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3 years ago

How many degrees does she rotate the telescope to see star b?

Mathematics

1 answer:

Lana71 [14]3 years ago

4 0

We have to use the law of cosines to solve for the missing angle.

cos(?) = (400^2 + 450^2 - 90^2) / (2*400*450).

Since, we want the exact value, we are going to take the inverse cosine of both sides

? = 10 degrees

The astronomer had to rotate her telescope 10 degrees to see star B

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At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500

kaheart [24]

Answer:

D. $31,337.27

Step-by-step explanation:

We have that the initial amount of the loan is $5500.

Miranda took the loan for 4 years. So, the total present value is $5500×4 = $22,000.

The rate of interest on the loan is 7.5% i.e. 0.075 and it was for the duration of 10 years.

Also, it is given that the loan was compounded annually.

We have the formula as,

$P=\frac{\frac{r}{n}\times PV}{1-(1+\frac{r}{n})^{-t\times n}}$

i.e. $PV=\frac{P\times [1-(1+\frac{r}{n})^{-t\times n}]}{\frac{r}{n}}$

Substituting the values, we get,

i.e. $PV=\frac{P\times [1-(1+\frac{0.075}{12})^{-10\times 12}]}{\frac{0.075}{12}}$

i.e. $22000=\frac{P\times [1-(1+0.00625)^{-120}]}{0.00625}$

i.e. $22000=\frac{P\times [1-(1.00625)^{-120}]}{0.00625}$

i.e. $22000=\frac{P\times [1-0.4735]}{0.00625}$

i.e. $22000=\frac{P\times 0.5265}{0.00625}$

i.e. $P=\frac{22000\times 0.00625}{0.5265}$

i.e. $P=\frac{137.5}{0.5265}$

i.e. $P=261.16$

Thus, the total lifetime cost to pay of the loans compounded annually = 261.16 × 120 = $31,339.2

Hence, the total cost close to the answer is $31,337.27

7 0

3 years ago

Read 2 more answers

I need to know how to do it in Distributive Property.

kotykmax [81]

A(b-c)=ab-ac

(1/7)(1/3h-1/2)=(1/7)(1/3h)-(1/7)(1/2)=1/21h-1/14

now we gots
6 and 1/7+1/21h-1/14
rearange
6 and 1/7-1/14+1/21h
make common denom which is 14
6 and 2/14-1/14+1/21h
6 and 1/14+1/21h

6 0

3 years ago

Ivan has a summer babysitting job that pays $15 per hour. He wants to know how many hours he has to babysit to afford a new bike

exis [7]

Answer: 20 hours

Step-by-step explanation:

Equation: 15x = 300

Isolate the variable.

Divide both sides by 15: ¹⁵ˣ⁄₁₅ = ³⁰⁰⁄₁₅

x = 20

Ivan needs to work 20 hours in order to afford the bicycle.

8 0

3 years ago

Find the value of cos 28°cos 62°– sin 28°sin 62°

Romashka [77]

<h2>Answer:</h2>

cos 28°cos 62°– sin 28°sin 62° = 0

<h2>Step-by-step explanation:</h2>

From one of the trigonometric identities stated as follows;

cos(A+B) = cosAcosB - sinAsinB -----------------(i)

We can apply such identity to solve the given expression.

Given:

cos 28°cos 62°– sin 28°sin 62°

Comparing the given expression with the right hand side of equation (i), we see that;

A = 28°

B = 62°

∴ Substitute these values into equation (i) to have;

⇒ cos(28°+62°) = cos28°cos62° - sin28°sin62°

Solve the left hand side.

⇒ cos(90°) = cos28°cos62° - sin28°sin62°

⇒ 0 = cos28°cos62° - sin28°sin62° (since cos 90° = 0)

Therefore,

cos28°cos62° - sin28°sin62° = 0

8 0

3 years ago

Please help with this question picture attached ASAP please

olga nikolaevna [1]

1 : 1.71 : 2.43

Step-by-step explanation:

What divided by 7= 1?

7/7 = 1

So use that answer for the other two dolls.

12/7 = 1.71

17/7 = 2.43

1 : 1.71 : 2.43

Have the same ratio as

7 : 12 : 17

5 0

3 years ago