Answer: B
Step-by-step explanation:
It cant be A or C since the intersection does not touch the y axis and it isn't D since it is closer to -4 than -4 1/2
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:
The volume of air that the beach ball will hold is ![36,000 \pi\ cm^{3}](https://tex.z-dn.net/?f=36%2C000%20%5Cpi%5C%20cm%5E%7B3%7D)
Step-by-step explanation:
we know that
The volume of a sphere ( a giant beach ball with air) is equal to
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
we have
![r=30\ cm](https://tex.z-dn.net/?f=r%3D30%5C%20cm)
![V=\frac{4}{3}\pi (30^{3})](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%2830%5E%7B3%7D%29)
![V=36,000 \pi\ cm^{3}](https://tex.z-dn.net/?f=V%3D36%2C000%20%5Cpi%5C%20cm%5E%7B3%7D)
Http://prntscr.com/anpfk3
2 rectangle shaped
1) Length = 160 mi ; Width = 40 mi
2) Length = 440 mi - 160 mi ; Width = 240 mi - 70 mi
1 triangle shape
1) base = 70 mi ; height = 440 mi - 160 mi
Area Rectangle 1 = 160 mi * 40 mi = 6,400 mi²
Area Rectangle 2 = 280 mi * 170 mi = 47,600 mi²
Area Triangle 1 = ((440 mi - 160 mi) * 70mi)/2 = (280mi * 70mi)/2 = 9,800 mi²
Total Area = 6,400 mi² + 47,600 mi² + 9,800 mi² = 63,800 mi²