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2 years ago

Determine which line is perpendicular to y = - 7/5x-2.

Mathematics

1 answer:

tatuchka [14]2 years ago

6 0

Answer:

y = 5/7 x - 6

Step-by-step explanation:

For two lines to be perpendicular, the product of their slope must be -1

The slope of the given function is -7/5

Let the slope of the required function be m

m * -7/5 = -1

7/5 m = 1

7 = 5m

m = 5/7

The slope of the line perpendicular to the line is 5/7

The required equation (using any value of the y-intercept) is expressed as;

y = 5/7 x - 6

Note that the y-intercept value was assumed and any value can be used

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Create an equation for the following.

bixtya [17]

1/2x + 5 = 35

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Hope this helps ! :)

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3 years ago

The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

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2 years ago

Chuck built a garden in the shape of a rectangle in his backyard. The width of the garden is 7 feet and the length of the garden

Nastasia [14]

The answer is 25 because of the Pythagorean theorem. 49+576=625 625 squared=25

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3 years ago

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zzz [600]

Answer:

x=17

Step-by-step explanation:

3x+5+2x=90

5x=85

x=17

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3 years ago

Read 2 more answers

The car at each vertex of a Ferris wheel holds a maximum of 5 people. The sum of the measures of the angles of the Ferris wheel

larisa [96]

Answer:

225

Step-by-step explanation:

The sum total of all the angles is 7,740 degrees,

The formula for the interior angle is 180(n - 2) where n is the number of sides in the polygon

Set this equal to 7740

180 (n-2) = 7740

Divide each side by 180

180/180 (n-2) = 7740/180

n-2 =43

Add 2 to each side

n-2+2 = 43+2

n = 45

Each vertex hold 5 people so take n and multiply by 5

45*5 = 225

The Ferris wheel holds 225 people

3 0

3 years ago

Determine which line is perpendicular to y = - 7/5x-2.​

Determine which line is perpendicular to y = - 7/5x-2.