The first step for this problem should always be to draw out the triangle so that you can right down the angles and side lengths. Afterward, you can use SOHCAHTOA to find the height of the tree. You would use tangent. The equation you would use is tan(28°)x/18. After solving for x, you will find the answer which is approximately 9.57 feet.
Hope this helped :)
Answer:
The volume is increasing at a rate of 16286 in³/min.
Step-by-step explanation:
a) The volume of a cone is given by:
Where:
r: is the radius
h: is the height
The rate of change of the volume can be calculated by using the chain rule:
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5B%5Cfrac%7Bdh%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20h%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
Since h = 4/3 r we have:
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5B%5Cfrac%7Bd%28%5Cfrac%7B4r%7D%7B3%7D%29%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20%5Cfrac%7B4r%7D%7B3%7D%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
![\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5B%5Cfrac%7Bdr%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20r%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
![\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5B%5Cfrac%7Bdr%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%202r%5E%7B2%7D%5Cfrac%7Bdr%7D%7Bdt%7D%5D%20)
(1)
With:
= 3 in/min
And by entering the above values into equation (1) we have:
![\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5B%283%20in%2Fmin%29%2A%2836%20in%29%5E%7B2%7D%20%2B%202%2A%2836%20in%29%5E%7B2%7D%2A3%20in%2Fmin%5D%20)
Therefore, the volume is increasing at a rate of 16286 in³/min.
I hope it helps you!
Hello I believe your answer is going to be 2 I assumed the b's were x's
Answer
The line of symmetry x = -4
Step by step explanation
Here we have to use the formula.
The symmetry of a parabola x = -b/2a
Now compare the given equation y = 3x^2 + 24x -1 with the general form y = ax^2 + bx + c and identify the value of "a" and "b"
Here a = 3 and b = 24. Now plug in these values in to the formula to find the line of symmetry.
x = -24/ 2(3)
x = -24/6
x = -4
Therefore, the line of symmetry x = -4.
Thank you.
