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kondor19780726 [428]
3 years ago
10

Aubrey invested $61,000 in an account paying an interest rate of 1.9% compounded continuously. Assuming no deposits or withdrawa

ls are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $73,600?
Mathematics
1 answer:
Hitman42 [59]3 years ago
4 0

Answer: 9.9 years.

Step-by-step explanation:

If interest is compounded continuously, then formula to compute final amount A = Pe^{rt}, where P =initial amount, r= rate of interest , t=time.

Given: P= $61,000, r= 1.9% =0.019  , A = $ 73600

Substitute all values in formula

73600=61000e^{0.019t}\\\\\Rightarrow\ \dfrac{73600}{61000}=e^{0.019t}\\\\\Rightarrow\ 1.20655738=e^{0.019t}

Taking natural log on both sides

\ln (1.20655738)=0.019t\\\\\\ 0.18777116=0.019t\\\\\\ t=\dfrac{0.18777116}{0.019}\\\\\\ t=9.88269263\approx9.9\ \text{years}

Hence, the required time = 9.9 years.

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The statue of Liberty stands on a 150 ft. pedestal. From a point 250 ft. from the base of the
bekas [8.4K]

Answer:

148ft

Step-by-step explanation:

To solve this question, you'll have to imagine the statue makes a right angle triangle with the base since it has an angle of elevation from the base to the top of the torch.

Assuming the height from the pedestal to the top of the torch is y

The height of the statue is x

But we know the height of the pedestal = 150ft

The distance from the observer to the base of the pedestal = 250ft

And the angle of elevation = 50°

See attached document for better illustration.

Tanθ = opposite / adjacent

θ = 50°

Adjacent = 250

Opposite = y

Tan50 = t / 250

y = 50 × tan50

y = 50 × tan50

y = 50 × 1.1917

y = 297.925ft

The height of the statue from the base of the pedestal to the top of the torch is 297.925ft

The height of the statue = x

x = (height of the statue + height of the pedestal) - height of the pedestal

x = y - 150

x = 297.925 - 150

x = 147.925ft

Approximately 148ft

The height of the statue is 148ft

4 0
3 years ago
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Irina18 [472]
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6 0
3 years ago
Which expressions are equivalent to 12x - 6? ​
iren2701 [21]
<h3>Answer</h3>

B and E

<h3>Explanation</h3>

A) It's wrong because

- 6 \times (2x - 1) =  - 12x + 6

B) It's right because

6 \times (2x - 1) = 12x - 6

C) It's wrong because

6x \times (2 - 1) = 6x \times 1 = 6x

D) It's wrong because

- 6x \times (2x - 1) =  - 12 {x}^{2} + 6

E) It's right because

- 6 \times ( - 2x + 1) = 12x - 6

F) It's wrong because

6 \times ( - 2x + 1) =  - 12x + 6

8 0
3 years ago
Let the function f(x) have the form f(x) = Acos(x-C). To produce a graph that
Gala2k [10]

Answer:

A has to be 2

Step-by-step explanation:

In the expression f(x)=A*cos(x-C), the multiplicative factor A represents what is called the "amplitude of the wave-shaped function that you obtain as the graph. Such amplitude is understood as half of the crest-to-through distance of the wavy curve.

From the drawing, the crest is at y=2 and the through at y=-2 (a distance of 4 units) therefore the value of A should be half of that distance: 4/2 = 2

6 0
3 years ago
Read 2 more answers
10) Will mark BRAINLIEST + 10 POINTS :)
Mariana [72]
Answer is A.

√6 + √2
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4 0
3 years ago
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