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Andrew [12]
3 years ago
13

Suppose r varies directly as the square of​ m, and inversely as s. If r equals 11 when m equals 6 and s equals 4​, find r when m

equals 12 and s equals 4.
Mathematics
1 answer:
77julia77 [94]3 years ago
7 0

Answer: r=44

Step-by-step explanation:

The combine variation equation will have the folllowing form:

y=\frac{kx}{z}

Where "k" is the constantn of variation.

You know that "r" varies directly as the square of​ "m", and inversely as "s". Then the equation is:

r=\frac{m^2k}{s}

Knowing that r=11 when m=6 and s=4, you can substitute values into the equation and solve for "k" in order to find its value:

11=\frac{6^2(k)}{4}\\\\\frac{11*4}{6^2}=k\\\\k=\frac{11}{9}

Now, to find the value of "r" when m=12 and s=4, you need tot substitute these values and the the constant of variation into  r=\frac{m^2k}{s} and then evaluate:

 r=\frac{(12^2)(\fra{11}{9}}{4}\\\\r=44

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Answer:  \textsf{y = -1/4x - 4}

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Given: \textsf{Slope = -1/4, Point through = (4, -5)}

Find:  \textsf{Equation for the line that passes through the given point}

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

<u>Plug in the values</u>

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Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

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