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3 years ago

13

50 POINTS. help I'm not rushing so late answers are appreciated!

2 answers:

aev [14]3 years ago

8 0

Data is discrete, so the graph is a series of unconnected points

Flura [38]3 years ago

4 0

Answer:

"The data is discrete, so the graph is a series of unconnected points."

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Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integ

liq [111]

Answer:

1/2

Step-by-step explanation:

The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

$\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy$

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.

Mx(x,y) = d/dx 8x²y = 16xy
Ly(x,y) = d/dy 7y²x = 14xy

Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy$

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2$

We conclude that the line integral is 1/2

4 0

2 years ago

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

Multiplying fracions with different numerators

Serjik [45]

So, this means that you are multiplying both of the numerators and denominators together to get the product

6 0

3 years ago

Read 2 more answers

Find the measurement of the angle

Shalnov [3]

Answer:

∠ 1 = 120°

Step-by-step explanation:

Note that ∠ Q and ∠ R are congruent, that is both 30°, thus

∠ 1 = 180° - (30 + 30)° = 180° - 60° = 120°

6 0

3 years ago

Help what are the answers im so stuck!

AnnZ [28]

Answer:

see below

Step-by-step explanation:

A percentage change is computed as follows:

percent change = ((new value) -(original value))/(original value) × 100%

For your first one, this looks like ...

percent change = ($25 -$75)/$75 × 100% = (-50/75) × 100% = -0.667×100%

percent change = -66.7%

__

When there are a lot of similar calculations to do, I like to use a spreadsheet. See below for the other percentage changes (rightmost column).

4 0

3 years ago