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3 years ago

Which equation represents a line which is perpendicular to the line 6x+y=1

1 answer:

6 0

I believe it’s A because if it is perpendicular you would have to flip 6X and change the sign so therefore it would be A. In slope intercept form it would be y=-6x+1.

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C xy2 ds, c is the right half of the circle x2 y2 = 4 oriented counterclockwise

Kryger [21]

Parameterize the contour by

$C:\mathbf r(t)=(2\cos t,2\sin t)\implies \dfrac{\mathrm d\mathbf r}{\mathrm dt}=(-2\sin t,2\cos t)$
$\implies\mathrm dS=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt=2$

where $-\dfrac\pi2\le t\le\dfrac\pi2$ . Then the line integral is given by

$\displaystyle\int_C xy^2\,\mathrm dS=2\int_{-\pi/2}^{\pi/2}(2\cos t)(2\sin t)^2\,\mathrm dt$
$=\displaystyle16\int_{-\pi/2}^{\pi/2}\cos t\sin^2t\,\mathrm dt=\dfrac{32}3$

6 0

4 years ago

You applied for your dream job and just found out you got it. Your contract states that you will be making $36,000 a year. To bu

Musya8 [376]

Answer:

see attached

Step-by-step explanation:

A spreadsheet is a useful tool for keeping track of the numbers. A picture of one is attached.

We have assumed that the dollar amount for housing computed in the first part remains the same (though the percentage changes). If that is not the case, you'll have to recompute.

Likewise, we assume that the "5%" retirement amount remains 5% of the nominal salary, rather than 5% of the salary after the mandatory retirement deduction. Similarly, we assume dance lessons remain at their original amount, and were not reduced when the company began taking mandatory retirement.

Feel free to build your own spreadsheet and recompute as needed for any assumptions I got wrong, or for any additional scenarios.

8 0

3 years ago

W+3>9 <br><br> I need to solve this inequality.... I’m not very good at this stuff.

mezya [45]

W+3>9
-3>-3 (getting the variable by its self)

w=6 (answer)

7 0

3 years ago

Which of the following is a counterexample of, "All rational numbers are integers"? is not an integer. 3 is an integer. -1 is a

Sever21 [200]

Answer:

It is (almost certainly) the first choice, however, you omitted the actual example there. See below.

Step-by-step explanation:

A counter-example to "All rational numbers are integers" is easy to find - it is any fraction that is reduced to simplest form and its denominator (bottom part) is not 1. Examples: 2/3, 7/5, 11/13 are all not integers but rational numbers and therefore are counter-examples to the statement. The statement is thus disproven. Please check your question - there is a value with the first choice that is likely one such fraction.

The remaining 3 choices to your answer are all not applicable.

4 0

3 years ago

Read 2 more answers

Y=4x<br> x+y=5 use substitution method

dalvyx [7]

Answer:

x = 1, y = 4

Step-by-step explanation:

y = 4x

x + y = 5

Since 4x is equal to the variable y, we can substitute it in for y in the second equation.

x + (4x) = 5

Solve for x.

x + 4x = 5

5x = 5

5x/5 = 5/5

x = 1

Now that we have solved for x, we need to solve for y.

y = 4x

x = 1 so substitute the x with 1.

y = 4(1)

y = 4

We can plug both of our answers into any one of the given equations to check our work

x + y = 5

x = 4 and y = 1

4 + 1 = 5

5 = 5

Our answers check out!

6 0

3 years ago