.A teacher has 70 markers inter drawer. She
1 answer:
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Answer:
8 feet
Step-by-step explanation:
First, draw a picture. The pole is 22 feet tall. Katherine is 5.5 feet tall. She is 24 feet from the pole. The light from the top of the pole to the tip of her shadow forms two similar right triangles. The length of her shadow is x.
Now use similar triangles to write a proportion:
22 / (24 + x) = 5.5 / x
Cross multiply:
22x = 5.5 (24 + x)
Distribute:
22x = 132 + 5.5x
Combine like terms:
16.5x = 132
Divide:
x = 8
The shadow is 8 feet long.
Ok, here we go. Pay attention. The formula for the arc length is 
. That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is 
(that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of 
. Integrating that we have 
from -1 to 2. 
gives us 
. Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly: 
which simplifies to 
. The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with . And there you go!