Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If $y$ varies inversely with $x$ and $y = 2$ when $x = 12$ , find $y$ when $x = 4$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

View step-by-step help

View step-by-step help

Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 2

when

x = 12

, find

y

when

x = 4

.

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

_____

Understand Inverse Variation: Understand the concept of inverse variation. $\newline$ Inverse variation means that one variable increases as the other decreases. The relationship can be described by the equation $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation $k$ . We are given that $y = 2$ when $x = 12$ . Substitute these values into the inverse variation equation $y = \frac{k}{x}$ . $2 = \frac{k}{12}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $12$ . $\newline$ $2 \times 12 = k$ $\newline$ $24 = k$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we know $k = 24$ , the inverse variation equation is $y = \frac{24}{x}$ .
Find $y$ : Find $y$ when $x = 4$ . $\newline$ Substitute $x = 4$ into the inverse variation equation $y = \frac{24}{x}$ . $\newline$ $y = \frac{24}{4}$ $\newline$ $y = 6$

More problems from Write and solve inverse variation equations

Question

Write an expression to represent:

\newline

3

more than the product of

2

x

Posted 4 months ago

Question

Write an expression to represent:

4

times the difference of

x

2

Posted 4 months ago

Question

Write an expression to represent:

4

less than the product of

1

x

Posted 4 months ago

Question

What happens to the value of the expression

35+k

k

\newline

1

\newline

(A) It increases.

\newline

(B) It decreases.

\newline

(C) It stays the same.

Posted 4 months ago

Question

h(x)=x^{-5}

\newline

h^{\prime}(2)=

Posted 3 months ago

Question

\mathrm{D}=\left[\begin{array}{ll}4 & -1 \\ 2 & -1\end{array}\right]

A=\left[\begin{array}{rrr} 3 & 1 & 0 \\ 2 & 1 & -2 \end{array}\right]

\newline

\mathrm{H}=\mathrm{DA}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

B=\left[\begin{array}{rr} 4 & 4 \\ 1 & 0 \\ -2 & 1 \end{array}\right] \text { and } F=\left[\begin{array}{ll} 0 & 3 \\ 0 & 1 \end{array}\right]

\newline

\mathrm{H}=\mathrm{BF}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

F=\left[\begin{array}{rr}2 & 3 \\ 0 & 5 \\ -1 & -1\end{array}\right]

\mathrm{D}=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]

\newline

\mathrm{H}=\mathrm{FD}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 5 \\ 5 & 5 & 0\end{array}\right]

F=\left[\begin{array}{rr}-2 & -1 \\ 5 & 2 \\ 5 & -2\end{array}\right]

\newline

\mathrm{H}=\mathrm{EF}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago

Question

\mathrm{C}=\left[\begin{array}{r} -1 \\ -2 \\ 2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 2 & 1 \end{array}\right]

\newline

\mathrm{H}=\mathrm{CD}

\mathrm{H}

\newline

\mathbf{H}=

Posted 3 months ago