Graph the image of the polygon after the given rotation. 90 degrees

Write this expression in radical form t^-3/4

ZanzabumX [31]

The first thing you should know are properties of exponents to solve the problem.
For this case the radical form is given by the writing of the expression in the form of root.
We have then:
t^-3/4 =4^root(t^-3)=4^root ((1)/(t^3))
answer t^-3/4=4^root((1)/(t^3))

5 0

3 years ago

PLEASE HELP WILL MARK BRAINLIEST!

pantera1 [17]

Answer:

Make a coordinate plane and you have to solve around the origin say 4,4 and 4,1.

Step-by-step explanation:

8 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

Natalie is a softball coach. She has a pitching private lesson with Kasey. Kasey’s mom pays Natalie $11 per hour plus a $6 tip.

nevsk [136]

Answer:

3

Step by Step:

Subtract the tip ($6) from the total ($39)

11x=33

Then divide 33 by 11, leaving you with the value of x.

x=3

The lesson was 3 hours long.

6 0

2 years ago

If Jane is not maximizing her utility with the original purchase combination, remembering the Law of Diminishing Marginal Utilit

gayaneshka [121]

Answer:

Using the Law of Diminishing Marginal Utility, Jane would not be better off buying one more fry, since the marginal utility she obtains from the fries are lower when compared to the chicken sandwich; therefore, she would be better off ordering another chicken sandwich

4 0

2 years ago