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Anna71 [15]
2 years ago
5

Suppose that 6 people sitting in a enclosed room are each generating about 400 BTUs of body heat per hour. If the room is 20 ft

× 15 ft × 10 ft, how many BTUs per cubic foot do they produce in 5 hours? A) 3 BTUs/ft3 B) 4 BTUs/ft3 C) 5 BTUs/ft3 D) 6 BTUs/ft3
Mathematics
1 answer:
Crazy boy [7]2 years ago
8 0

Answer:  B) 4 BTUs/ft^3

Step-by-step:

For a cuboid of length L, width W and height H, the volume is:

V = L*W*H

In this case, we have:

L = 20ft

W = 15ft

H = 10ft

Then the volume of the room is:

V = 20ft*15ft*10ft = 3000 ft^3

Now we have 6 people, and each generate 400 BTUs per hour.

Then in total, they generate:

6*400 BTUs per hour

2400 BTUs per hour.

Now we want to find the BTUs per ft^3 produced in 5 hours.

Then if they generate 2400 BTUs per hour, in 5 hours they generate a total of:

5*2400 BTUs = 12000 BTUs

Now we take the quotient between the total BTUs and the volume of the room:

Q = (12000 BTUs)/(3000 ft^3) = 4 BTUs/ft^3

The correct option is B.

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Answer:

Demand is inelastic at p = 9 and therefore revenue will increase with

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Step-by-step explanation:

Given a demand function that gives <em>q</em> in terms of <em>p</em>, the elasticity of demand is

E=|\frac{p}{q}\cdot \frac{dq}{dp}  |

  • If E < 1, we say demand is inelastic. In this case, raising prices increases revenue.
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  • If E = 1, we say demand is unitary.

We have the following demand equation D(p)=-\frac{3}{4}p+29; p = 9

Applying the above definition of elasticity of demand we get:

E(p)=\frac{p}{q}\cdot \frac{dq}{dp}

where

  • p = 9
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  • \frac{dq}{dp}=\frac{d}{dp}(-\frac{3}{4}p+29)

\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{d}{dp}\left(\frac{3}{4}p\right)+\frac{d}{dp}\left(29\right)\\\\\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{3}{4}

Substituting the values

E(9)=\frac{9}{-\frac{3}{4}(9)+29}\cdot -\frac{3}{4}\\\\E(9)=\frac{36}{89}\cdot -\frac{3}{4}\\\\E(9)=-\frac{27}{89}\approx -0.30337

|E(9)|=|\frac{27}{89}| < 1

Demand is inelastic at p = 9 and therefore revenue will increase with an increase in price.

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Answer:

Cat = 6kg

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the cat is 6kg and the dog is 18kg

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