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4 years ago

Please help im so confused

Mathematics

2 answers:

nydimaria [60]4 years ago

8 0

A and D because the first factor is less than 10 and greater than 1, and the power of 10 is not 0

hope that helps :)

neonofarm [45]4 years ago

5 0

i am doing this in school and i cant tell the answer but i can walk you through on how to do this

here is how to do it

5.4x10^3 so what you are going to do is move the decimal to the right so your answer would be 5400.

same with negatives exept you will do move the decimal to the left

and question e the answer is 1 you have 10x10^-1 so you are moving the decimal to the left and you wind up with 1.0 i hope this helps if you have anymore questions then message me :)

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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

4 years ago

How to find an equation for a line through two given points?

xz_007 [3.2K]

Answer:

The equation of the line is: $y = 0.6x + 0.6$

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept.

Two points:

We have these following two points in this exercise:

x = -6, y = -3, so (-6,-3)

x = 4, y = 3, so (4,3)

Finding the slope:

Given two points, the slope is given by the change in y divided by the change in x.

Change in y: 3 - (-3) = 3 + 3 = 6

Change in x: 4 - (-6) = 4 + 6 = 10

$m = \frac{6}{10} = 0.6$

Then

$y = 0.6x + b$

Finding b:

We replace one of the points in the equation to find b. I will use (4,3).

$y = 0.6x + b$

$3 = 0.6*4 + b$

$2.4 + b = 3$

$b = 0.6$

The equation of the line is: $y = 0.6x + 0.6$

4 0

3 years ago

The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W

melamori03 [73]

Answer:

hello your question is incomplete attached below is the complete question

estimating: Ft( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30⁰c

when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c that the actual temperature rises

estimating: Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15⁰c

when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by about 0.15⁰c for every km/h that the wind speed

Step-by-step explanation:

A) Estimating the values of Ft(−15, 40) and fv(−15, 40)

attached below is a detailed solution

To estimate the value of Ft( -15,40 ) we have to take an average value hence Ft ( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30

and this means that when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c that the actual temperature rises

To estimate the value of Fv(-15,40 ) we have to take an average value

hence Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15

and this means that when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by about 0.15⁰c for every km/h that the wind speed

3 0

3 years ago

-2X-10=14X-7<br> HELP ME

Vesnalui [34]

Answer:

x= -3/16

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0

3 years ago

Read 2 more answers

Question 6

marin [14]

Answer:

18 miles per hour is an outlier

the outlier decreases the mean speed

Step-by-step explanation:

the low number of 18 is way different from the other numbers being in the 30's and 40's

this 18 will bring the mean of all the numbers own because it is a smaller number.

8 0

3 years ago