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VladimirAG [237]
2 years ago
11

Sarah works as a waiter. She earns 15% in tips on meals served. This weekend, Sarah earned $172.50 in all. What is the dollar am

ount of the meals that Sarah served?
Mathematics
1 answer:
xxMikexx [17]2 years ago
4 0

Answer:

$1150 amount of the meals that Sarah served.

Step-by-step explanation:

As given

Sarah works as a waiter.

She earns 15% in tips on meals served.

This weekend, Sarah earned $172.50 in all.

Let us assume that the x dollar amount of the meals that Sarah served .

15% is written in the decimal form.

= \frac{15}{100}

= 0.15

Than the equation becomes

x × 0.15 = 172.50

Solving the above equation

x = \frac{172.50}{0.15}

x = $1150

Therefore $1150  amount of the meals that Sarah served.

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240^0

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\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

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Using the trigonometric identity;

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\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\  \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

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\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\  \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\  \\ Thus, \\ sec240^0=-2 \end{gathered}

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