Answer:
A. 2(Pi)rh+2(Pi)r^2
Step-by-step explanation:
The surface area of a cylinder is the sum of the lateral area and the area of the two circular ends.
The lateral area is the product of the circumference of the cylinder and its height:
lateral area = 2πrh
The area of the two ends is twice the area of each of those circles, so is ...
total end area = 2(πr²)
Then the total surface area of a cylinder is ...
SA = 2πrh +2πr²
Answer:
Thank you so much.
Step-by-step explanation:
Answer:
The absolute maximum is
and the absolute minimum value is 
Step-by-step explanation:
Differentiate of
both sides w.r.t.
,


Now take 



![\Rightarrow 1-2\sin ^2t =\sin t \quad \quad [\because \cos 2t = 1-2\sin ^2t]](https://tex.z-dn.net/?f=%5CRightarrow%201-2%5Csin%20%5E2t%20%3D%5Csin%20t%20%20%5Cquad%20%5Cquad%20%20%5B%5Cbecause%20%5Ccos%202t%20%3D%201-2%5Csin%20%5E2t%5D)






In the interval
, the answer to this problem is 
Now find the second derivative of
w.r.t.
,

![\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cleft%5Bf%27%27%28t%29%5Cright%5D_%7Bt%3D%5Cfrac%20%7B%5Cpi%7D6%7D%3D-2%5Ctimes%20%5Cfrac%20%7B%5Csqrt%203%7D2-4%5Ctimes%20%5Cfrac%7B%5Csqrt%203%7D2%3D-3%5Csqrt%203)
Thus,
is maximum at
and minimum at 
![\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0](https://tex.z-dn.net/?f=%5Cleft%5Bf%28t%29%5Cright%5D_%7Bt%3D%5Cfrac%20%7B%5Cpi%7D6%7D%3D2%5Ctimes%20%5Cfrac%20%7B%5Csqrt%203%7D2%2B%5Cfrac%7B%5Csqrt%203%7D2%3D%5Cfrac%7B3%5Csqrt%203%7D2%5C%3B%5Ctext%7Band%7D%5C%3B%5Cleft%5Bf%28t%29%5Cright%5D_%7Bt%3D%5Cfrac%7B%5Cpi%7D2%7D%3D%202%5Ctimes%200%2B0%3D0)
Hence, the absolute maximum is
and the absolute minimum value is
.
Answer:
18. Supplementary
19. Vertical
20. x = 7
23. x = 25
Step-by-step explanation:
Use angle relationships to make equations which you can solve for x.
Example:
18. These two angles form a line. These are called supplementary.
19. These angles are across a vertex from each other and are equal or the same.
20. 9x + 1 = 7x - 9 + 5x - 11
9x + 1 = 12x - 20
9x - 9x + 1 = 12x - 9x - 20
1 = 3x - 20
1 + 20 = 3x - 20 + 20
21 = 3x
7 = x
23. These two angles are across a vertex from each other. This means the angles are equal. Think of it as a reflection. If you folded the paper on that vertex, the lines would be in the exact same place.
So set the two expressions equal to each other. Then use inverse operations to isolate x and solve.
5x + 4 = 8x - 71
5x - 5x + 4 = 8x - 5x - 71
4 = 3x - 71
4 + 71 = 3x - 71 + 71
75 = 3x
25 = x
Answer:
you have to do, x axis times y axis which should give you your answer.
Step-by-step explanation: