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3 years ago

Two rectangular prisms each have a surface area of 600 square inches. What are the possible dimensions of the prism?

Mathematics

2 answers:

liraira [26]3 years ago

7 0

The area of a rectangular prism is 200 so I divided 600 by 3 and so the possible dimensions are 200 by 200 by 200.

Nesterboy [21]3 years ago

5 0

Answer:

l = 10 inches, b = 5 inches ⇒ h = $\frac{50}{3}$ inches

Step-by-step explanation:

Two rectangular prisms each have surface area of 600 square inches.

The surface area of rectangular prisms = 600 inches²

Formula of surface area of rectangular prism

⇒ 2 ( lb + bh + hl ) = 600

⇒ lb + bh + hl = 300

If l = b = h ⇒ 3l² = 300

l² = 100

⇒ l = 10 inches

Hence, dimension of the prism l = 10 inches,

If l = 10 inches, b = 5 inches ⇒ h = $\frac{50}{3}$ inches or 16.6666 inches

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Answer: $\pi 36r^{2}$

Step-by-step explanation:

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aleksandr82 [10.1K]

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

erma4kov [3.2K]

Answer:

$\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

Step-by-step explanation:

Given

5 tuples implies that:

$n = 5$

$(h,i,j,k,m)$ implies that:

$r = 5$

Required

How many 5-tuples of integers $(h, i, j, k,m)$ are there such that $n\ge h\ge i\ge j\ge k\ge m\ge 1$

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

$^{n}C_r => ^{n + 4}C_5$

$^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}$

$^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}$

Expand the numerator

$^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}$

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