Step-by-step explanation:
<h3><u>Given :-</u></h3>
[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]
<h3>
<u>Required To Prove :-</u></h3>
[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)
<h3><u>Proof :-</u></h3>
On taking LHS
[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]
We know that
Tan θ = 1/ Cot θ
and
Cot θ = 1/Tan θ
=> (1+Cot²θ)(1+Tan²θ)
=> (Cosec² θ) (Sec²θ)
Since Cosec²θ - Cot²θ = 1 and
Sec²θ - Tan²θ = 1
=> (1/Sin² θ)(1/Cos² θ)
Since , Cosec θ = 1/Sinθ
and Sec θ = 1/Cosθ
=> 1/(Sin²θ Cos²θ)
We know that Sin²θ+Cos²θ = 1
=> 1/[(Sin²θ)(1-Sin²θ)]
=> 1/(Sin²θ-Sin²θ Sin²θ)
=> 1/(Sin²θ - Sin⁴θ)
=> RHS
=> LHS = RHS
<u>Hence, Proved.</u>
<h3><u>Answer:-</u></h3>
[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)
<h3><u>Used formulae:-</u></h3>
→ Tan θ = 1/ Cot θ
→ Cot θ = 1/Tan θ
→ Cosec θ = 1/Sinθ
→ Sec θ = 1/Cosθ
<h3><u>Used Identities :-</u></h3>
→ Cosec²θ - Cot²θ = 1
→ Sec²θ - Tan²θ = 1
→ Sin²θ+Cos²θ = 1
Hope this helps!!
26.80 x .15 gives you the answer, which is $4.02 in tip
Answer:
13.9cm
Step-by-step explanation:
13^2 = 169
5^2 = 25
169 + 25
= 194
13.9
Answer:
10.9361
Step-by-step explanation:
The lower control limit for xbar chart is
xdoublebar-A2(Rbar)
We are given that A2=0.308.
xdoublebar=sumxbar/k
Rbar=sumR/k
xbar R
5.8 0.42
6.1 0.38
16.02 0.08
15.95 0.15
16.12 0.42
6.18 0.23
5.87 0.36
16.2 0.4
Xdoublebar=(5.8+6.1+16.02+15.95+16.12+6.18+5.87+16.2)/8
Xdoublebar=88.24/8
Xdoublebar=11.03
Rbar=(0.42+0.38+0.08+0.15+0.42+0.23+0.36+0.4)/8
Rbar=2.44/8
Rbar=0.305
The lower control limit for the x-bar chart is
LCL=xdoublebar-A2(Rbar)
LCL=11.03-0.308*0.305
LCL=11.03-0.0939
LCL=10.9361
Answer:
The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.
Step-by-step explanation:
Volume of the Cylinder=400 cm³
Volume of a Cylinder=πr²h
Therefore: πr²h=400

Total Surface Area of a Cylinder=2πr²+2πrh
Cost of the materials for the Top and Bottom=0.06 cents per square centimeter
Cost of the materials for the sides=0.03 cents per square centimeter
Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)
C=0.12πr²+0.06πrh
Recall: 
Therefore:



The minimum cost occurs when the derivative of the Cost =0.






r=3.17 cm
Recall that:


h=12.67cm
The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.