The circumference of a circle is 28 x inches. What is the length of the radius of this circle?

use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4

Firdavs [7]

The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

The power-reducing formula, for cosine, is,

cos² θ = (1/2)[1 + cos 2θ].

In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.

We can do it as follows:

cos⁴ θ

= (cos² θ)²

= {(1/2)[1 + cos 2θ]}²

= (1/4)[1 + cos 2θ]²

= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}

= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)

= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]

= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8

= 3/8 + cos 2θ/4 + cos 4θ/8

= [ 3 + 2cos 2θ + cos 4θ]/8.

Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

Learn more about reducing trigonometric powers at

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5 0

2 years ago

!!!3 QUESTIONS!!!

RUDIKE [14]

Answer:

1.) He still owes $100 of debt

2.) 1 rose would be .75 cents and 1 carnation would be .90 cents

3.) C 8 and 3/8

Step by Step explanation

(/ means divided by in the first 2 equations but / in the last question is for the fractions.)

1.) _(1,500 / 3 =500. 1,500 - 500 =1,000 / 5 =200 x 3 =600. 700 - 600 =$100)

2.)_(1.50/2 =.75 cents. 2.70/3 =.90 cents.)

3.) i first added the fractions ( i equalized them) then i added the whole numbers (the u in the equation was to separate the whole num. and fraction )

Before i equalized it: (6u3/4 + 1u1/8 = 7u1/8 + 1/8 = 8u3/8)

After i equalized it: (6u6/8 + 1u1/8 = 7u1/8 + 1/8 = 8u3/8)

6 0

3 years ago

Danelle and Jim Baraja have obtained a $70,000 mortgage loan at an annual interest rate of 6.00 for years. What is the monthly p

musickatia [10]

Total Paid:$147,060.36
Monthly payment $408.50
Total Interest Paid $77,060.36
Hope I helped!!

5 0

3 years ago

A farmer has 100 m of fencing to enclose a rectangular pen. Which quadratic equation gives the area (A) of the pen, given its wi

inn [45]

A(w)=50w-w2 if the perimeter is 100, I plugged in possible values for the width...I used w=15 and length = 35 for a perimeter of 100. then I plugged these values in the possible equations until I found the correct one giving me an area of 525 (15x35) . I could not think of an easier way.

5 0

3 years ago

Read 2 more answers

Which inequality can be used to represent this problem? A company spent $15,000 developing a new graffiti repelling paint. The c

AleksandrR [38]

Answer:

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

Step-by-step explanation:

Given that the total cost of manufacturing by the company is $15000.

Let x be the number of gallons the company sells.

It is also mentioned that the company earns $10 on each gallon.

So the total profit will be the the difference of the selling cost of gallons and manufacturing cost

Mathematically,

$10x-15000$

Now it is mentioned that the profit should be at least 50000 dollars which means the profit can be minimally 50000 and also can be greater than it so

$10x-15000 \geq 50000$

The number of gallons can be found by solving the obtained inequality.

Hence,

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

7 0

3 years ago