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3 years ago

Determine the slope of the line passing through the given points (1,2) and (2,-1)

Mathematics

2 answers:

Semmy [17]3 years ago

8 0

The slope is 2, rise over run, 2 over 1

alex41 [277]3 years ago

3 0

I hope this helps you

slope=y2-y1/x2-x1

slope=2-(-1)/1-2

slope=3/-1

slope= -3

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Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

3 years ago

Brainiest to whoever right

sasho [114]

Is there more context to the question?

6 0

3 years ago

Read 2 more answers

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Li

snow_lady [41]

Answer:

b. multinomial population

Step-by-step explanation:

The data is categorical and non-overlapping. That is, there are multiple options(either the student is in the Liberal Arts College, Business College or Education College), and he cannot be in more than one option.

So this is an example of a multinomial population.

The correct answer is:

b. multinomial population

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3 years ago

Ms. Pearson kept track of student absences versus final average grades in her math dass for one semester, The

sammy [17]

The correct statement about the data collected by Ms. Pearson is that there is no association between a student's absences and the final average grades.

<h3>When do variables have a linear relationship?</h3>

The equation that represents a linear relationship is: a + bx

Where x represents the rate of increase. Thus, for linear equations, the functiion increases by a constant term.

Looking at the table, the average final grade does not increase by a constant term.

To learn more about linear functions, please check: brainly.com/question/26434260

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2 years ago

6 - 8a + 5a - 35

Fittoniya [83]

Ok, so after you do -8a+5a, you also have to do 6 -35, getting the equation
-29-3a

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3 years ago