Answer:
couted by 10
Step-by-step explanation:
Answer:
0.7x/0.8y = x/y * 0.7/0.8 = x/y * 0.875
So the fraction is reduced by 12.5%
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:
a.) 26.2
Step-by-step explanation:
b.)13.8
hope this helps
Answer:
1/6
Step-by-step explanation:
there are 6 numbers so the chances he rolls 5 is 1 out of 6 chances