step-by-step explanation:
if we assume that the southern fence is not required and if we denote a= length of each lateral side and b= length of the front side , we will have:
Area=A= a*b
Total length of fence=L= 2*a+b
therefore
L= 2*a+b → b= L- 2*a
A= a*(L-2*a) = a*L - 2*a²
therefore
A= a*L - 2*a² → 2*a² - a*L + A = 0
a= [L ± √((-L)²- 4*2*A)]/(2*2) = L/4 ± √(L²- 8*A) /4
a= L/4 ± √(L²- 8*A) /4
when A goes bigger √(L²- 8*A) diminishes, but since the minimum possible value √(L²- 8*A) is 0 , then A can not go higher than L²- 8*A=0
therefore
L²- 8*A max=0 → A max = L²/ 8 = (200m)²/8= 5000 m²
and since √(L²- 8*A)=0
a=L/4 = 200m/4 = 50 m
b= L- 2*a = 200m - 2* 50m = 100 m
Gabriel invests $9600 in two different accounts. The first account paid 13 %, the second account paid 6 % in interest. At the end of the first year he had earned $926 in interest. How much was in each account?
Answers
Answer:The principal for the first account is $5000
The principal for second account is $4600
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P = principal
T = time in years
R = interest rate on the principal.
Let x represent the amount invested in the first account
Let y represent the amount invested in the second account
Gabriel invests $9600 in two different accounts. This means that
x + y = 9600 - - - - - - - -1
For first account, The interest rate is 13%. The duration is one year.
Therefore
P = x
T = 1 year
R = 13%
Therefore
I = (x × 13 × 1)/100
I = 0.13x
For second account, he interest rate is 6%. The duration is one year.
Let y represent the principal for the second account. Therefore
P = y
T = 1 year
R = 6
Therefore
I = (y × 6 × 1)/100
I = 0.06y
At the end of the first year he had earned $926 in interest. This means that
0.13x + 0.06y = 926 - - - - - - - -2
Substituting x = 9600 - y into equation 2, it becomes
0.13(9600 - y) + 0.06y = 926
1248 - 0.13y + 0.06y = 926
- 0.13y + 0.06y = 926 - 1248
- 0.07y = -322
y = - 322/- 0.07 = 4600
x = 9600 - y
x = 9600 - 4600
x = 5000
A research firm conducted a survey to determine the mean amount Americans spend on coffee during a week. They found the distribution of weekly spending followed the normal distribution with a population standard deviation of $5. A sample of 64 Americans revealed that X¯¯¯=$20 . What is the 95% confidence interval estimate of μ?
Answers
Answer:
95% confidence Interval would be between $18.775 and $20.225.
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
M is the sample mean Americans spend on coffee during week. ($20)ME is the margin of error from the meanAnd margin of error (ME) around the mean calculated as
ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where
z is the corresponding statistic in 95% confidence level (1.96)s is the population standard deviation ($5)N is the sample size (64)Using the numbers, we get:
ME=[tex]\frac{1.96*5}{\sqrt{64} }[/tex] =1.225
Then 95% confidence Interval would be 20±1.225 or between $18.775 and $20.225
Answer:
The confidence interval is between 18.775 and 21.225.
Step-by-step explanation:
Mr .Cruz is the director of an after school program. He says that 170 or 85%of the students went on to attend collage. A parent wants to know the total number of students in the program
Answers
Answer:
200 students were in the program
Step-by-step explanation:
The parent should know how to figure ...
170/85% = total/100%
This is the same as ...
total = 170/0.85 = 200
200 students were in the program.
_____
Critical Thinking
There are three declarative statements here. There is no question. We have made up a question to answer.
Another possible answer to the non-question could be, "The parent can ask his student how many students were in the program."
Answer:
Step-by-step explanation:
20
cause i said so
In one month you earn $16 for mowing the lawn $15 for babysitting and $20 for allowance you spend$12 at the movie theater how much more money do you need to buy a $45 video game
Answers
Answer:
$6
Step-by-step explanation:
so you add 16 15 and 20 to see how much you earned in total, to get 51 dollars. we subtract 12 because we used it at the movies and get 39 dollars in total. now we subtract this from 45 to see how much more we need to get 6.
equation: 45-(15+16+20-12)........this equals 6 as well
You need to earn more money to buy a $45 video game and it is equal to $6.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
It is given that , you earn some money by doing different works. The earn money from different works is given.
By mowing the lawn money earned = $16
For babysitting money earned = $15
Money earned for the allowance = $20
So , the total money earned is :
= $16 + $15 + $20
= $51
Now , you have spend $12 at the movie theatre. That meant the money now left is :
= $51 - $12
= $39
You need to buy a video game which costs $45. So , you need to earn some more money which is :
= $45 - $39
= $6
Therefore , you need to earn more money to buy a $45 video game and it is equal to $6.
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ASAP PLS NEED HELP’
how does the graph f(x) =(x-8)^3+4 compare to the paren function g(x)=x^3?
no multiple choice! I need this answer in 30 minutes.
Answers
Answer:
Their intercepts are unique.
Explanation:
[tex]\displaystyle x^3 - 24x^2 + 192x - 508 = (x - 8)^3 + 4[/tex]
This graph's x-intercept is located at approximately [6,41259894, 0], and the y-intercept located at [0, −508].
[tex]\displaystyle g(x) = x^3[/tex]
The parent graph here, has both an x-intercept and y-intercept located at the origin.
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The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ? The mean is 20 and the standard deviation is 102.
A) The mean is 20 and the standard deviation is 50.
B) The mean is 22 and the standard deviation is 102.
C) The mean is 22 and the standard deviation is 100.
D) The mean is 22 and the standard deviation is 50.
Answers
Answer:
C) The mean is 22 and the standard deviation is 100.
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
If [tex] X\ sim N(\mu_x =5, \sigma_x =25)[/tex]
And the random variable Y =2+4X.
If we are interested in find the mean and the standard deviation for this new variable we need to apply the concepts of expected value and Variance of random variables.
Using the concept of expected value we have:
[tex]E(Y) =E(2+4X) = E(2) +E(4X)= 2+ 4E(X) =2+4(5) =2+20=22[/tex]
So on this case the [tex]E(Y) =\mu_Y =22[/tex]
Using the concept of variance we have:
[tex]Var(Y)=Var(2+4x)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]
But since 2 is a constant we don't have variance for this and the [tex]Cov(2,4x)=0[/tex] because the covariance of a random variable with a constant is zero. So applying these concepts we have:
[tex]Var(Y)= Var(4x)=4^2 Var (X)= 16 \sigma^2_x =16(25^2)=10000[/tex]
And then if we need the standard deviation we just need to take the square root:
[tex]sd(Y) = \sqrt{10000}=100[/tex]
So the best option for this case would be:
C) The mean is 22 and the standard deviation is 100.
Answer:
Option c) is correct.
Step-by-step explanation:
Given :
[tex]\mu_x = 5[/tex] and [tex]\sigma_x = 25[/tex]
Y = 2 + 4X
Calculation:
This problem can be solved by using concept of expected value and variance of random variables.
By expected value concept,
[tex]\rm E(Y) = E(2 + 4X)= E(2) + E(4X)= 2 + 4E(X)=2+4(5)=22[/tex]
Therefore, [tex]\mu_y = 22[/tex]
By variance concept,
[tex]\rm Var(Y)= Var(2+4X)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]
[tex]\rm Cov(2,4X)=0[/tex]
Var(2) = 0
Therefore,
[tex]\rm Var(Y) = Var(4X)= 4^2Var(X)= 16\sigma_x^2=16(25^2)=10000[/tex]
Therefore,
Standard deviation(Y) = [tex]\sqrt{10000}[/tex] = 100
Hence, option c) is correct.
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he sum of two numbers is 58. The difference of the two numbers is 32.
What are the two numbers?
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 58."
Answers
Answer:x+y=58
Step-by-step explanation:
Sum means addition
A government began the year with $10 trillion of public debt. During the year, it collected taxes of $8 trillion and spent $10 trillion on transfers and government purchases of goods and services. The public debt at the end of the year was $_____ trillion.
Answers
Answer: 12 trillion dollars
Step-by-step explanation: The government started with 10 trillion than collected 8 trillion in taxes, reducing their debt to 2 trillion dollars. Then the government spent 10 trillion dollars and now their debt is 12 trillion dollars.
Answer:
12
Step-by-step explanation:
A travel trailer is bought at the price of $35,000. The price decreases at the rate of .25 every year (t). The exponential expression is 35,000(.75)^t. Find the price of the trailer at 5 years.
Answers
Answer:
$ 8300 (Approximately)
Step-by-step explanation:
Given:
Initial price of the trailer is, [tex]P_0=\$35000[/tex]
Rate of decrease per year is, [tex]r=0.25[/tex]
The time in years is, [tex]t=5[/tex]
The exponential expression for the decrease in price after 't' years is given as:
[tex]P=P_0(1-r)^t[/tex]
Plug in all the given values and solve for 'P'. This gives,
[tex]P=35000(1-0.25)^5\\P=35000(0.75)^5\\P=35000(0.2373)\\P=\$8305.5\approx \$8300[/tex]
Rounding it to the nearest whole number, the price of the travel trailer after 5 years is $ 8,300.
Abby Matthew store manager for Sears does not know how to price a refrigerator that cost $900 Abby knows her boss wants a 40% markup on cost When should the price of the refrigerator be?
Answers
Answer:
The 40% marked up price of refrigerator is $1260.
Step-by-step explanation:
The cost price of the refrigerator = $900
Now, the mark up should be 40%
Calculating the markup on the cost price , we get
40 % of $900 = [tex]\frac{40}{100} \times 900 = 360[/tex]
or, 40 % mark up = $360
Now, the Marked up cost = Cost Price + Marked up Price
= $900 + $360 = $1260
Hence, the 40% marked up price of refrigerator is $1260.
For the month of JanuaryJanuary in a certain city, 51% of the days are cloudycloudy. Also in the month of JanuaryJanuary in the same city, 252% of the days are cloudycloudy and foggyfoggy. What is the probability that a randomly selected day in JanuaryJanuary will be foggyfoggy if it is cloudycloudy?
Answers
Answer: Our required probability is 0.48.
Step-by-step explanation:
Since we have given that
Probability that days are cloudy in January = 51%
Probability that days are cloudy and foggy = 25%
So, we need to find the probability that a randomly selected day in January will be foggy if it is cloudy.
So,P( Foggy|cloudy) is given by
[tex]\dfrac{P(Foggy\cap cloudy)}{P(cloudy)}\\\\=\dfrac{25}{51}\\\\=0.48[/tex]
Hence, our required probability is 0.48.
Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.2 kg · m2 and an angular velocity of +7.4 rad/s. Disk B is rotating with an angular velocity of -9.7 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single unit with an angular velocity of -2.3 rad/s. The axis of rotation for this unit is the same as that for the separate disks. What is the moment of inertia of disk B?
Answers
Answer:
[tex]4.2 kgm^2[/tex]
Step-by-step explanation:
As there's no external force when the disks are attached, the angular momentum of the system should be conserved.
[tex] I_A\omega_A + I_B\omega_B = (I_A + I_B)\omega[/tex]
[tex] 3.2*7.4 + I_B(-9.7) = (3.2 + I_B)(-2.3)[/tex]
[tex] 23.68 - 9.7I_B = -7.36 - 2.3I_B[/tex]
[tex]31.04 = 7.39I_B[/tex]
[tex]I_B = 31.04/7.39 = 4.2 kgm^2[/tex]
The moment of inertia of disk B when it rotates round the axis will be 4.2kgm².
How to calculate the moment of inertia?Let the moment of inertia be represented by Ib.
Therefore, the moment of inertia will be calculated thus:
IaWa + IbWb = (Ia + Ib)w
(3.2 × 7.4) + Ib(-9.7) = (3.2 + In)(-2.3)
23.68 - 9.7Ib = -7.36 - 2.3Ib
Collect like terms
23.58 + 7.36 = -2.3Ib + 9.7Ib
31.04 = 7.39Ib
Divide through by 7.39
7.39Ib/7.39 = 31.04/7.39
= 4.2kgm²
Therefore, the moment of inertia of disk B when it rotates round the axis will be 4.2kgm².
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Sonya paid $2.75 per pound for fresh fish last week. This week, she paid a total of $1.20 more when she purchased 3 pounds of fish. What is the price per pound this week, in dollars per pound?
Answers
The price of fish this week is $3.15 per pound
Step-by-step explanation:
We have to find the total price of 3 pound fish for last week
So,
Price of fish per pound = $2.75
Price of 3 pound fish = 2.75 * 3 = $8.25
As she made $1.20 more in total for 3 pound fish this week
Price of 3 pound fish this week = 8.25+1.20 = $9.45
$9.45 is the total price for 3 pound fish this week.
So,
Price per pound this week will be:
[tex]=\frac{9.45}{3}\\=3.15[/tex]
Hence,
The price of fish this week is $3.15 per pound
Keywords: Measurements, Unit price
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What is the area of a trapezoid with height 5 m and bases 8 m and 1 m?
A. 6.5 m^2
B. 22.5 m^2
C. 24 m^2
D. 45 m^2
If anyone has the answers to the rest, that would be great!
Answers
Answer:
B. 22.5m^2
Step-by-step explanation:
To find the area of a trapezoid, you must use the formula:
1/2 × height × (base 1+ base 2)
1. 1/2 × 5m × (8+1)
2. 1/2 x 5m x (9)
3. Switch it around to make it easier to solve
5m × 9× 1/2 (We can do this because of the commutative property.)
4. 45m × 1/2 = 45 ÷ 2 = 22.5m^2
In the context of the problem, this means that the area of the trapezoid is 22.5m^2.
A food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 10.2 and the sample standard deviation is 0.25, find the 95% confidence interval of the true mean________.
A. (10.06, 10.34)B. (10.07, 10.33)D. (10.14, 10.26)
Answers
Answer: the correct option is A
Step-by-step explanation:
We want to find 95% confidence interval for the mean of the weight of pretzels.
Number of samples. n = 15 bags
Mean, u = 10.2
Standard deviation, s = 0.25
We will use the t- test
Degree of freedom = n - 1 = 15 - 1= 14
Alpha, a = (1-confidence interval )/2
a = (1-0.95)/2 = 0.025
Looking at the t-distribution table, the corresponding z value is 2.131
Confidence interval = z × standard deviation/√n
Confidence interval = 2.131 × 0.25/√15
Confidence interval = 0.13755545851
Approximately 0.138
At 95% confidence interval,
The lower end is 10.2 - 0.138 = 10.062 Approximately 10.06
The upper end is 10.2 - 0.138 = 10.338. Approximately 10.34
10. What happens if the insured tenant and the insurance company fail to agree on the amo
a. Either the tenant or the company can request an appraisal, so that an impartial thir
request an appraisal, so that an impartial third party determines
the amount of loss
b. The insurance policy becomes null and void
The insurance company is forced to pay the current online market price for the item
d. The landlord or owner of the building must make up the difference in the disputed value
Answers
Answer:
A is the answer
Step-by-step explanation:
If you fail to agree on the actual cash value, amount of loss, or cost of repair or replacement, either can make a written demand for appraisal. ... The two appraisers will then set the amount of loss, stating separately the actual cash value and loss to each item.
When the insured tenant and the insurance company fail to agree on the amount of loss; Choice A is what happens: Either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.
Discussion:
Situations such as in the question may arise when quantifying the amount of loss in an insurance situation.
In such scenarios; the best option is for either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.
The essence of this, is to ensure fairness in quantification of the amount of loss.
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How many pentagons can you make using five points as vertices?
Answers
Answer:
56 pentagon.
Step-by-step explanation:
Here is the complete question: Eight point lies on the circle. How many pentagons can you make using five points as vertices?
Given: Five points on vertices.
Using the combination formula to find the number of pentagon.
[tex]_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}[/tex]
⇒ [tex]_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}[/tex]
⇒[tex]_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}[/tex]
∴ [tex]_{8}^{5}\textrm{C}= 56[/tex]
∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices
A line contains the points (a, b) and (a + 3, b + 3). Find the equation of the line in terms of a and b in point-slope form, and then convert it to slope-intercept form.
Answers
Answer:
y -b = x -ay = x + (b-a)Step-by-step explanation:
The slope is the ratio of the change in y to the change in x:
m = ((b+3) -b)/((a +3) -a) = 3/3 = 1
The point-slope form of the equation of a line through point (h, k) with slope m is ...
y -k = m(x -h)
Here, we have (h, k) = (a, b) and m=1, so the equation in point-slope form is ...
y -b = x -a
Adding b puts this in slope-intercept form:
y = x + (b-a)
Please help me out with this
Answers
Answer:
A) 4x - 2y + 3z = - 3
B) 2x - 3y + 2z = 1
C) 6x + 10z = -2
Multiply A) by -1.5
A) -6x +3y -4.5z = 4.5 Then adding to B)
B) 2x - 3y + 2z = 1
D) -4x -2.5z = 5.5 then we add this to C)
C) 6x + 10z = -2 Now we multiply D) by 1.5
D) -6x -3.75z = 8.25 Adding C) + D)
6.25z = 6.25
z = 1 Then putting z = 1 into A) and B)
A) 4x - 2y + 3 = - 3 equals A) 4x -2y = -6
B) 2x - 3y + 2 = 1 equals B) 2x -3y = -1 we divide A) by -2
A) -2x + y = 3 then adding to B
B) 2x - 3y = -1
-2y = 2
y = -1
FINALLY solving for x we'll use equation A)
A) 4x - 2*-1 + 3*1 = - 3
A) 4x +2 + 3 = -3
A) 4x = -8
x = -2
(Yes, it's just that easy. LOL)
Step-by-step explanation:
Affect or use is 1/8 of a barrel of raisins in each batch of granola bars yesterday the factory use 1/2 of a barrel of raisins how many batches of granola bars did the factory made yesterday?
Answers
Answer:
Factory made 4 batches of granola bars yesterday.
Step-by-step explanation:
Given:
1 batch of granola bar is made of 1/8 barrel of raisins.
1/8 barrels can be rewritten as 0.125 barrels.
Hence we can say 1 batch of granola bar is made of 0.125 barrels.
Also Given:
Yesterday Factory used 1/2 barrel of raisins.
1/2 barrels can be rewritten as 0.5 barrels.
Hence we need to find how much batches of granola bars were made using 0.5 barrels of raisins.
Now,
For 0.125 barrels raisins = 1 batch of granola bar
for 0.5 barrels of raisins = Batches of granola bar for 0.5 barrels of raisins
By Using Unitary method we get;
Batches of granola bar for 0.5 barrels of raisins = [tex]\frac{1\times 0.5}{0.125}=4[/tex]
Hence Factory made 4 batches of granola bars yesterday.
1.a.) Find the next four terms: a8,a9,a10,a11
[tex]a_{n}[/tex]=0, 9, -26, 65, -124, 217, -342
1.b) Find a direct formula for [tex]a_{n}[/tex], [Hint: You may want to look at perfect squares, perfect cubes, powers of 2, powers of 3...]
Answers
Answers:
1a) The next four terms are: 513, -728, 1001, -1330
1b) The direct formula is [tex]a_n = (-1)^n*n^3+1[/tex]
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Explanation:
It helps to start with part B first. The direct formula will help us find the next four terms in a very efficient manner.
Start with the sequence {0, 9, -26, 65, -124, 217, -342}
Subtract 1 from each term to get this new sequence {-1, 8, -27, 64, -125, 216, -343}, which closely resembles the sequence {1, 8, 27, 64, 125, 216, 343}. This is the sequence of perfect cubes. The only difference is that each term alternates from positive to negative and vice versa.
So we will have an n^3 as part of the equation and also a (-1)^n as part of the equation. The (-1)^n portion allows us to alternate in signs. Put together we have (-1)^n*n^3 so far
The last thing we do is add 1 to this so that we undo the operation "subtract 1" we did earlier to the original list.
Therefore the formula is [tex]a_n = (-1)^n*n^3+1[/tex]
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To help verify we have the right formula, plug in n = 1 and we get
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_1 = (-1)^1*1^3+1[/tex]
[tex]a_1 = 0[/tex]
and plug in n = 2 to get
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_2 = (-1)^2*2^3+1[/tex]
[tex]a_2 = 9[/tex]
and so on. I'll let you check the other terms
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Let's find the terms a8,a9,a10,a11
This is simply a matter of plugging n = 8, n = 9, n = 10, and n = 11
Plug in n = 8
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_8 = (-1)^8*8^3+1[/tex]
[tex]a_8 = 513[/tex]
Repeat for n = 9
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_{9} = (-1)^9*9^3+1[/tex]
[tex]a_{9} = -728[/tex]
Repeat for n = 10
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_{10} = (-1)^{10}*10^3+1[/tex]
[tex]a_{10} = 1001[/tex]
Repeat for n = 11
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_{11} = (-1)^{11}*11^3+1[/tex]
[tex]a_{11} = -1330[/tex]
Diep buys a loaf of bread 65 centimeters long. For lunch every afternoon, he cuts 15 centimeters of bread for his sandwich. Diep wants to determine the length of the loaf of bread, l, after d days. What is the equation of the scenario?
Is the graph of the equation continuous or discrete? l = 65 – 15d; discrete l = 65 – 15d; continuous 65 = l – 15d; discrete 65 = l – 15d; continuous
Answers
Answer:
The equation is I = 65 - 15d and it's continuous
Step-by-step explanation:
First, let's discart the options. The last two options cannot be because if you solve for I in those equations, you'll get the following:
65 = I - 15d
I = 65 + 15d
Now, suppose that after 1 day, you want to know the length of the bread:
I = 65 + 15(1) = 80
This is impossible because the bread is being cut and it's not growing each afternoon. Therefore these options, wheter is discrete or continuous are discarted.
The correct equation to use is then
I = 65 - 15d
Now, how do you know if the graph is continuous or discrete?. A graph is continuous when all the points belonging to a set, can take any value within an interval. A discrete graph all the values belonging to a set, are distinct and separate one of another, in other words, the values are unconnected.
In this case, if you graph this equation, you have the following (see attached graph)
As you can see, all the values are connected and continuous.
Answer : B
Step-by-step explanation: