Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An inverse variation includes the points $(12,\,3)$ and $(4,\,n)$ . Find $n$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $n = \,\_\_\_\_$

View step-by-step help

View step-by-step help

Write and solve inverse variation equations

Full solution

Q. An inverse variation includes the points

(12,\,3)

and

(4,\,n)

. Find

n

.

\newline

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

\newline

n = \,\_\_\_\_

Identify general form: Given that there is an inverse variation between two variables. $\newline$ Identify the general form of inverse variation. $\newline$ In inverse variation, the product of the two variables is constant. $\newline$ Inverse variation: $y = \frac{k}{x}$ where $k$ is the constant of variation.
Find constant of variation: We know that the point $(12, 3)$ lies on the inverse variation curve. $\newline$ Use this point to find the constant of variation $k$ . $\newline$ Substitute $12$ for $x$ and $3$ for $y$ in $y = k / x$ . $\newline$ $3 = k / 12$
Write inverse variation equation: Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $12$ . $3 \times 12 = (k / 12) \times 12$ $36 = k$ We have found the constant of variation $k = 36$ .
Substitute $x=4$ : Use the constant of variation $k$ to write the inverse variation equation. $\newline$ Substitute $k = 36$ into $y = \frac{k}{x}$ . $\newline$ The inverse variation equation is $y = \frac{36}{x}$ .
Solve for $n$ : We want to find $n$ when $x = 4$ . Substitute $4$ for $x$ in the inverse variation equation $y = \frac{36}{x}$ . $n = \frac{36}{4}$
Solve for $n$ : We want to find $n$ when $x = 4$ . $\newline$ Substitute $4$ for $x$ in the inverse variation equation $y = \frac{36}{x}$ . $\newline$ $n = \frac{36}{4}$ Solve for $n$ . $\newline$ $n = \frac{36}{4}$ $\newline$ $n = 9$ $\newline$ We have found the value of $n$ .

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 3 months ago

Question

Write an expression to represent:

4

times the difference of

x

2

Posted 3 months ago

Question

Write an expression to represent:

4

less than the product of

1

x

Posted 3 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 3 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