Answer:
The debris will be at a height of 56 ft when time is 0.5 s and 7 s.
Step-by-step explanation:
Given:
Initial speed of debris is, [tex]s=120\ ft/s[/tex]
The height 'h' of the debris above the ground is given as:
[tex]h(t)=-16t^2+120t[/tex]
As per question, [tex]h(t)=56\ ft[/tex]. Therefore,
[tex]56=-16t^2+120t[/tex]
Rewriting the above equation into a standard quadratic equation and solving for 't', we get:
[tex]-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0[/tex]
Using quadratic formula to solve for 't', we get:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s[/tex]
Therefore, the debris will reach a height of 56 ft twice.
When time [tex]t=0.5\ s[/tex] during the upward journey, the debris is at height of 56 ft.
Again after reaching maximum height, the debris falls back and at [tex]t=7\ s[/tex], the height is 56 ft.
Final answer:
To find when the debris will be 56 feet above the ground, we solve the quadratic equation -16t² + 120t = 56 using the quadratic formula. This will yield two possible solutions for t, which are the times at which the debris reaches 56 feet.
Explanation:
To determine when the debris will be 56 feet above the ground, we need to solve the given quadratic equation for t, which represents time in seconds. The equation provided is:
h = -16t² + 120t
Where h is the height in feet. To find the times when the debris is 56 feet above the ground, we set h to 56:
56 = -16t² + 120t
This equation can be solved by factoring or using the quadratic formula. To factor, we first set the equation to zero:
-16t² + 120t - 56 = 0
16t² - 120t + 56 = 0
Dividing by 4
4t² - 30t + 14 = 0
Again reducing by dividing by 2
2t² - 15t + 7 = 0
Now, we need two numbers which add to give 15 and multiply to give 14.
The two numbers are 1 and 14.
2t²- 14t - t + 7 = 0
2t (t - 7) - 1(t - 7) = 0
(t - 7)(2t - 1) = 0
t = 7 or 1/2
Since 1/2 second cannot be an answer, the required answer is 7 seconds
find values of x y and z
Answer:
Well, we know x has to add up to 180 degrees since a triangle has 180 degrees in it!
63 + 36 = _99__
180 - 99 = 81
81 = x
180 - 81 = 99
99 is z
99 + 13 = 112
180 - 112 = 68
68 is y
Since 13 is an angle measurement. We add to get 180.
68 = y
99 = z
81 = x
What are three rational numbers between 2 and -2
Answer: -1, 0, and 1
Step-by-step explanation: -1 is an integer and all integers are rational numbers so -1 is rational.
0 is also an integer and all integers are rational numbers. Therefore, 0 is considered a rational number.
1 is a natural number and all natural numbers are rational numbers. Therefore, 1 would be a rational number.
A rug is shaped like a parallelogram with a base of 41⁄2 ft. and a height of 2 1⁄4 ft. What is the area of the rug? Draw and label the dimensions of the shape then find the area.
Answer:
46.125 square feet or [tex]46\dfrac{1}{8}[/tex] sq. feet.
Step-by-step explanation:
The rug is shaped like a parallelogram with a base of [tex]\frac{41}{2} = 20.5[/tex] feet. and a height of [tex]2\dfrac{1}{4} = 2.25[/tex] feet.
Now, the area of a parallelogram is given by the product of one side as the base and the perpendicular distance of that side from the opposite parallel side as height.
Now, the area of the given parallelogram is (20.5 × 2.25) = 46.125 square feet. (Answer)
8 solid iron sphare with radius 'a cm' each are melted to form a sphare with radius 'b cm'. find the ratio of a:b
8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2
Solution:
Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'
Need to find the ratio of a:b
As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.
For sake of simplicity, let volume of 1 sphere of radius a cm is represented by [tex]V_a[/tex] and volume of 1 sphere of radius b cm is represented by [tex]V_b[/tex]
So volume of 8 solid iron sphere with radius 'a cm' = volume of 1 solid iron sphere with radius 'b cm'
[tex]=>8 \times} \mathrm{V}_{\mathrm{a}}=\mathrm{V}_{\mathrm{b}}[/tex]
[tex]\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{b}}}=\frac{1}{8}[/tex] ---- eqn 1
[tex]\text {Let's calculate } {V}_{a} \text { and } V_{b}[/tex]
Formula for volume of sphere is as follows:
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Where r is radius of the sphere
Substituting r = a cm in the formula of volume of sphere we get
[tex]V_{a}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi a^{3}[/tex]
Substituting r = b cm in the formula of volume of sphere we get
[tex]V_{b}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi b^{3}[/tex]
[tex]\text { Substituting value of } V_{a} \text { and } V_{b} \text { in equation }(1) \text { we get }[/tex]
[tex]\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}[/tex]
[tex]\begin{array}{l}{=>\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}} \\\\ {=>\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{2}\right)^{3}} \\\\ {=>\frac{a}{b}=\frac{1}{2}}\end{array}[/tex]
a : b = 1 : 2
Hence the ratio of a:b is 1 : 2
Final answer:
The ratio of the radius 'a' of the original smaller spheres to the radius 'b' of the new larger sphere formed by melting the 8 smaller spheres together is 1:2, obtained by equating the volumes and simplifying.
Explanation:
The question pertains to using the concept of volumes of spheres in Mathematics to find the ratio of radii of the original smaller spheres to the new larger sphere formed by melting them together. Given that there are 8 solid iron spheres each with radius 'a cm', and they are melted to form one single sphere with radius 'b cm', we preserve the volume during the melting process.
We know that the volume of a sphere is calculated using the formula [tex]V=\frac{4}{3}\pi r^{3}[/tex]. When combining the volumes of the 8 smaller spheres into one large sphere, the volumes on both sides must be equal since no material is lost during melting. The equation to find the volume of the large sphere is [tex]V=8(\frac{4}{3}\pi a^{3}) = \frac{4}{3}\pi b^{3}[/tex].
Simplifying this equation, we obtain the cubic ratio of radii a³/b³ = 1/8. Taking the cube root of both sides, the simple ratio of the radii is a/b = ∛[1/8], which simplifies to a/b = 1/2. Therefore, the ratio of the radius of the smaller sphere to the radius of the larger sphere, a:b, is 1:2,
what does the y-intercept represnt
Answer: The y-intercept represents what is the value of y when x=0.
Using the double number line shown, for the equation 5 x + 4 = 14 5x+4=14, what is the value of x?
Number line is the line in which the numbers are marked at the intervals to the show the inequality. The value of the x, is 2 which is shown on the number line by attached image below.
Given information-The equations given in the problem are,
[tex] 5 x + 4 = 14[/tex]
Number lineNumber line is the line in which the numbers are marked at the intervals to the show the inequality.
Here in the problem the given equation is,
[tex] 5 x + 4 = 14[/tex]
Solve it for the x,
[tex]\begin{aligned}\\ 5 x &= 14-4\\ 5x&=10\\ x&=\dfrac{10}{5} \\ x&=2\\ \end[/tex]
The value of the x is 2. It can be shown on the number line graph by making a circle on the number 2.
As the inequality is shown with the equal sign in the given equation. Therefore the direction would be nigher side. The graph for the given equation number line shown in the attached image.
Hence the value of the x, is 2 which is shown on the number line by attached image below.
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Final answer:
To solve the equation 5x + 4 = 14, subtract 4 from both sides, then divide by 5. This gives x = 2, which can be checked by substitution back into the equation and verifying it holds true.
Explanation:
To solve the equation 5x + 4 = 14, we need to isolate the variable x. First, we subtract 4 from both sides of the equation to get 5x = 10. Next, we divide both sides of the equation by 5 to find the value of x:
5x ÷ 5 = 10 ÷ 5
x = 2
This means that the value of x that satisfies the equation 5x + 4 = 14 is 2. We can check our answer by substituting 2 back into the original equation to see if it makes a true statement:
5(2) + 4 = 10 + 4 = 14
Since the left side of the equation equals the right side, x = 2 is indeed the solution.
During a Grand Prix car race, the tyres on a car are reduced in mass by 3%. If their mass is 388 kg at the end of the race, what was their mass at the start?
Answer:
Their mass at the start was 400 kg.
Step-by-step explanation:
Given:
The tyres on a car during a grand prix race are reduced in mass by 3%. Their mass is 388 kg at the end of the race.
Now, to find the mass at the start.
Let the mass at the start be [tex]x[/tex].
According to question:
[tex]x - 3 \%ofx= 388[/tex]
⇒[tex]x-\frac{3}{100}\times x = 388[/tex]
⇒[tex]x-0.03x =388[/tex]
⇒[tex]0.97x=388[/tex]
Dividing both sides by 0.97 we get:
⇒[tex]x=400[/tex]
Therefore, their mass at the start was 400 kg.
To find the original mass of the tyres before the 3% decrease, we make a simple percentage calculation. By setting up the equation 97/100 * x = 388, we find that the original mass of the tyres was 400 kg.
Explanation:The question posted is a mathematics problem related to understanding percentages and its application to real-life situations such as a Grand Prix race.
Given that the tyres at the end of the race have a mass of 388 kg, which is 97% of their original mass (since they lost 3%), we can find their original mass by setting up a simple percentage equation. We denote the original mass as 'x' and set up the equation: 97/100 * x = 388. To solve for 'x', we divide both sides of the equation by 97/100, which is equivalent to multiplying by its reciprocal, 100/97.
The solution to the problem is then calculated as following: x = 388 * (100/97) = 400 kg.
Hence, the original mass of the tyres was 400 kg.
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if h=-16t ²+160t represents the height of a rocket in T seconds after it was fired when will the rocket hit the ground?
Answer:
The time after which the rocket hit the ground is 5 seconds
Step-by-step explanation:
Given as :
The distance of the cover by rocket at the height h = - 16 t² + 160 t
Let the time after which rocket hit the ground = T seconds
Now, When the rocket hits the ground, then at that time, the velocity of the rocket becomes zero.
I.e velocity = [tex]\frac{\partial h}{\partial t}[/tex] = 0
Or, v = [tex]\frac{\partial h}{\partial t}[/tex] = 0
Now, v = [tex]\frac{\partial h}{\partial t}[/tex]
Or, v = [tex]\frac{\partial (-16t^{2}+160t)}{\partial t}[/tex]
or, v = - 32 t + 160
Now, ∵ velocity of rocket after reaching the ground becomes zero
So, v = - 32 t + 160 = 0
Or, 32 t = 160
Or, t = [tex]\frac{160}{32}[/tex]
∴ t = 5 sec
So, The time after which the rocket hit the ground = 5 sec
Hence The time after which the rocket hit the ground is 5 seconds answer
To find when the rocket will hit the ground using the quadratic equation h = -16t² + 160t, solve for t when h=0; the rocket will hit the ground after 10 seconds.
Explanation:To determine when the rocket will hit the ground given the equation h = -16t² + 160t, we need to find the value of t at which the height h is zero. The equation represents a quadratic equation, where t is the time in seconds after the rocket was fired, and h is the height of the rocket at any time t.
To solve for the time when the rocket hits the ground, we set h to zero and solve for t:
0 = -16t² + 160t0 = t(160 - 16t)Therefore, t = 0 or t = 10 secondsWe discard the t = 0 since it represents the initial time at launch. Thus, the rocket will hit the ground after 10 seconds.
During this entire period, while the rocket is ascending and descending, it is important to consider the horizontal motion if analyzing its trajectory in more detail, but for this problem, we are only concerned with the vertical motion.
The equation of a number and 15 is no greater than 450.what are the possible values for the number
Answer:
x ≤ 435
Step-by-step explanation:
Given is the following condition.
The sum of a number and 15 is less than and equal to 450.
So, if the number is x, then we have
x + 15 ≤ 450
⇒ x + 15 - 15 ≤ 450 - 15
⇒ x ≤ 435
Therefore, the solutions of the number are either 435 or less than 435 up to negative infinity. ( Answer )
What is the quotient of 120 and 0.03
(equation and answer)
Is 1600 a perfect square?
Yes or no
Show work to explain why
Please and thank you
Answer:
the quotient is 4000 and the square is a perfect square
Step-by-step explanation:
120/0.03=4000
40 time 40 is 1600 so its perfectly square.
hope this helps
Solve for the unknown by using the additive inverse. Type the FULL answer in the box, without using any spaces (ex., X=5).
2Y – 3 = Y – 4
Answer:
Henry consistently makes seven out every ten free throws he shoots. At the same rate, how many free throws will he make after he shoots 90 of them?
If the average football player weighs 250 pound, how much would the starting defense weigh? (There are 11 players on each team on the field)
Answer:
2750
Step-by-step explanation:
As there are 11 players on the field, each averaging 250 pounds, this means that we can add 250 11 times, 1 for each player. Another way to say this would be to multiply 250 and 11, as we are adding 250 11 times. Our answer is then 250*11 = 2750.
Find out
[tex] {5}^{10} + {8}^{3} [/tex]
Answer:
[tex]5^{10}+8^3[/tex]
[tex]5^{10}=9765625[/tex]
[tex]8^3=512[/tex]
[tex]=9765625+512[/tex]
[tex]=9766137[/tex]
OAmalOHopeO
What is y=-7x+9 in standard form
Answer:
7 x + y = 9
Step-by-step explanation:
Evaluate the expression when b=5 and x=-3
Answer:
-33
Step-by-step explanation:
x-6b when b=5 and x=-3
-3-6(5)=-3-30=-33
Stephanie is packing her bags for her vacation. She has 7 unique books, but only
3 fit in her bag. How many different groups of
3 books can she take?
Answer:
35
Step-by-step explanation:
a cat owner paid the vet a fee of$269.50 for a years worth of visits. he made 14 visits that year. what was the average per cost?
Answer:
The average per cost is $19.25.
Step-by-step explanation:
Given:
The fee paid by cat owner = $269.50. Total visits he made that year 14.
Now, to find the average per cost.
So, to get the average per cost we divide the total fee by total visits:
Average per cost = Total fee ÷ Total visits
= [tex]269.50\div 14[/tex]
= [tex]19.25[/tex]
Therefore, average per cost is $19.25.
Answer:
The Average cost of per visit to the vet = $ 19.25
Step-by-step explanation:
Here, the total visits to the vet in a year = 14
Also, the total amount paid to the vet in a year = $269.50
Now, Let us assume the average cost per vet visit = m
So,[tex]\textrm{Average cost of per visit} = \frac{\textrm{Total amount paid in n visits}}{\textrm{ n visits}}\\ \implies m = \frac{269.50}{14} = 19.25[/tex]
or, m = $ 19.25
Hence, the Average cost of per visit to the vet = $ 19.25
There are 10 marbles. What is the probability of drawing two yellow marbles if the first one is not placed back into the bag before the second draw?
Answer: 1/10
Step-by-step explanation:
There is 1 yellow marble out of the 10 marbles
Answer:
Step-by-step explanation:
1/9
is y=-x-10 linear or nonlinear
Answer:
Linear
Step-by-step explanation:
Because it has no exponents
If it has no exponents than its always linear
Answer:
Linear
Step-by-step explanation:
It is in Slope-Intercept Form [y = mx + b], and this formula is ALWAYS a linear function [NO EXPONENTS].
I am joyous to assist you anytime.
if AB=16 then AD is?
Answer:
8
Step-by-step explanation:
AD is half of AB
1/2 * 16 = 8
Answer:
8
Step-by-step explanation:
CD is an altitude. It is perpendicular to AB, and it splits AB in half. If AB=16, and CD splits AB in half, to find AD you would do this:
1/2AB
1/2·16=8
8 is your answer.
Yu can also see that AD and DB are congruent, so their values must be the same.
~Stay golden~:)
|x|, if x=10; .3; 0; −2.7; −9
Answer:
if x = 10, then
x
=
;
if x = .3, then
x
=
;
if x = 0, then
x
=
;
if x = −2.7, then
x
=
;
if x = −9, then
x
=
Answer:
For [tex]\left | x \right |[/tex] we will have positive values only.
[tex]\left | -2.7 |\right =2.7[/tex]
[tex]\left | -9 |\right =9[/tex]
Rest are positive so will give positive values out of the modulus function.
Step-by-step explanation:
The absolute value of any number is its positive value only.
As for example [tex](-2.7)[/tex] and [tex](2.7)[/tex] both are having equal distance from [tex]0[/tex] in a number line, one on the left other on the right side of the number line but are equidistant from [tex]0[/tex].
So absolute value of a number is its distance on number line from reference point [tex]0[/tex].
One by one we will work with all of our question.
[tex]\left | 10 |\right =10[/tex]
[tex]\left | 0.3 |\right =0.3[/tex]
[tex]\left | 0 |\right =0[/tex]
[tex]\left | -2.7 |\right =2.7[/tex]
[tex]\left | -9 |\right =9[/tex]
So we have to take the positive number out of the modulus function that is also called absolute value.
Lynn,Jude,and Anne were given the function f(x)=2x+32, and they were asked to find f(3).Lynn’s answer was 14,judes answer was 4, and Anne’s answer +4. Who is correct?
Answer:
Option 1. Lynn, only
Step-by-step explanation:
The correct question is
Listen Lynn, Jude, and Anne were given the function f(x)=-2x^2+32, and they were asked to find f(3). Lynn's answer was 14, Jude's answer was 4, and Anne's answer was (+/-)4. Who is correct?
1. Lynn, only
2. Jude, only
3. Anne, only
4. Both Lynn and Jude
we have
[tex]f(x)=-2x^{2} +32[/tex]
This is a vertical parabola open downward (leading coefficient is negative)
The vertex is a maximum
we know that
f(3) means, the value of f(x) when the value of x is equal to 3
so
For x=3
substitute in the quadratic equation and solve for f(x)
[tex]f(3)=-2(3^{2}) +32[/tex]
[tex]f(3)=-18 +32[/tex]
[tex]f(3)=14[/tex]
therefore
Lynn's answer is correct
To determine the value of the function f(x) = 2x + 32 at x=3, we substitute x with 3, and solve to obtain f(3) = 38. Therefore, all students' answers were incorrect.
Explanation:In the function f(x) = 2x + 32, to find the value of f(3), you first need to substitute 'x' with 3. The equation it becomes f(3) = 2 * 3 + 32
By solving the equation, you obtain is f(3) = 6 + 32 which equals to f(3) = 38.
Thus, all the students, Lynn, Jude, and Anne, unfortunately provided incorrect answers.
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Suppose you have a $60,000 loan with an annual percentage rate of 8% for 25 years.
What would be the effect of paying the required monthly rate and an additional $100 each month on the cost of the two loan?
.
Paying an extra $100 each month on a $60,000 loan with an 8% APR over 25 years will reduce the loan term and total interest paid. To calculate the effect, compute the total cost of the loan with and without the extra payments and subtract these two sums.
Explanation:The subject at hand pertains to understanding the impact of additional payments on a loan, which falls under the domain of financial mathematics. Let's dissect the impact of paying an extra $100 per month on a $60,000 loan with an 8% annual interest rate over 25 years.
Firstly, we need to calculate the monthly payment for a 25-year loan of $60,000 at 8% interest. This can be calculated by using a loan calculator or the loan payment formula. Then, calculate the total cost of the loan by multiplying this monthly payment by the number of months in the loan term (25 years x 12 months).
You then do a similar calculation, but this time add an extra $100 to the monthly payment. The extra repayment will reduce the loan term and decrease the total interest paid. To see the effect, compare the total cost of the loan with and without the extra $100.
Therefore, the difference between these two sums will give you the saved amount due to the additional $100 monthly payment. This saving is the effect of making additional payments on the loan.
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Making additional monthly payments can shorten the loan term and save money on interest payments.
Explanation:To calculate the effect of making additional monthly payments on the cost of the loan, we can compare the total interest paid and the duration of the loan with and without the additional payments. Without any additional payments, the monthly payment for a $60,000 loan with an 8% APR and a 25-year term would be $459.18. With an additional $100 each month, the monthly payment would increase to $559.18.
By making the additional $100 payments, the loan would be paid off faster, reducing the term from 25 years to approximately 17 years and saving the borrower 8 years of monthly payments. Additionally, the total interest paid over the course of the loan would also be significantly reduced compared to just paying the required monthly payments.
In summary, making extra monthly payments of $100 can shorten the loan term and save the borrower money on interest payments.
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In a auditorium, there are 9 rows of seats with 18 seats in each row. There are also 6 rows of seats with 24 in each row. How many seats are there in the auditorium? Estimate first. Then check for reasonableness
Answer:
there are 306 in total
Step-by-step explanation:
What is the equation of the line that passes through the point (-4, 8) and has a slope of zero
Answer:
here you go If the slope is undefined, it means that it is a vertical line. This means that it passes through all points in the y direction. Since the x value is -4, and the line is vertical, that's the only x value on that line. So you just say the equation of the line is x=-4
Step-by-step explanation:
Answer:
y=8
Step-by-step explanation:
y-y1=m(x-x1)
m=0
y-8=0(x-(-4))
y-8=0(x+4)
y-8=0
y=0+8
y=8
What is the simple interest for a principal of $650 invested at a rate of 9% for 5 years?
Answer: 292.50 dollars
Work Shown:
P = 650 is the the principal.
r = 0.09 is the interest rate in decimal form.
t = 5 is the number of years.
i = P*r*t
i = 650*0.09*5
i = 292.50 is the simple interest.
Given values:
Principle,
P = $650Rate,
r = 9% or 0.09Time,
t = 5 yearsAs we know,
→ [tex]i = R\times r\times t[/tex]
By substituting the values, we get
[tex]= 650\times 0.09\times 5[/tex]
[tex]= 292.50[/tex]
Thus the response above is right.
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Please answer this correctly is the answer
7:49am
3:31pm
6:31pm
9:49am
Answer:
3:31 PM
Step-by-step explanation:
When the planes arrives in San Francisco, the time is 4:91 or 5:31 PM(central time/yellow). From Central time period to pacific time period, the time decreases by 2 hours. 5:31 - 2 hours is 3:31. The time is still PM. Answer is 3:31 PM.
Answer:
3:31pm
Step-by-step explanation:
Because each 60mins=1hr
51+40=91 which equals an hour and thirty 1 minutes plus an hour and 40 minutes which equals 3:31
Hope I'm right good luck!!1
my new car radio was $179.95 plus 20 percent for installation. what did I end up paying?
Answer:
$215.94
Step-by-step explanation:
You do 20% × $179.95 to get $35.99
Since the 20% is being added to your bill, you add it to your base price
$179.95 + $35.99 = $215.94
Which term best describes the relationship between time and number of labels printed?
A. double
B. decreasing
C. proportional
Answer:
C proportional
Step-by-step explanation:
The answer is c because
proportional means equal
and as u can see in the photo you have represented a proportional relationship because ther line is going in and equal line across the axis and it is increasing at a proportional rate!
and there you go!