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3 years ago

Determine if each function is linear or nonlinear.

Mathematics

1 answer:

Akimi4 [234]3 years ago

3 0

Answer:

Linear: y = x, y = x/2 - 3, 3x + 2 = 12

Nonlinear: y = 6/x - 2, y = 3x^3 + 5

Step-by-step explanation:

Linear functions form straight lines while nonlinear functions do not.

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3 years ago

Evaluate the integral by making an appropriate change of variables.

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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

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-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

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

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2 years ago

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Sphinxa [80]

Answer:

50 total

Step-by-step explanation:

when it's asking for a total you add the numbers together, and whatever number you get is your answer :)

sorry if it's wronggg :( !!

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3 years ago