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Ainat [17]
3 years ago
7

A swimming pool is a shape of a rectangular prism. The pool is 10 feet deep. It length is 3 times it's width. The volume of the

pool is 27000 cubic feet. Find the length and the width of the pool.
Mathematics
1 answer:
Lady_Fox [76]3 years ago
6 0

Answer:

Step-by-step explanation:

V = l * w * h

27000ft3 = (2w) * w * 10ft

27000ft3 = 2w^2 * 10ft

2700 = 2w^2

1350 = w^2

W = 36.74

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Art [367]

Answer:

\displaystyle E=26log2-24log3+8log 5

Step-by-step explanation:

<u>Logarithms</u>

There are certain properties of the logarithms we'll need to recall in order to simplify the expression given in the question. We'll list them below

log(x.y)=logx+logy\\log(x/y)=logx-logy\\logx^y=y.logx

We'll also need to factor the following numbers into their prime factors:

20=2^2\cdot 5

16=2^4

15=3\cdot 5

25=5^2

24=2^3\cdot 3

81=3^4

80=2^4\cdot 5

The original expression is

\displaystyle E=log20+16log\frac{16}{15}+12log\frac{25}{24}+log\frac{81}{80}

Plugging in the factored values

\displaystyle E=log(2^2\cdot 5)+16log\frac{2^4}{3\cdot 5}+12log\frac{5^2}{2^3\cdot 3}+log\frac{3^4}{2^4\cdot 5}

Applying the properties we have

\displaystyle E=log2^2+log 5+16(log2^4-log3-log 5)+12(log5^2-log2^3-log 3)+log3^4-log2^4-log 5

\displaystyle E=2log2+log 5+16log2^4-16log3-16log 5+12log5^2-12log2^3-12log 3+log3^4-log2^4-log 5

\displaystyle E=2log2+log 5+64log2-16log3-16log 5+24log5-36log2-12log 3+4log3-4log2-log 5

Simplifying

\boxed{\displaystyle E=26log2-24log3+8log 5}

7 0
4 years ago
PLSSSSSS I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
il63 [147K]

Answer:

3 - \sqrt{19}

Step-by-step explanation:

\sqrt{(3 - \sqrt{19})^2}

The ^2 in the square root cancels each other so

3 - \sqrt{19}

5 0
4 years ago
Read 2 more answers
4) Which pair of triangles is congruent by Angle - Angle- Side?
mixas84 [53]

Answer:

I think its 2

4 0
3 years ago
Read 2 more answers
Math need help please
AnnyKZ [126]

Answer:

none

Step-by-step explanation:

4x - 6 = 2(2x + 3)

4x - 6 = 4x + 6

Everything cancels out meaning there are no real solutions

5 0
2 years ago
There are 600 seats in the Marshall Middles School Auditorium. Students are sitting in 4/5 of the seats in the auditorium. Teach
Gemiola [76]

Answer:

B. 65

Step-by-step explanation:

600 * 4/5 = 480 seats used by students

55 teachers + 480 students= 535 seats used

600-535 = 65 seats left over

5 0
3 years ago
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