tis a little of plain differentiation.
we know the radius of the cone is decreasing at 10 mtr/mins, or namely dr/dt = -10, decreasing, meaning is negative.
we know the volume is decreasing at a rate of 1346 mtr/mins or namely dV/dt = -1346, also negative.
so, when h = 9 and V = 307, what is dh/dt in essence.
we'll be needing the "r" value at that instant, so let's get it
now let's get the derivative of the volume of the cone
![V=\cfrac{1}{3}\pi r^2 h\implies \cfrac{dV}{dt}=\cfrac{\pi }{3}\stackrel{product~rule}{ \left[ \underset{chain~rule}{2r\cdot \cfrac{dr}{dt}}\cdot h+r^2\cdot \cfrac{dh}{dt} \right]} \\\\\\ -1346=\cfrac{\pi }{3}\left[2\sqrt{\cfrac{307}{3\pi }}(-10)(9)~~+ ~~ \cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\right]](https://tex.z-dn.net/?f=V%3D%5Ccfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Ccfrac%7B%5Cpi%20%7D%7B3%7D%5Cstackrel%7Bproduct~rule%7D%7B%20%5Cleft%5B%20%5Cunderset%7Bchain~rule%7D%7B2r%5Ccdot%20%5Ccfrac%7Bdr%7D%7Bdt%7D%7D%5Ccdot%20h%2Br%5E2%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20-1346%3D%5Ccfrac%7B%5Cpi%20%7D%7B3%7D%5Cleft%5B2%5Csqrt%7B%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%7D%28-10%29%289%29~~%2B%20~~%20%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%20%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cright%5D)
![-\cfrac{4038}{\pi }=-\cfrac{180\sqrt{307}}{\sqrt{3\pi }}+\cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\implies \left[ -\cfrac{4038}{\pi }+\cfrac{180\sqrt{307}}{\sqrt{3\pi }} \right]\cfrac{3\pi }{307}=\cfrac{dh}{dt} \\\\\\ -\cfrac{12114}{307}+\cfrac{180\sqrt{3\pi }}{\sqrt{307}}=\cfrac{dh}{dt}\implies -7.920939735970634 \approx \cfrac{dh}{dt}](https://tex.z-dn.net/?f=-%5Ccfrac%7B4038%7D%7B%5Cpi%20%7D%3D-%5Ccfrac%7B180%5Csqrt%7B307%7D%7D%7B%5Csqrt%7B3%5Cpi%20%7D%7D%2B%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%20%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cimplies%20%5Cleft%5B%20-%5Ccfrac%7B4038%7D%7B%5Cpi%20%7D%2B%5Ccfrac%7B180%5Csqrt%7B307%7D%7D%7B%5Csqrt%7B3%5Cpi%20%7D%7D%20%5Cright%5D%5Ccfrac%7B3%5Cpi%20%7D%7B307%7D%3D%5Ccfrac%7Bdh%7D%7Bdt%7D%20%5C%5C%5C%5C%5C%5C%20-%5Ccfrac%7B12114%7D%7B307%7D%2B%5Ccfrac%7B180%5Csqrt%7B3%5Cpi%20%7D%7D%7B%5Csqrt%7B307%7D%7D%3D%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cimplies%20-7.920939735970634%20%5Capprox%20%5Ccfrac%7Bdh%7D%7Bdt%7D)
Answer:
the probability that a sample of 4 bags will have a mean weight less than 9.8 pounds is 0.05
Step-by-step explanation:
Given the data in the question;
μ_x = 10 pound bags
standard deviation s_x = 0.24 pounds
sample size n = 4
The bag weights are normally distributed so;
p( x' less than 9.8 ) will be;
p( (x'-μ_x' / s_x') < (9.8-μ_x' / s_x') )
we know that;
μ_x' = μ_x = 10
and s_x' = s_x/√n = 0.24/√4
so; we substitute
p( z < ( (9.8 - 10) / (0.24/√4) )
p( z < -0.2 / 0.12 )
p( z < -1.67 )
{ From z-table }
⇒ p( z < -1.67 ) = 0.0475 ≈ 0.05
Therefore, the probability that a sample of 4 bags will have a mean weight less than 9.8 pounds is 0.05
Answer:
c = 4.79 feet
Step-by-step explanation:
Given question is incomplete without a picture; find the question with the attachment.
Two poles AD and DB of same length are leaning against each other.
Distance between the poles (AB) = 45 feet
m(∠ADB) = 180°- (60 + 50)°
= 70°
By sine rule,
= 36.68 ft
Similarly,
DB = 
= 41.47 ft
Now c = DB - AD
= 41.47 - 36.68
= 4.79 feet
Answer:
125/12
Step-by-step explanation:
1st problem-no
2nd problem-yes
3rd problem-yes
4th problem-no
