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4 years ago

7

Mr. Shepard uses a pick up truck that can carry 3/4 ton of rock each load and fills it 5 times. He organizes his rocks into pile

s that are 1/2 ton each. How many 1/2 ton piles of rock does Mr. Shepard have when he uses the 5 full loads of rock?

1 answer:

kodGreya [7K]4 years ago

8 0

I think its 15 dont know for sure

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A very large tank initially contains 100L of pure water. Starting at time t = 0 a solution with a salt concentration of 0.8kg/L

Scorpion4ik [409]

Answer:

1. $\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}$

2. $y(40) = 110.873 \ kg$

Step-by-step explanation:

Given that:

A very large tank initially contains 100 L of pure water.

Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min.

. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.

As 5L/min is entering and 3L/min is drained out, there is a 2L increase per minute. Therefore, the amount of water at any given time t = (100 +2t) L

t = (50 + t ) L

Since it is given that we should consider y(t) to be the amount of salt (in kilograms) in the tank after t minutes.

Then , the differential equation that y satisfies can be computed as follows:

$\dfrac{dy}{dt}=rate_{in} - rate_{out}$

$\dfrac{dy}{dt}=(0.8)(5) -\dfrac{y(t)}{100+2t} \times3$

$\dfrac{dy}{dt}=(0.8)(5) -\dfrac{3y}{100+2t}$

$\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}$

How much salt is in the tank after 40 minutes?

So,

suppose : $e^{\int \dfrac{3}{100+2t} \ dt} = (t+50)^{3/2}$

Then ,

$( t + 50)^{3/2} y' + \dfrac{3}{2}(t+50)^{1/2} y = 4(t+50)^{3/2}$

$( t + 50)^{1.5} y' + \dfrac{3}{2}(t+50)^{0.5} y = 4(t+50)^{3/2}$

$[y\ (t + 50)^{1.5}]' = 4(t+ 50)^{1.5}$

Taking the integral on both sides; we have:

$[y(t + 50)^{1.5}] = 1.6 (t + 50)^{2.5} + C$

$y = 1.6 (t+50)+C(t+50)^{-1.5}$

$y(0) = 0 = 1.6(0+50) + C ( 0 + 50)^{-1.5}$

$0 = 1.6(50) + C ( 50)^{-1.5}$

$C= -1.6(50)^{2.5}$

$y(40) = 1.6 (40 + 50)^1 - 1.6 (50)^{2.5}(50+40)^{-1.5}$

$y(40) = 144 - 1.6 \times 17677.66953 (90)^{-1.5}$

$y(40) = 144 - 1.6 \times 17677.66953 \times 0.001171213948$

$y(40) = 144 - 33.12693299$

$y(40) = 110.873 \ kg$

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4 years ago

Write the equation of the line through (5,9) and (5, -3)

seropon [69]

Answer:

undefined

Step-by-step explanation:

This is a vertical line and cannot be written in any form.

7 0

3 years ago

A kiddie pool contains 72 cubic feet of water. A Jacuzzi contains 125% more water than does the kiddie pool. How much water does

ohaa [14]

Answer:

162 cubic feet

Step-by-step explanation:

72*2= 144 which is for the 100% so,

to find the 25% you would do 72 divided by 4 which= 18

So 125% would be 18+144= 162

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3 years ago

What is the radius of a circle?

polet [3.4K]

Answer:

3,925

Step-by-step explanation:

I think you have to divide 7,850 by 2 and you get 3,925

I hope this helps out!

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3 years ago

Read 2 more answers

Place a point on the number line to show the quotient of 1/14

solong [7]

The decimal fro 1/14 would be 0.071429 i hope this helps

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3 years ago