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MrRa [10]
3 years ago
10

Arianna is saving money for college so she invests $1,000 into a savings account that earns interest every year. If the amount i

n the savings account is represented by the function
9x2+50x+1000, where x is the number of years. How much money does Arianna have in her account after 6 years?
Mathematics
1 answer:
Verdich [7]3 years ago
7 0

Answer: $1,624

Step-by-step explanation:

The amount after x-years is given as :

9x^{2} + 50x + 1000

Since x represents number of years , this means that after 6 years , the amount will be :

9(6^{2} ) + 50(6) + 1000

⇒9(36) + 300 + 1000

⇒324 + 300 + 1000 =

Therefore, the amount after 6 years will be $1,624

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Find the length of the arc and express your answer as a fraction times pie
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Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}

To find the length of the arc, s, the formula is

\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}

Substitute the variables into the formula to find the length of an arc, s above

\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}

Hence, the length of the arc, s, is 3π units.

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