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3 years ago

I need help plsssss--What is the volume of the prism?

Mathematics

1 answer:

Svetach [21]3 years ago

7 0

Answer:

1,200

Step-by-step explanation:

Multiply the Height, Length, Width, and Base:

4 x 5 x 10 x 6

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

$\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}$

Solve for S(t):

$\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}$

$e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}$

The left side is the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}$

Integrate both sides:

$e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt$

$e^{t/800}S(t)=64e^{t/800}+C$

$S(t)=64+Ce^{-t/800}$

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

$0=64+C\impleis C=-64$

and so (b) the amount of sugar in the tank at time t is

$S(t)=64\left(1-e^{-t/800}\right)$

As $t\to\infty$ , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

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4 years ago

Find the height of the building below by using your knowledge of trigonometry.

Lilit [14]

Answer:

50 $\sqrt{3}$

Step-by-step explanation:

The figure represents a 30-60-90 special triangle

in this special right triangle the measure of sides lengths is represented by

a, a $\sqrt{3}$ , and 2a

The side length that sees angle measure 30 is represented by a and here we see a = 50m

The height of the building, which sees angle measure 60, is equal to

50 $\sqrt{3}$

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3 years ago

What is the value of 7(10 - 2^3) + 8 divided by 2

Zielflug [23.3K]

$7(10-2^3)+8 \div 2 \\ \\ 7(10-8)+8 \div 2 \\ \\ 7(2)+8 \div 2 \\ \\ 7(2)+4 \\ \\ 14+4 \\ \\ \boxed{18}$

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2 years ago

How to change 611/17 to improper fractions

Annette [7]

This is the answer ....

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4 years ago

Read 2 more answers

Ron and Freddy built structures out of snap cubes. Ron's tower had an 8-inch square base. Freddy had a 6-inch square base. If Ro

Sphinxa [80]

Answer: Ron tower's

Step-by-step explanation:

Given

Ron tower has a base of $A_r=8\ in.^2$

Freddy tower has a base of $A_f=6\ in.^2$

Suppose the tower is in the shape of a square prism

The volume of Ron and Freddy tower is $320\ \text{and}\ 180\ in.^3$

The volume of a square-based prism is $V=\frac{1}{3}a^2h$

$\therefore \text{height of Ron tower is}\ h_r=\dfrac{3V}{A_r}\\\\\Rightarrow h_r=\dfrac{3\times 320}{8}=120\ in.$

The height of Freddy tower is

$\Rightarrow h_f=\dfrac{3V}{A_f}\\\\\Rightarrow h_f=\dfrac{3\times 180}{6}=90\ in.$

Thus, the height of Ron's tower is more than Freddy's tower by $30\ in.$

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3 years ago