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Gekata [30.6K]
3 years ago
9

By the age of 21, the best violinist and pianist will have practiced at least 10,000 hours. If you practice and instrument 45 mi

nutes (or 0.75 hours) a day for 365.25 days, the length of a year, how many hours will you have practiced?
Mathematics
1 answer:
Alika [10]3 years ago
8 0

Answer:

273.94 hours.

Step-by-step explanation:

1 day = 0.75 hours of practicing in a day.

365.25 = x

1/365.25 = 0.75/x        Cross multiply

x = 0.75 * 365.25        Combine

x =  273.94 hours

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Find the exact value of cos(theta) for an angle (theta) with tan (theta)= -2/3 and with its terminal side in Quadrant II.
Naya [18.7K]

Answer:

-\frac{3\sqrt{13}}{13}.

Step-by-step explanation:

Since we are in quadrant two, cosine value is negative while sine value is positive.

We are going to use the Pythagorean Identity: 1+\tan^2(\theta)=\sec^2(\theta).

1+(\frac{-2}{3})^2=\sec^2(\theta)

1+\frac{4}{9}=\sec^2(\theta)

\frac{9+4}{9}=\sec^2(\theta)

\frac{13}{9}=\sec^2(\theta)

\pm \sqrt{\frac{13}{9}}=\sec(\theta)

\pm \frac{\sqrt{13}}{3}=\sec(\theta)

Since cosine and secant are reciprocals then they will have the same sign as along as they both exist.

\sec(\theta)=-\frac{\sqrt{13}}{3}

\cos(\theta)=-\frac{3}{\sqrt{13}}.

I don't see this answer as I'm going to rationalize the denominator.

\cos(\theta)=-\frac{3}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}.

\cos(\theta)=-\frac{3\sqrt{13}}{13}.

8 0
4 years ago
Read 2 more answers
100pts!! Ellis is painting wooden fenceposts before putting them in his yard. They are each 7 feet tall and have a diameter of 1
NeX [460]

Answer:

39.25 cubic feet of paint will be needed by Ellis.

Step-by-step explanation:

Step-by-step explanation:

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The volume of a cylinder of radius r and height h is given by:

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How much paint will Ellis need to paint all the surfaces of the 10 fenceposts?

This is the combined volume of these 10 fenceposts.

They are each 5 feet tall and have a diameter of 1 foot.

Radius is half the diameter, so r = \frac{1}{2} = 0.5. Also h = 5

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Each has the same volume, so:

V = 10(3.14)r^2h = 31.4(0.5)^2(5) = 39.25

39.25 cubic feet of paint will be needed by Ellis.

hope this helps

6 0
2 years ago
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How did you find this?
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