The expression is equal to listen to thi the expression is equal to this 4(2x 11-x)

What is the equation of the line through the origin and (2,5)

mezya [45]

Answer:

2y=5x+2c

Step-by-step explanation:

7 0

3 years ago

(4 pts) If a rock is thrown vertically upward from the surface of Mars with an initial velocity of 15m/sec

Yuliya22 [10]

Answer:

Step-by-step explanation:

I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.

The position equation is

$s(t)=-1.86t^2+15t$ That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.

The first derivative of position is velocity:

v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):

0 = -3.72t + 15 and solve for t:\

-15 = -3.72t so

t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:

s(4.03) = -1.86(4.03)² + 15(4.03) so

s(4.03) = 30.2 meters.

Calculus is amazing. Much easier than most methods to solve problems like this.

7 0

2 years ago

During rush hour, Geoffrey counted that he had to stop at 8 different red lights. He went through a total of 25 intersections. W

omeli [17]

I think the answer is 32% because if you turn 32% into a decimal (which would be 0.32) then multiply it by 25 you would get 8. Which then means if he stopped 8 times and went through 25 intersections then he stopped at 32% of the intersections. I hope this helps :)

6 0

3 years ago

A membership price for the local pool went

Katarina [22]

I think the percent change would be 25%

7 0

3 years ago

Solve dis attachment and show all work ( I got it all wrong and I want to know how to solve it )

DedPeter [7]

(a) First find the intersections of $y=e^{2x-x^2}$ and $y=2$ :

$2=e^{2x-x^2}\implies \ln2=2x-x^2\implies x=1\pm\sqrt{1-\ln2}$

So the area of $R$ is given by

$\displaystyle\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\left(e^{2x-x^2}-2\right)\,\mathrm dx$

If you're not familiar with the error function $\mathrm{erf}(x)$ , then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.

(b) Find the intersections of the line $y=1$ with $y=e^{2x-x^2}$ .

$1=e^{2x-x^2}\implies 0=2x-x^2\implies x=0,x=2$

So the area of $S$ is given by

$\displaystyle\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}(2-1)\,\mathrm dx+\int_{1+\sqrt{1-\ln2}}^2\left(e^{2x-x^2}-1\right)\,\mathrm dx$
$\displaystyle=2\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\mathrm dx$

which is approximately 1.546.

(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve $y=e^{2x-x^2}$ and the line $y=1$ , or $e^{2x-x^2}-1$ . The area of any such circle is $\pi$ times the square of its radius. Since the curve intersects the axis of revolution at $x=0$ and $x=2$ , the volume would be given by

$\displaystyle\pi\int_0^2\left(e^{2x-x^2}-1\right)^2\,\mathrm dx$

5 0

3 years ago