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olya-2409 [2.1K]
3 years ago
12

2 POINTS What is the slope of the line that contains the points (-1,2) and (4,3)?

Mathematics
2 answers:
Mazyrski [523]3 years ago
4 0

Answer:

Slope is 1/5.

Step-by-step explanation:

You find slope by doing rise over run. The line rises 1 unit from and runs 5 points.

ycow [4]3 years ago
3 0
1/5
Y2-y1/x2-x1 is the slope formula
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Answer:

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Which of the following functions are solutions of the differential equation y" + y = 7 sin(x)? (Select all that apply.)
Nikitich [7]

The homogeneous equation

y'' + y = 0

has characteristic equation

r² + 1 = 0

with roots at r = ± √(-1) = ± i, and so the characteristic solution is

y = C₁ cos(x) + C₂ sin(x)

Using the method of undetermined coefficients, suppose

y = a x cos(x) + b x sin(x)

(we would normally consider y = a cos(x) + b sin(x), but cos(x) and sin(x) are already part of the characteristic solution)

The derivatives are

y' = a cos(x) - a x sin(x) + b sin(x) + b x cos(x)

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and

y'' = -a sin(x) + (b - a x) cos(x) + b cos(x) - (a + b x) sin(x)

y'' = (-2a - b x) sin(x) + (2b - a x) cos(x)

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y'' + y = (-2a - b x) sin(x) + (2b - a x) cos(x) + a x cos(x) + b x sin(x)

7 sin(x) = -2a sin(x) + 2b cos(x)

and it follows that a = -7/2 and b = 0.

So, the general solution to the DE is

y = C₁ cos(x) + C₂ sin(x) - 7/2 x cos(x)

which means the only valid solutions from the given choices are

y = 7 sin(x)

y = 7 cos(x)

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Natali5045456 [20]
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3 years ago
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Lilit [14]

Answer:

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3 years ago
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