Answer: Choice A -- f(x) = (1/3)*|x|
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The input of a function is x and the output is y = f(x)
To vertically compress a function, we will multiply the y value by some fraction smaller than 1. This is so that the y coordinates are a fraction of what they once were.
In this case, we multiply y by 1/3 so that something that has a y coordinate of y = 81 becomes y = 27 (divide by 3)
So we have y = f(x) become (1/3)*y = (1/3)*f(x) = (1/3)*|x|
Answer:
576
Step-by-step explanation:
4 feet^2 = 2 feet*2 feet = 24 inch * 24 inch. 24*24 = 576.
The length of pendulum is 2.485 feet
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Solution:</em></u></h3>
Given that,
The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth
<u><em>Therefore, the given formula is:</em></u>
![T=2\pi \sqrt{\frac{L}{32} }](https://tex.z-dn.net/?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7B32%7D%20%7D)
We have to find the length of pendulum that makes one full swing in 1.75 seconds
So the modify the given equation to find "L"
![T=2\pi \sqrt{\frac{L}{32} }\\\\ \sqrt{\frac{L}{32} }=\frac{T}{2 \pi}\\\\\text{Taking square root on both sides }\\\\\frac{L}{32} = \frac{T^2}{4 \pi^2}\\\\L = \frac{T^2}{4 \pi^2} \times 32\\\\L = \frac{T^2}{\pi^2 } \times 8](https://tex.z-dn.net/?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7B32%7D%20%7D%5C%5C%5C%5C%20%5Csqrt%7B%5Cfrac%7BL%7D%7B32%7D%20%7D%3D%5Cfrac%7BT%7D%7B2%20%5Cpi%7D%5C%5C%5C%5C%5Ctext%7BTaking%20square%20root%20on%20both%20sides%20%7D%5C%5C%5C%5C%5Cfrac%7BL%7D%7B32%7D%20%3D%20%5Cfrac%7BT%5E2%7D%7B4%20%5Cpi%5E2%7D%5C%5C%5C%5CL%20%3D%20%5Cfrac%7BT%5E2%7D%7B4%20%5Cpi%5E2%7D%20%5Ctimes%2032%5C%5C%5C%5CL%20%3D%20%5Cfrac%7BT%5E2%7D%7B%5Cpi%5E2%20%7D%20%5Ctimes%208)
Substitute T = 1.75 seconds and ![\pi = 3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D%203.14)
![L = \frac{1.75^2}{3.14 \times 3.14} \times 8\\\\L = \frac{3.0625}{9.8596} \times 8\\\\L = 2.485](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B1.75%5E2%7D%7B3.14%20%5Ctimes%203.14%7D%20%5Ctimes%208%5C%5C%5C%5CL%20%3D%20%5Cfrac%7B3.0625%7D%7B9.8596%7D%20%5Ctimes%208%5C%5C%5C%5CL%20%3D%202.485)
Thus length of pendulum is 2.485 feet approximately
To estimate, round 3102 to 3100
round 1-10 to 2500
1-70 to 2100
1-80 to 2900
2900+2100+2500+3100=10600mi
Yes it is reasonable because you add and subtract numbers when estimating, however it is not exact
3x + 4 = x+ 8 > 3x - x = 2x > 2x + 4 = 8 > 8 - 4 = 4 > 2x / 2 crosses out > 4 / 2 = 2 > x=2
2y + 5 = y + 7 > 2y - y = y > y+ 5 = 7 > 7-5= 2 > y=2
the perimeter of the kite is 4