Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Suppose that $z$ varies jointly with the cube of $x$ and the square of $y$ . Find the constant of proportionality $k$ if $z = 3600$ when $y = 3$ and $x =5$ .

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q. Suppose that

z

varies jointly with the cube of

x

and the square of

y

. Find the constant of proportionality

k

if

z = 3600

when

y = 3

and

x =5

.

Identify general form: Identify the general form of joint variation. $\newline$ Joint variation is expressed as $z = k \times x^n \times y^m$ , where $k$ is the constant of proportionality, and $n$ and $m$ are the powers to which $x$ and $y$ are raised, respectively. In this case, since $z$ varies jointly with the cube of $x$ and the square of $y$ , the equation becomes $z = k \times x^3 \times y^2$ .
Substitute values into equation: Substitute $z = 3600$ , $y = 3$ , and $x = 5$ into the joint variation equation $z = k \times x^3 \times y^2$ . $\newline$ $3600 = k \times 5^3 \times 3^2$
Calculate $x^3$ and $y^2$ : Calculate the values of $x^3$ and $y^2$ . $\newline$ $5^3 = 5 \times 5 \times 5 = 125$ $\newline$ $3^2 = 3 \times 3 = 9$
Substitute calculated values: Substitute the calculated values into the equation. $\newline$ $3600 = k \times 125 \times 9$
Solve for constant of proportionality: Solve the equation for the constant of proportionality, $k$ . $3600 = k \times (125 \times 9)$ $3600 = k \times 1125$ $k = \frac{3600}{1125}$
Perform division: Perform the division to find the value of $k$ . $k = \frac{3600}{1125}$ $k = 3.2$

More problems from Write and solve direct variation equations

Question

Which equation has a constant of proportionality equal to

2

\newline

1

\newline

y=\frac{10}{5} x

\newline

y=\frac{2}{2} x

\newline

y=\frac{2}{4} x

\newline

y=\frac{22}{2} x

Posted 3 months ago

Question

Which equation has a constant of proportionality equal to

10

\newline

1

\newline

y=\frac{2}{20} x

\newline

y=\frac{30}{3} x

\newline

y=\frac{12}{2} x

\newline

y=\frac{5}{5} x

Posted 3 months ago

Question

z

varies jointly with the cube of

x

and the square of

y

. Find the constant of proportionality

k

z = 3600

y = 3

x =5

k

from above write the variation equation in terms of

x

y

Posted 2 months ago

Question

z

varies jointly with the cube of

x

and the square of

y

. Find the constant of proportionality

k

z = 3600

y = 3

x =5

k

from above write the variation equation in terms of

x

y

k

from above find

z

x=

12

x=

13

Posted 2 months ago

Question

z

varies jointly with the cube of

x

and the square of

y

. Find the constant of proportionality

k

z = 3600

y = 3

x =5

k

from above write the variation equation in terms of

x

y

k

from above find

z

x =

12

x=

13

Posted 2 months ago

Question

In the following expression, both

\newline

A

\newline

B

are variables that can take positive values.

\newline

A^{(B)}(B+2)

\newline

Which of these actions will cause the expression's value to increase?

\newline

2

\newline

\newline

A

constant and increasing

\newline

B

\newline

\newline

A

constant and decreasing

\newline

B

\newline

\newline

A

\newline

B

\newline

\newline

A

\newline

B

Posted 1 day ago

Question

Graph the function

f(x)=4 x^{2}+8 x-1

\newline

Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Posted 5 hours ago

Question

2 x+4 y=6 x+3 y

Posted 5 hours ago

Question

Graph the function

f(x)=x^{2}+4 x+5

\newline

Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

\newline

\newline

\newline

\newline

\newline

100

Posted 5 hours ago

Question

brainly.in > question

\newline

What is the median of

7,10,7,5,9,10

? Write th correct alternative ...

Posted 5 hours ago