Answer:
-18
Step-by-step explanation:
4bc-b
Let b = -3 and c=2
4 * (-3)* 2 - (-3)
-24 +6
-18
Answer:
the fence needed to enclose the garden = 140 ft.
Step-by-step explanation:
given:
rectangular garden is 25 ft. by 45 ft.
find:
how many feet of fence are needed to enclose it?
use the perimeter of a rectangle formula = 2L + 2W
let L = 45 ft.
let W = 25 ft.
plugin values into the formula
P = 2L + 2W
P = 2(45) + 2(25)
P = 90 + 50
P = 140 ft.
therefore,
the fence needed to enclose the garden = 140 ft.
When the diameter is 10 m the volume is <span>523.6 m^3</span>
Answer:
Step-by-step explanation:
We have volume of cone as
![V=\frac{1}{3} \pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
and for a cone always r/h = constant
Given that r' = rate of change of radius = -7 inches/sec
(Negative sign because decresing)
V' =- 948 in^3/sec
Radius = 99 inches and volume = 525 inches
Height at this instant = ![\frac{525}{\frac{1}{3} \pi (99)^2} \\=\frac{0.1607}{\pi}](https://tex.z-dn.net/?f=%5Cfrac%7B525%7D%7B%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%2899%29%5E2%7D%20%5C%5C%3D%5Cfrac%7B0.1607%7D%7B%5Cpi%7D)
Let us differentiate the volume equation with respect to t using product rule
![V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%5C%5CV%27%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2rhr%27%2Br%5E2%20h%27%5D%5C%5C-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2%2899%29%28-7%29%28%5Cfrac%7B0.1607%7D%7B%5Cpi%7D%29%2B99%5E2%20h%27%5D%5C%5C)
![-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514](https://tex.z-dn.net/?f=-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2%2899%29%28-7%29%28%5Cfrac%7B0.1607%7D%7B%5Cpi%7D%29%2B99%5E2%20h%27%5D%5C%5C-948%20%3D%2033%283.14%29%28-2.25%2F3.14%20%20%2B%2099%20h%27%29%5C%5C-9.149%3D-0.72%2B99h%27%5C%5C-8.429%20%3D%2099h%27%5C%5Ch%27%20%3D%200.08514)
Rate of change of height = 0.08514 in/sec
Answer:
-15(7/20) = -307/20 = -15.35, which is less than -15.
Step-by-step explanation:
Aight