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2 years ago

The area of a rectangular cocktail table is x²-18x +32. If the width is x-16, what is it's length?

Mathematics

1 answer:

Ad libitum [116K]2 years ago

5 0

Answer:

x-2

Step-by-step explanation:

The formula for area of rectangle is length x width
And we know that width is x-16
And we know that the area is $x^{2} -18x +32$

So we know that when x-2 is multiplied with x-16, it gives off $x^{2} -18x +32$

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4 years ago

You invest $5,000 into an account where interest compounds continuously at 3.5%. How long will it take your money to double? Rou

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Step-by-step explanation:

Continuous Compounding Formula

$\large \text{$ \sf A=Pe^{rt} $}$

where:

A = Final amount
P = Principal amount
e = Euler's number (constant)
r = annual interest rate (in decimal form)
t = time (in years)

Given:

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Substitute the given values into the formula and solve for t:

$\sf \implies 10000=5000e^{0.035t}$

$\sf \implies \dfrac{10000}{5000}=e^{0.035t}$

$\sf \implies 2=e^{0.035t}$

$\sf \implies \ln 2=\ln e^{0.035t}$

$\sf \implies \ln 2=0.035t\ln e$

$\sf \implies \ln 2=0.035t(1)$

$\sf \implies \ln 2=0.035t$

$\sf \implies t=\dfrac{\ln 2}{0.035}$

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Therefore, it will take 20 years (to the nearest year) for the initial investment to double.

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