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Olegator [25]
3 years ago
9

Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Jos

hua borrow to buy the computer?
Mathematics
1 answer:
rusak2 [61]3 years ago
4 0

Answer: Josh borrowed $ 876  to buy the computer.

Step-by-step explanation:

Formula for simple interest : I = Prt

, where P = principal amount

r= rate of interest ( in decimal)

t=time (in years)

Total amount with simple interest to pay : A = P+I

⇒ A = P +Prt

⇒ A = P(1 +rt)         (i)

As per given , A = $1,244.34

r= 12.4% = 0.124

t= 3 years

Now, put these values in (i) , we get

1244.34=P(1+0.124)^3\\\\\Rightarrow\ 1244.34=P(1.124)^3\\\\\Rightarrow\ 1244.34=P(1.420034624)\\\\\Rightarrow\ P=\dfrac{1244.34}{1.420034624}\\\\\Rightarrow\ P=876.27

Hence, Josh borrowed $ 876  to buy the computer.

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Firdavs [7]

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

The power-reducing formula, for cosine, is,

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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]

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= 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 <u>[ 3 + 2cos 2θ + cos 4θ]/8</u>.

Learn more about reducing trigonometric powers at

brainly.com/question/15202536

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