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2 years ago

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An exercise class had 20 people. If each person produced 2,200 BTUs of body heat during the class and the room is 30 ft × 40 ft

× 15 ft, how many BTUs per cubic foot did they produce? (to the nearest hundredth) A) 0.12 BTUs/ft3 B) 1.83 BTUs/ft3 C) 2.44 BTUs/ft3 D) 36.66 BTUs/ft3

1 answer:

nika2105 [10]2 years ago

8 0

We are given the average body heat equal to 2200 BTU. In this problem, we are asked to determine the total body heat in BTU per cubic foot given the dimensions of the room. The volume of the room is 18000 ft3. we multiply the average heat by 20 persons.hence the answer to this problem is 2.44 BTU/ft3.

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Help I will be marking brainliest!!!

Keith_Richards [23]

<h3>Answer: A. 18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

----------------------

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

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ozzi

Answer:

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Step-by-step explanation:

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