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Naddika [18.5K]

2 years ago

8

Flying against the wind, an airplane travels 5760 kilometers in 6 hours. Flying with the wind, the same plane travels 6300 kilom

eters in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?

1 answer:

Aleks [24]2 years ago

5 0

<h2>Speed of plane = 1110 kmph</h2><h2>Speed of wind = 150 kmph</h2>

Step-by-step explanation:

Let the speed of plane be p and speed of wind be w.

Flying against the wind, an airplane travels 5760 kilometers in 6 hours.

Here

Speed = (p-w) kmph

Time = 6 hours

Distance = 5760 kmph

Distance = Speed x Time

5760 = (p-w) x 6

p-w = 960 -----eqn 1

Flying with the wind, the same plane travels 6300 kilometers in 5 hours.

Here

Speed = (p+w) kmph

Time = 5 hours

Distance = 6300 kmph

Distance = Speed x Time

6300 = (p+w) x 5

p+w = 1260 -----eqn 2

eqn 1 + eqn 2

p-w + p +w = 960 + 1260

2p = 2220

p = 1110 kmph

Substituting in eqn 2

1110 + w = 1260

w = 150 kmph

Speed of plane = 1110 kmph

Speed of wind = 150 kmph

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Marrrta [24]

Answer :

Depends on the rate compound interest is accrued. See answers.

Step-by-step explanation:

We need the compound interest formula which is:

$A = P (1+\frac{r}{n} )^{nt}$

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

It doesn't say how frequently the interest is compounded, so we will do monthly, quarterly, and yearly.

MONTHLY

So we know the car costs $25,480 and he made a down payment of $10,000. By subtracting the down payment from the purchase price we find the loan amount.

$25,480 - $10,000 = $15,480

P = 15,480

r = 4.75% = .0475

n = 12 (12 months in a year)

t = 2

Plug everything into the compound interest formula.

$A = P (1+\frac{r}{n} )^{nt}$

$A = 15480(1+\frac{.0475}{12})^{12*2}$

$A = 15480(1+\frac{.0475}{12})^{24}$

$A = 15480(1+.00396)^{24}$

$A = 15480(1.00396)^{24}$

$A = 15480*1.0992$

$A = $17016.14$

Mr. Lee paid $17,016.14 when the bill came due at 2 years with interest compounded monthly.

QUARTERLY

P = 15,480

r = 4.75% = .0475

n = 4 (4 quarters in a year)

t = 2

$A = P (1+\frac{r}{n} )^{nt}$

$A = 15480(1+\frac{.0475}{4})^{4*2}$

$A = 15480(1+\frac{.0475}{4})^{8}$

$A = 15480(1+.0119})^{8}$

$A = 15480(1.0119)^{8}$

$A = 15480*1.099$

$A = 15480(1.099)$

$A = 17013.20$

Mr. Lee paid $17,013.20 when the bill came due at 2 years with interest compounded quarterly.

YEARLY

P = 15,480

r = 4.75% = .0475

n = 1

t = 2

$A = P (1+\frac{r}{n} )^{nt}$

$A = 15480(1+\frac{.0475}{1})^{1*2}$

$A = 15480(1+\frac{.0475}{12})^{2}$

$A = 15480(1+.0475})^{2}$

$A = 15480(1.0475)^{2}$

$A = 15480*1.0973$

$A = 16985.53$

Mr. Lee paid $16,985.53 when the bill came due at 2 years with interest compounded yearly.

4 0

3 years ago

If you take a number, times by 8 then add 6. You get the same as if you took the number multiply it by 3 then subtract 7. What i

Gennadij [26K]

Answer:

x = -13/5

Step-by-step explanation:

let x be the number

8x + 6 = 3x - 7

move variables to left and numbers to right

8x - 3x = - 7 -6

5x = -13

x = -13/5

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2 years ago

Friends?<br>.............................

Vlad [161]

Ok sure—————-_______—-____

7 0

3 years ago

Find the value of x to the nearest tenth. (The last answer is 13.3)

Julli [10]

Your answer is the first option, 8.0. You can find this by using the sine rules for sides, so:
10/sin(90) = x/sin(53)
× sin(53)
7.98 = x
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I hope this helps!

8 0

2 years ago

Read 2 more answers

Please help!!!!!!!!!!!

boyakko [2]

Answer:

(7√6)/2

Step-by-step explanation:

The side ratios in these special triangles are ...

30°-60°-90° triangle: 1 : √3 : 2

45°-45°-90° triangle: 1 : 1 : √2

This tells you the length of the horizontal line is 7√3, and the value of x is ...

(7√3)/√2 = (7√6)/2

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<em>Additional comment</em>

Call the length of the horizontal line "y". Then the given ratios tell you ...

7 : y = 1 : √3 ⇒ y/7 = √3/1 ⇒ y = 7√3

and

x : y = 1 : √2 ⇒ x/y = 1/√2 ⇒ x = y/√2

When we rationalize the denominator, we get ...

x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2

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2 years ago