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k0ka [10]
4 years ago
13

What is the a nswer to 5(r-11)=2(r-4)-6

Mathematics
1 answer:
Deffense [45]4 years ago
6 0
5 (r - 11) = 2 (r - 4) - 6   Use the Distributive Property on both sides
 5r - 55 = 2r - 8 - 6      Combine like terms (-8 and - 6)
 5r - 55 = 2r - 14          Subtract 2r from both sides
 3r - 55 = -14                Add 55 to both sides
        3r = 41                  Divide both sides by 3
          r = 14\frac{2}{3}
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10

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Shelby is following a recipe to make punch for her party. the recipe calls for 5 cups of juice for every 2 cups of soda. how man
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find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6
taurus [48]

Answer:

f(x) = \frac{6}{x^2} -8 or f(x) = -\frac{6}{x^2} + 4

Step-by-step explanation:

Given

(x,y) = (1,-2) --- Point

\int\limits^6_2 {(1 + 144x^{-6})} \, dx

The arc length of a function on interval [a,b]:  \int\limits^b_a {(1 + f'(x^2))} \, dx

By comparison:

f'(x)^2 = 144x^{-6}

f'(x)^2 = \frac{144}{x^6}

Take square root of both sides

f'(x) =\± \sqrt{\frac{144}{x^6}}

f'(x) = \±\frac{12}{x^3}

Split:

f'(x) = \frac{12}{x^3} or f'(x) = -\frac{12}{x^3}

To solve fo f(x), we make use of:

f(x) = \int {f'(x) } \, dx

For: f'(x) = \frac{12}{x^3}

f(x) = \int {\frac{12}{x^3} } \, dx

Integrate:

f(x) = \frac{12}{2x^2} + c

f(x) = \frac{6}{x^2} + c

We understand that it passes through (x,y) = (1,-2).

So, we have:

-2 = \frac{6}{1^2} + c

-2 = \frac{6}{1} + c

-2 = 6 + c

Make c the subject

c = -2-6

c = -8

f(x) = \frac{6}{x^2} + c becomes

f(x) = \frac{6}{x^2} -8

For: f'(x) = -\frac{12}{x^3}

f(x) = \int {-\frac{12}{x^3} } \, dx

Integrate:

f(x) = -\frac{12}{2x^2} + c

f(x) = -\frac{6}{x^2} + c

We understand that it passes through (x,y) = (1,-2).

So, we have:

-2 = -\frac{6}{1^2} + c

-2 = -\frac{6}{1} + c

-2 = -6 + c

Make c the subject

c = -2+6

c = 4

f(x) = -\frac{6}{x^2} + c becomes

f(x) = -\frac{6}{x^2} + 4

3 0
3 years ago
What does 5a−12=−2 equal?
777dan777 [17]

Answer:

a = 2

Step-by-step explanation:

5a−12=−2

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Step-by-step explanation:

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