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Delvig [45]
3 years ago
8

Casey is a real estate agent. She earns 8.15% commission on each sale she makes. After working with a potential buyer for 3.5 mo

nths, she finally sold a house for $877,000. What did casey earn in commissions for this sale
Mathematics
1 answer:
jeka57 [31]3 years ago
8 0

Given parameters:

Commission per sale  = 8.15%

Cost of house sold = $877,000

Unknown:

Amount of commission earned  = ?

Solution;

 The amount of commissioned earned;

          = Commission per sale x cost of house sold

          = \frac{8.15}{100}  x 877,000

          = $71,475.5

The commission earned on this sale is  $71,475.5

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Answer:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

Step-by-step explanation:

We are given the trigonometric equation of:

\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}

Let u = 4x then:

\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Convert u-term back to 4x:

\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Divide both sides by 4:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

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