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:
384 Square Inches
Step-by-step explanation:
Given a square pyramid with base side edge and slant height
In the given pyramid:
- Slant Height=20 inches
- Base Edge = 8 Inches
Therefore:
Area of Base, A =8 X 8 =64 Square Inches
Perimeter of base, p =4 X 8 =32 Inches
(1) 12, (2) 5, (3) 13, (4) 30
Step-by-step explanation:
(1) Given expression 2x.
Substitute x = 6 in expression 2x.
⇒ 2 × 6 = 12
(2) Given expression 8 + 3 – x
Substitute x = 6 in expression 8 + 3 – x.
⇒ 8 + 3 – 6 = 11 – 6 = 5
(3) Given expression 6 + 7 – 6 + x
Substitute x = 6 in expression 6 + 7 – 6 + x.
⇒ 6 + 7 – 6 + x = 6 + 7 – 6 + 6 = 13
(4) Given expression 5x
Substitute x = 6 in expression 5x.
⇒ 5× 6 = 30
Answer:
3/4
Step-by-step explanation:
2 - 1.25 - 0.75
0.75 = 3/4
Your answer is 3/4.
I hope this helps, have a nice day.
