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3 years ago

Find an identity for cos(4t)

1 answer:

5 0

We must know that $\cos(2x)=2\cos^2(x)-1$ . So:

$\cos(4t)=\cos(2\cdot2t)\\\\
\cos(4t)=2\cos^2(2t)-1\\\\
\cos(4t)=2(2\cos^2(t)-1)^2-1\\\\
\cos(4t)=2(4\cos^4(t)-4\cos^2(t)+1)-1\\\\
\cos(4t)=8\cos^4(t)-8\cos^2(t)+2-1\\\\
\boxed{\cos(4t)=8\cos^4(t)-8\cos^2(t)+1}$

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Pranav ate pizza for dinner on Monday night and had 2/3 of the pizza left over. On Tuesday night, he ate 1/2 of what was left. H

ale4655 [162]

Answer: 1/3

Step-by-step explanation:

From the question, we are informed that Pranav ate pizza for dinner on Monday night and had 2/3 of the pizza left over. We are further told that on Tuesday night, he ate 1/2 of what was left.

The amount of pizza that Pranav ate on Tuesday will be:

= 1/2 × 2/3

= 1/3

She ate 1/3 on Tuesday

6 0

3 years ago

The value of a dirt bike decreases by 15% each year. If you purchased this dirt bike today for $500, to the nearest dollar how m

guapka [62]

$500 x 0.85 = 425
$425 x 0.85 = 361.25
$361.25 x 0.85 = 307.10
$307.1 x 0.85 = 261
$261 x 0.85 = 221.85

5 0

4 years ago

-2x+2y=6 y=3 ft me after ill paypal u 252 622 0255

Katen [24]

Answer:

-2x +6 = 6

-2x = 6- 6

-2x =0

x = 0

7 0

3 years ago

Read 2 more answers

What is the answer to 55>-7x + 6

IRISSAK [1]

55>-7x + 6
Get -7x by itself
Subtract 6 from both sides
49>-7x
Divide by -7 (Remember to flip the inequality sign when dividing by negatives)
-7

5 0

3 years ago

Can someone please help me with math.

krek1111 [17]

Answer:

Step-by-step explanation:

1) Number of nickels = x

Number of quarter = y

x + y = 7 ----------------------(I)

x = 7 - y ------------------------(II)

0.05x + 0.25y = 0.55 -----------(III)

Substitute s = 7 - y in equation (III)

0.05*(7 - y) + 0.25y = 0.55

0.05*7 - 0.05*y + 0.25y = 0.55

0.35 - 0.05y + 0.25y = 0.55 {Combine like terms}

0.35 + 0.20y = 0.55 {Subtract 0.35 from both sides}

0.2y = 0.55 - 0.35

0.2y = 0.2 {Divide both sides by 0.2}

y = 0.2/0.2

y = 1

Substitute y =1 in equation (II)

x = 7 - 1

x = 6

Number of nickels = 6

Number of quarter = 1

2) Number of children tickets = x

Number of adult tickets = y

x + y = 40 -----------------(I)

x = 40 - y -----------------(II)

2x + 5y = 170 -----------------(III)

Substitute x = 40 - y in equation (III)

2*(40-y) + 5y = 170

2*40 - 2*y + 5y = 170

80 - 2y + 5y = 170 {Combine like terms}

80 + 3y = 170 {Subtract 80 from both sides}

3y = 170 - 80

3y = 90 {Divide both sides by 3}

y = 90/3

y = 30

Substitute y = 30 in equation (II)

x = 40 - 30

x = 10

Number of children tickets = 10

Number of adult tickets =30

3 0

3 years ago