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Talja [164]
3 years ago
9

A FISH TANK AT AN AQUARIUM HAS A VOLUME OF 1568 CUBIC FEET AND A DEPTH OF 8 FEET. IF THE BASE OF THE TASNK IS SQUARE WHAT IS THE

LENGHT OF SIDE OF THE TANK
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
8 0

Answer:

14 feet

Step-by-step explanation:

The volume is basically length * width * height

The depth can be taken as height, which is 8

Now, since the base is a square, the length and width are both x, so we can write:

Volume = length * width * height

1568 = x * x * 8

1568/8 = x^2

196 = x^2

x = Sqrt(196)

x = 14

The length of the side of the tank is 14 feet

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Let n be the smallest positive integer that is a multiple of 75 and has exactly 75 positive integral divisors, including itself
Juli2301 [7.4K]

Answer:

n=2^4 3^4 5^2 =32400 and then we have:

\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432

Step-by-step explanation:

From the info given by the problem we need an integer defined as the smallest positive integer that is a multiple of 75 and have 75 positive integral divisors, and we are assuming that 1 is one possible divisor.

Th first step is find the prime factorization for the number 75 and we see that

75=3 5^2

And we know that 3 =2+1 and 5=3+2 and if we replace we got:

75 = (2+1)(4+1)^2 = (2+1)(4+1)(4+1)

And in order to find 75 integral divisors we need to satisify this condition:

n= a^{r_1 -1}_1 a^{r_2 -1}_2 *...... such that a_1 *a_2*....=75

For this case we have two prime factors important 3 and 5. And if we want to minimize n we can use a prime factor like 2. The least common denominator between 2 and 4 is LCM(2,4) =4. So then the need to have the prime factors 2 and 3 elevated at 4 in order to satisfy the condition required, and since 5 is the highest value we need to put the same exponent.

And then the value for n would be given by:

n=2^4 3^4 5^2 =32400 and then we have:

\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432

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Step-by-step explanation:

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Answer:

7. 250%

8. 400%

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Step-by-step explanation:

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