Answer:
option ;;c ;; is right answer
Step-by-step explanation:
4x -28 =24 (z is the middle point) 4x =24+28 x =52/4 x = 13 RZ =4x-28 =4(13)-28 =24 ZT =24 RT =ZT +RZ =24+24 =48
X =13 RZ =24 RT =48
Answer:
Water level in the reservoir is falling at the rate of 0.398 ft per minute.
Step-by-step explanation:
From the figure attached,
Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.
Let the level of water in the reservoir after time t is h where radius of the water level becomes r.
ΔABE and ΔCDE are similar.
Therefore, their corresponding sides will be in the same ratio.
![\frac{r}{h}=\frac{4}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%3D%5Cfrac%7B4%7D%7B10%7D)
--------(1)
Now volume of the water V = ![\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
From equation (1),
V = ![\frac{1}{3}\pi (\frac{2}{5}h)^{2} h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7B2%7D%7B5%7Dh%29%5E%7B2%7D%20h)
V = ![\frac{4\pi h^{2}\times h}{75}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20h%5E%7B2%7D%5Ctimes%20h%7D%7B75%7D)
![\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bd%7D%7Bdt%7D%28h%5E%7B3%7D%29)
![\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%283h%5E%7B2%7D%29%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B12%5Cpi%20h%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Since
feet³ per minute and h = 5 feet
![5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B12%5Cpi%20%285%29%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![5=4\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D4%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{5}{4\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B5%7D%7B4%5Cpi%7D)
feet per minute
Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.
Yes. Parallel means same slope as original line. So it’s 2
We can use the definition of the sine to help us solve this problem.
The sine of an angle is the opposite side divided by the hypotenuse.
Using this information, we can create an equation that solves for x.
![sin(35)= \dfrac {x}{4.1}](https://tex.z-dn.net/?f=sin%2835%29%3D%20%5Cdfrac%20%7Bx%7D%7B4.1%7D)
Multiply both sides by 4.1
![x=4.1*sin(35)](https://tex.z-dn.net/?f=x%3D4.1%2Asin%2835%29)
Use a calculator to help solve for sin(35).
![x=2.3516...](https://tex.z-dn.net/?f=x%3D2.3516...)
![\approx 2.4](https://tex.z-dn.net/?f=%5Capprox%202.4)
I hope this helps! :)