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iragen [17]
3 years ago
6

An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. the yard has 3 sprinkler head

s that each cover a circular area with no overlap. what is the approximate total area that will be watered? 1963.5 ft 1963.5 ft² 5890.5 ft 5890.5 ft²
Mathematics
2 answers:
Illusion [34]3 years ago
8 0

Answer:

D

Step-by-step explanation:

just answered it

frutty [35]3 years ago
3 0

Answer:

Option D. 5890.5 feet²

Step-by-step explanation:

An individual head of a sprinkler system covers a circular are of grass with a radius of 25 feet.

Yard has three sprinkler heads that each cover circular area with no overlap.

We have to calculate the approximate area watered by these 3 sprinkler heads.

Area covered by one sprinkler = π×r² = π×(25)² = 625π feet²

Therefore area covered by three sprinkler heads = 3 × 625π = 5892.85 feet²

which matches the approximate value of Option D. 5890.5 feet²

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The relative growth rate for a certain type of mutual fund is 15% per year. An account is opened with a balance of $3,000. How m
wlad13 [49]

We have been given that an account is opened with a balance of $3,000 and relative growth rate for a certain type of mutual fund is 15% per year.  

In order to tackle this problem we have to find the value of mutual fund after 5 years. For our purpose we will use compound interest formula.

A=P(1+r)^{t} ,where A= amount after t years, P= principal amount, r= interest rate (decimal) and t= number of years.

After substituting our given values in above formula we will get

A=3000(1+.15)^{5}

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Therefore, after 5 years mutual fund is worth $6034.07.


8 0
4 years ago
Select Equal or Not Equal to correctly classify each statement.
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The first problem is true because with multiplication it doesn't matter which order it is in.

The second problem is false because you will get a different quotient depending on which numbers are on which side of the equation.
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3 years ago
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Find all solutions of each equation on the interval 0 ≤ x < 2π.
Korvikt [17]

Answer:

x = 0 or x = \pi.

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}.

\displaystyle \sec{x} = \frac{1}{\cos{x}}.

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, \sin^{2}{x} = 1 - \cos^{2}{x}. Therefore, for the square of tangents,

\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}.

This equation will thus become:

\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2.

To simplify the calculations, replace all \cos^{2}{x} with another variable. For example, let u = \cos^{2}{x}. Keep in mind that 0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1.

\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2.

\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2.

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\cos^{2}{x} = 1,

x = k \pi, where k\in \mathbb{Z} (i.e., k is an integer.)

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8 0
3 years ago
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Can someone please help me!! And can you show your work
Debora [2.8K]

Answer:

1) 8.073 (multiply 0.621 by 13km)

2)1,320,000,000(5280ft times 250,000)

3)37.850(10,000 divided by 264.2)

4)4hrs

5)157680000

(60 seconds in one minute and 60 min in one hr so 60 times 60 =3600 in one hr. then multiply 3600 by 24 for the entire day which is 86400sec. Then multiply that day by 365 which is 31536000 times 5 years which gets us our total of 157680000 seconds.

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