Answer:
C
Step-by-step explanation:
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
The question in the picture is very different from the question before the picture.
Half of 12 is ____
is a different question than
12 is ____ halves
When you say, "Halves of 12, 10, ..." it looks like you're asking the first version.
One of something is 2 halves. That is, the number of halves is exactly two times the number of "somethings." Hopefully, you can multiply each of these numbers by 2.
12*2 = 24
10*2 = 10
13*2 = 26
15*2 = 30
8*2 = 16
5*2 = 10
Answer:
Step-by-step explanation:
f(3)=2*3^2 - 3*3^2 + 1
=2*9 - 3*9 + 1
=18-27+1
=19-27
=-8