There would be 252 robbers because the rate of change is 21 and 12*21=252
Answer:
Angles 2 and 3 are supplementary to each other
Step-by-step explanation:
A supplementary angle is 2 angles that when you add the sum is 180.
Answer:
Therefore,the level of paint is rising when the bucket starts to overflow at a rate
cm per minute.
Step-by-step explanation:
Given that, at a rate 4 cm³ per minute,a cylinder bucket is being filled with paint
It means the change of volume of paint in the cylinder is 4 cm³ per minutes.
i.e
cm³ per minutes.
The radius of the cylinder is 20 cm which is constant with respect to time.
But the level of paint is rising with respect to time.
Let the level of paint be h at a time t.
The volume of the paint at a time t is
![\Rightarrow V=\pi (20)^2h](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D%5Cpi%20%2820%29%5E2h)
![\Rightarrow V=400\pi h](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D400%5Cpi%20h)
Differentiating with respect to t
![\frac{dV}{dt}=400\pi \times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D400%5Cpi%20%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Now putting the value of ![\frac{dV}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D)
![\Rightarrow 4=400\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=%5CRightarrow%204%3D400%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\Rightarrow \frac{dh}{dt}=\frac{4}{400\pi}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B4%7D%7B400%5Cpi%7D)
![\Rightarrow \frac{dh}{dt}=\frac{1}{100\pi}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B100%5Cpi%7D)
To find the rate of the level of paint is rising when the bucket starts to overflow i.e at the instant h= 70 cm.
![\left \frac{dh}{dt}\right|_{h=70}=\frac{1}{100\pi}](https://tex.z-dn.net/?f=%5Cleft%20%5Cfrac%7Bdh%7D%7Bdt%7D%5Cright%7C_%7Bh%3D70%7D%3D%5Cfrac%7B1%7D%7B100%5Cpi%7D)
Therefore, the level of paint is rising when the bucket starts to overflow at a rate
cm per minute.
The greatest common factor (GCF) of the expressions is a product of the GCF of the numerical coefficients and the variables. The GCF of the 24 and 80 is 8. Additionally, the GCF of x^4 and x^5 if x^4. Thus, the GCF is 8x^4. The answer to this problem is letter C.
cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer