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2 years ago

Find the surface area of this prism please (no links please)

Mathematics

1 answer:

horsena [70]2 years ago

4 0

Answer:

192 ft^2

Step-by-step explanation:

to find the surface area of a shape, you must find the area of each side and add them together. the base of this shape is a rectangle with a length of 11ft and a height of 3ft; to calculate the area of a rectangle, you multiply the length by the height. 3*11 is 33, so the base of this prism has an area of 33ft^2. since this is a prism, we know that the side parallel to the base are the same shape, so they both have an area of 33ft^2. 33*2= 66. the two other large sides have a height of 4.5 and a length of 11; 4.5*11 is 49.5, there are two shapes with these dimensions, so 49.5*2=99. finally, the two shapes on either end of the prism have a height of 4.5 and a length of 3. 4.5*3= an area of 13.5, two of them, so 13.5*2=27. now you just add all of these numbers together: 66+99+27=192.

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A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

Please help!!!!!!<br><br> Rewrite this equation in terms of y<br> 2x-3y=22

Leona [35]

The answer is y = 2/3x - 22/3

4 0

2 years ago

Read 2 more answers

In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio o

Kruka [31]

Answer:

1/14:5/7:3/14

Step-by-step explanation:

Since orange=15

Apple=5

Coconut milk=50

50+15+5

Orange=15/70

Divide both by 5

=3/14

Apple=5/70

Divide both by 5

=1/14

Coconut milk=50/70

Divide both by 10

=5/7

So the ratio of apple to coconut to orange

1/14:5/7:3/14

8 0

2 years ago

The mean number of hours of part-time work per week for a sample of 526526 college students is 2828. If the margin of error for

sveta [45]

Answer:

The 99% confidence interval for the mean number of hours of part-time work per week for all college students is between 25.8 and 30.2.

Step-by-step explanation:

A confidence interval has the following format.

$\mu_{x} \pm M$

In which $\mu_{x}$ is the mean of the sample and M is the margin of error.

In this problem, we have that:

$\mu_{x} = 28, M = 2.2$

$\mu_{x} - M = 28 - 2.2 = 25.8$

$\mu_{x} + M = 28 + 2.2 = 30.2$

The 99% confidence interval for the mean number of hours of part-time work per week for all college students is between 25.8 and 30.2.

4 0

3 years ago

Help me plzzz I need area and perimeter

Alexeev081 [22]

Answer:

Area = 37.5

Perimeter = 36

Step-by-step explanation:

Have a good day! :)

5 0

3 years ago

Read 2 more answers