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3 years ago

Write the equation of the line that passes through (-3,5) and (2, 10) in slope-intercept form.

Mathematics

1 answer:

cupoosta [38]3 years ago

7 0

Answer:

$y=x+8$

Step-by-step explanation:

Slope of straight line can be calculated as

$m=\frac{y_2-y_1}{x_2-x_1}$

Here $(x_1, y_1)=(-3, 5) \ and \ (x_2, y_2) = (2, 10)$

$m =\frac{10-5}{2-(-3)}\\m=1$

Equation of straight line in slope intercept form is

$y-y_1=m(x-x_1)\\y-5=(x+3)$

$y=x+8$

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Yakvenalex [24]

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3 years ago

F ind the volume under the paraboloid z=9(x2+y2) above the triangle on xy-plane enclosed by the lines x=0, y=2, y=x

olga nikolaevna [1]

Answer:

The answer is 48 units³

Step-by-step explanation:

If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

$V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {z} \, dx dy\\V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {9(x^{2}+y^{2})} \, dx dy$

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

$V=9\int\limits^2_0 {4y^{3}/3} \, dy$

After performing the elementary y integral we obtain the desired volume as below,

$V= 48 units^{3}$

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3 years ago

Under what circumstances may a health insurer charge a higher premium to a woman with a genetic disposition to breast cancer? a)

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Answer:

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3 years ago

If ∠G is supplementary to ∠H and the measure of ∠G is 65° what is the measure of ∠H?

Elina [12.6K]

Solution:

Given:

∠G = 65°

Supplementary angles are a pair of angles that sum up to 180°.

It should be noted:

If ∠G and ∠H are a pair of supplementary angles, they both sum up to 180°.

Equation formed: ∠G + ∠H = 180

Substitute the values into the equation.

∠G + ∠H = 180
=> 65 + ∠H = 180

Subtract 65 both sides.

=> 65 - 65 + ∠H = 180 - 65
=> ∠H = 180 - 65 = 115°

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