Question

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Solve each problem involving direct or inverse variation.

26. If y varies directly as x, and y = 15/4 when x = 15, find y when x = 11

27. If y varies inversely as x, and y = 4 when x = 9, find when x = 7

Answer 1

Answer:

see explanation

Step-by-step explanation:

26

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = $\frac{15}{4}$ when x = 15

$\frac{15}{4}$ = 15k ( divide both sides by 15 )

$\frac{\frac{15}{4} }{15}$ = k , then

k = $\frac{15}{4}$ × $\frac{1}{15}$ = $\frac{1}{4}$

y = $\frac{1}{4}$ x ← equation of variation

when x = 11 , then

y = $\frac{1}{4}$ × 11 = $\frac{11}{4}$

27

given y varies inversely as x then the equation relating them is

y = $\frac{k}{x}$ ← k is the constant of variation

to find k use the condition y = 4 when x = 9

4 = $\frac{k}{9}$ ( multiply both sides by 9 )

36 = k

y = $\frac{36}{x}$ ← equation of variation

when x = 7 , then

y = $\frac{36}{7}$

Answer 2

Answer:

26)  y = 11/4

27)  y = 36/7

Step-by-step explanation:

Question 26

Direct variation is a mathematical relationship between two variables where a change in one variable directly corresponds to a change in the other variable. It is represented by the equation y = kx, where y and x are the variables and k is the constant of variation.

To find the constant of variation, k, substitute the given values of y = 15/4 when x = 15 into the direct variation equation and solve for k:

$\begin{aligned}y&=kx\\\\\dfrac{15}{4}&=15k\\\\k&=\dfrac{1}{4}\end{aligned}$

To find the value of y when x = 11, substitute the found value of k and x = 11 into the direct variation equation, and solve for y:

$\begin{aligned}y&=kx\\\\y&=\dfrac{1}{4} \cdot 11\\\\y&=\dfrac{11}{4}\end{aligned}$

Therefore, if y varies directly as x, then y = 11/4 when x = 11.

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Inverse variation is a mathematical relationship between two variables where an increase in one variable results in a corresponding decrease in the other variable, and vice versa, while their product remains constant. It is represented by the equation y = k/x, where y and x are the variables and k is the constant of variation.

To find the constant of variation, k, substitute the given values of y = 4 when x = 9 into the inverse variation equation and solve for k:

$\begin{aligned}y&=\dfrac{k}{x}\\\\4&=\dfrac{k}{9}\\\\k&=36\end{aligned}$

To find the value of y when x = 7, substitute the found value of k and x = 7 into the inverse variation equation, and solve for y:

$\begin{aligned}y&=\dfrac{k}{x}\\\\y&=\dfrac{36}{7}\end{aligned}$

Therefore, if y varies inversely as x, then y = 36/7 when x = 7.