Answer:
So for Biker A for every 2 hrs they drive 50 km
For Biker B for every 3 hrs they drive 72 km
Step-by-step explanation:
so for every hour biker A rides 25 km
but for biker B they ride 24 km
The question is an illustration of related rates.
The rate of change between you and the ball is 0.01 rad per second
I added an attachment to illustrate the given parameters.
The representations on the attachment are:
![\mathbf{x = 100\ m}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%3D%20100%5C%20m%7D)
---- the rate
![\mathbf{\theta = \frac{\pi}{4}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ctheta%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%7D)
First, we calculate the vertical distance (y) using tangent ratio
![\mathbf{\tan(\theta) = \frac{y}{x}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ctan%28%5Ctheta%29%20%3D%20%5Cfrac%7By%7D%7Bx%7D%7D)
Substitute 100 for x
![\mathbf{y = 100\tan(\theta) }](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20100%5Ctan%28%5Ctheta%29%20%7D)
![\mathbf{\tan(\theta) = \frac{y}{100}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ctan%28%5Ctheta%29%20%3D%20%5Cfrac%7By%7D%7B100%7D%7D)
Differentiate both sides with respect to time (t)
![\mathbf{ \sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dy}{dt}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%5Csec%5E2%28%5Ctheta%29%20%5Ccdot%20%5Cfrac%7Bd%5Ctheta%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B100%7D%20%5Ccdot%20%5Cfrac%7Bdy%7D%7Bdt%7D%7D)
Substitute values for the rates and ![\mathbf{\theta }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ctheta%20%7D)
![\mathbf{ \sec^2(\pi/4) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%5Csec%5E2%28%5Cpi%2F4%29%20%5Ccdot%20%5Cfrac%7Bd%5Ctheta%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B100%7D%20%5Ccdot%202%7D)
This gives
![\mathbf{ (\sqrt 2)^2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%28%5Csqrt%202%29%5E2%20%5Ccdot%20%5Cfrac%7Bd%5Ctheta%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B100%7D%20%5Ccdot%202%7D)
![\mathbf{ 2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}](https://tex.z-dn.net/?f=%5Cmathbf%7B%202%20%5Ccdot%20%5Cfrac%7Bd%5Ctheta%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B100%7D%20%5Ccdot%202%7D)
Divide both sides by 2
![\mathbf{ \frac{d\theta}{dt} = \frac{1}{100} }](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%5Cfrac%7Bd%5Ctheta%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B100%7D%20%7D)
![\mathbf{ \frac{d\theta}{dt} = 0.01 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%5Cfrac%7Bd%5Ctheta%7D%7Bdt%7D%20%3D%200.01%20%7D)
Hence, the rate of change between you and the ball is 0.01 rad per second
Read more about related rates at:
brainly.com/question/16981791
Answer:
62.28
Step-by-step explanation:
Ok, so since we know the radius of the circle and the area of the shaded region, we can find the fraction of the whole circle the shaded region is, and apply that to the total circumference to find the length of the arc.
1. area of whole circle = 17^2*3.14 = 907.46in^2
2. 529.35/907.46 = 0.5833314967
3. circumference of whole circle = 2*3.14*17 = 106.76
4. length of arc = 106.76*0.5833314967 = 62.2764705877 --> 62.28