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3 years ago

12

The human body generates about 400 BTUs of body heat per hour while active. If an office that is 18 ft × 38 ft × 12 ft has 12 wo

rkers, how many BTUs per cubic foot do they produce in 5 hours? (to the nearest tenth)

1 answer:

Cerrena [4.2K]3 years ago

6 0

You would put # of people x BTUs x # of hours over cubic feet
12 x 400 x 5 / 18 x 38 x 12
the answer is 2.9 BTUs/ft^3

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The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

Given the following functions, find and simplify (f • g)(x) f(x)=—x+3 g(x)=-x-1

Hitman42 [59]

Answer:

$(f\circ g)(x)= x + 4$

Step-by-step explanation:

<u>Composite Function</u>

Given f(x) and g(x) as real functions, the composite function $(f\circ g)(x)$ is defined as:

$(f\circ g)(x)=f(g(x))$

It can be found by substituting g into f.

We are given the functions:

f(x) = -x + 3

g(x) = -x -1

Find

$(f\circ g)(x)=f(g(x))= - (-x -1) + 3$

Removing parentheses:

$(f\circ g)(x)= x + 1 + 3$

Simplifying:

$\mathbf{(f\circ g)(x)= x + 4}$

5 0

3 years ago

A box of donuts containing 6 maple bars, 3 chocolate donuts, and 3 custard filled donuts is sitting on a counter in a work offic

Svetlanka [38]

Probabilities are used to determine the chances of selecting a kind of donut from the box.

The probability that Warren eats a chocolate donut, and then a custard filled donut is 0.068

The given parameters are:

$\mathbf{Bars = 6}$

$\mathbf{Chocolate = 3}$

$\mathbf{Custard= 3}$

The total number of donuts in the box is:

$\mathbf{Total= 6 + 3 + 3}$

$\mathbf{Total= 12}$

The probability of eating a chocolate donut, and then a custard filled donut is calculated using:

$\mathbf{Pr = \frac{Chocolate}{Total}\times \frac{Custard}{Total-1}}$

So, we have:

$\mathbf{Pr = \frac{3}{12}\times \frac{3}{12-1}}$

Simplify

$\mathbf{Pr = \frac{3}{12}\times \frac{3}{11}}$

Multiply

$\mathbf{Pr = \frac{9}{132}}$

Divide

$\mathbf{Pr = 0.068}$

Hence, the probability that Warren eats a chocolate donut, and then a custard filled donut is approximately 0.068

Read more about probabilities at:

brainly.com/question/9000575

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2 years ago

4. The Blackhawk Eagles scored 4 points more than the Lane Vikings. The

konstantin123 [22]

Answer:

Lane Viking's Score is 17

Black Eagles's Score is 21

Step-by-step explanation:

Let Lane Viking's Score be x and Black Eagles's Score be y.

Black Eagles's Score = 4+ Lane Viking's Score

so y = 4 + x (Equation 1)

Total Score = 38

Black Eagles's Score + Lane Viking's Score = 38

so y + x =38 (Equation 2)

Putting y's value from Equation 1 in Equation 2

4 + x + x = 38

2x = 38-4

x=34/2

x=17

Putting value of x in Equation 1

y = 4 + 17

y = 21

7 0

3 years ago

The circumference of a circle is 9.58. Find the length of the diameter. Give your answer to 2DP

harkovskaia [24]

Answer:

d≈3.05

Step-by-step explanation:

d= C/π

d=9.58/π

d≈3.04941

d≈3.05

6 0

4 years ago