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3 years ago

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Al and Ike decide to drive to Sandy Shores Lake. As they leave home in Summerville, they notice that the car odometer reads 12,3

14 miles. When they stop at Winterton to have lunch, they notice that the odometer reads 12,573 miles, and they see this road sign: Sandy Shores Lake 41 miles. What is the distance from Summerville to Sandy Shores Lake? Show your work.

1 answer:

ArbitrLikvidat [17]3 years ago

7 0

Answer: Just add all the numbers up for your answer

Step-by-step explanation:

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Find the following quotients and show your work:<br><br> a.6/4 divided 3/4

IRISSAK [1]

The answer to the question is 2

4 0

3 years ago

A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flo

djverab [1.8K]

Answer:

a) $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) $31690.7 g/L$

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is $\frac{dy}{dt}=R_{i}-R_{o}$ , where $R_{i}$ is the rate of salt entering and $R_{o}$ is the rate of salt going outside.

Then we have, $R_{i}=80\frac{L}{min}*50\frac{g}{L}=4000\frac{g}{min}$ , and

$R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}$

So we obtain. $\frac{dy}{dt}=4000-\frac{2y}{25}$ , then

$\frac{dy}{dt}+\frac{2y}{25}=4000$ , and using the integrating factor $e^{\int {\frac{2}{25}} \, dt=e^{\frac{2t}{25}$ , therefore $(\frac{dy }{dt}+\frac{2y}{25}}=4000)e^{\frac{2t}{25}$ , we get $\frac{d}{dt}(y*e^{\frac{2t}{25}})= 4000 e^{\frac{2t}{25}$ , after integrating both sides $y*e^{\frac{2t}{25}}= 50000 e^{\frac{2t}{25}}+C$ , therefore $y(t)= 50000 +Ce^{\frac{-2t}{25}}$ , to find $C$ we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions $y(0)=10$ , so $10= 50000+Ce^{\frac{-0*2}{25}}$

$10=50000+C\\C=10-50000=-49990$

Finally we can write an expression for the amount of salt in the tank at any time t, it is $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) The tank will overflow due Rin>Rout, at a rate of $80 L/min-40L/min=40L/min$ , due we have 500 L to overflow $\frac{500L}{40L/min} =\frac{25}{2} min=t$ , so we can evualuate the expression of a) $y(25/2)=50000-49990e^{\frac{-2}{25}\frac{25}{2}}=50000-49990e^{-1}=31690.7$ , is the salt concentration when the tank overflows

4 0

3 years ago

An angle measures 76° more than the measure of its supplementary angle. What is the measure of each angle?

DedPeter [7]

Answer:

7° and 83°

Step-by-step explanation:

4 0

3 years ago

What is the answer to this along with steps to doing it?

pashok25 [27]

1/2*(2*8)=3*(-12)
1/2*16=3*(-12)
1/2*16= -36
8= -36
The equality is false because the left hand and right hand side are different

8 0

2 years ago

Describe the graph of a function g by observing the graph of the base function f ?

never [62]

Answer:

Choice 3 is your answer

Step-by-step explanation:

The format of the function when you move it side to side or up and down is

f(x) = (x - h) + k,

where h is the side to side movement and k is up or down. The k is easy, since it will be positive if we move the function up and negative if we move the function down from its original position.

The h is a little more difficult, but just remember the standard form of the side to side movement is always (x - h). If our function has moved 3 units to the left, we fit that movement into our standard form as (x - (-3)), which of course is the same as (x + 3). Our function has moved up 5 units, so the final translation is

g(x) = f(x + 3) + 5, choice 3 from the top.

5 0

3 years ago