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3 years ago

14. Find the volume of this pentagonal prism. Use the formula V=B-H

Mathematics

1 answer:

alexandr1967 [171]3 years ago

5 0

Answer:

yes

Step-by-step explanation:

srry im broke need coin

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Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

5 0

4 years ago

Victoria moved into a new apartment and called to install her cable. They told her they charge $45 to install the cable box and

tiny-mole [99]

Answer:

$y=45+60x$

Step-by-step explanation:

Step one:

given data

The charge is $45 to install the cable box and $60 for each month of service

Required

The linear expression for the situation.

Step two:

let the number of months be x and let the total charges be y

Hence the expression for the total charges is

$y=45+60x$

6 0

3 years ago

Point L was plotted at (-4, 1), then L was transformed creating point L’ at (-1, -4).Which transformation rule could have been u

Rudiy27

Answer:

6 r.c g fig fu t DJ HD cvn and auntie and auntie

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3 years ago

What is the output of the following function for x=2 <br> F(x)= 2x^4-x^3+5x-9

viktelen [127]

Answer:25

Step-by-step explanation:

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3 years ago

Help please it’s geometry ...........

Anon25 [30]

Answer:

4 i think

Step-by-step explanation:

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3 years ago