2. Patrick worked 5.25 hours on Monday,

Find the volume of the solid under the plane 3x+2y−z=0 and above the region enclosed by the parabolas y=x^2 and x=y^2.

Yuri [45]

The region in the x-y plane is the set of points

$R=\{(x,y)\mid0\le x\le 1,x^2\le y\le\sqrt x\}$

The height of the solid falls between the x-y plane (for which z = 0) and the equation of the plane, z = 3x + 2y.

So the volume is

$\displaystyle\int_0^1\int_{x^2}^{\sqrt x}\int_0^{3x+2y}\mathrm dz\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^1\int_{x^2}^{\sqrt x}(3x+2y)\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^1(3x^{3/2}+x-3x^3-x^4)\,\mathrm dx$

$=\displaystyle\frac65+\frac12-\frac34-\frac15=\boxed{\dfrac34}$

5 0

3 years ago

Help me on this ,appreciate it.

Anni [7]

Answer:

I would say that the travling time is 3.5 hours and the Stationary time would be 2.5 hours.

Step-by-step explanation:

I'm sorry if I'm worng, (Can I get brainliest??)

8 0

3 years ago

Quadrilateral with E(-2,-7),F(4,-3),G(0,1),and H(-4,-2);scale factor 0.5

Ulleksa [173]

Answer:

New scale will be

E(-1, -3.5), F(2, -1.5), G(0, 0.5), H(-2, -1). This is one-half the original scale

Step-by-step explanation:

The question is incomplete. Here is the complete question.

"Given the Quadrilateral with vertices E(-2,-7),F(4,-3),G(0,1),and H(-4,-2), find the coordinates of the image after a dilation having a scale factor of 0.5."

Dilation factor is the same as scale of 1/2 i.e 1:2. Scale of 1:2 means that the quadrilateral has been reduced by one-half. We need to know the new vertices of the quadrilateral after being reduced by one-half.

Given the original axis before dilation

E (x1, y1) = E(-2, -7)

F (x2, y2) = F(4, -3)

G (x3, y3) = G(0, 1)

H (x4, y4) = H(-4, -2)

After dilation by scale factor of 0.5, the axis will result into one half of its original scale as shown:

E (0.5x1, 0.5y1) = E(-2/2, -7/2)

F (0.5x2, 0.5y2) = F(4/2, -3/2)

G (0.5x3, 0.5y3) = G(0/2, 1/2)

H (0.5x4, 0.5y4) = H(-4/2, -2/2)

New scale will be:

E(-1, -3.5), F(2, -1.5), G(0, 0.5), H(-2, -1)

Check the attachment for diagram.

4 0

3 years ago

For the last 20 years, Mr. Bean has weighed 120 pounds,give or take 4 pounds. Write anabsolute value inequality that models this

irga5000 [103]

An absolute value inequality that models this situation: $|x-120|\leq 4$

The required compound inequality representing all possible weights for Mr. Bean.: $116\leq x\leq 124$

Given: For the last 20 years,

Mr. Bean has weighed 120 pounds, give or take 4 pounds.

To write: a) An absolute value inequality that models this situation.

b) a compound inequality representing all possible weights for Mr. Bean.

Computation:

Let x be the actual weight of Mr. Bean,

then

Required absolute inequality: $|x-120|\leq 4$

It can be written as

$-4 \leq x-120\leq 4$

Add 120 on all sides , we get

$120-4\leq x\leq120+4$

$116\leq x\leq 124$

The required compound inequality representing all possible weights for Mr. Bean.: $116\leq x\leq 124$

Learn more:

brainly.com/question/13054155?referrer=searchResults

8 0

3 years ago

What is the slope of the line that passes through the points A(-2, -1) and D(3,5) ?

Rasek [7]

Answer: y = 1.2x + 1.4

Step-by-step explanation:

1. Write down the coordinates of the first point. Let's assume it is a point with x₁ = -2and y₁ = -1.

2. Write down the coordinates of the second point as well. Let's take a point with x₂ = 3 and y₂ = 5.

3. Use the slope intercept formula to find the slope:

m = (y₂ - y₁)/(x₂ - x₁) = (5-1)/(3-2) = 4/1 = 1.2

4. Calculate the y-intercept. You can also use x₂ and y₂ instead of x₁ and y₁ here.

b = y₁ - m * x₁ = -1 - 1.2*-2 = 1.4

5. Put all these values together to construct the slope intercept form of a linear equation:

y = 1.2x + 1.4

7 0

3 years ago