Math / Algebra

QuestionMake $y$ the subject of the formula $c=w-4 a y^{3}$

Studdy Solution

STEP 1

1. The equation $c = w - 4ay^3$ is a polynomial equation.
2. We need to isolate $y$ on one side of the equation to make it the subject.

STEP 2

1. Isolate the term containing $y$ .
2. Solve for $y^3$ .
3. Solve for $y$ .

STEP 3

First, isolate the term containing $y$ by subtracting $w$ from both sides of the equation:
$c = w - 4ay^3$ $c - w = -4ay^3$

STEP 4

Next, divide both sides by $-4a$ to solve for $y^3$ :
$c - w = -4ay^3$ $\frac{c - w}{-4a} = y^3$
Simplify the expression:
$y^3 = \frac{w - c}{4a}$

STEP 5

Finally, take the cube root of both sides to solve for $y$ :
$y = \sqrt[3]{\frac{w - c}{4a}}$
The expression for $y$ as the subject of the formula is:
$y = \sqrt[3]{\frac{w - c}{4a}}$

Was this helpful?

QuestionMake $y$ the subject of the formula $c=w-4 a y^{3}$

Studdy Solution

STEP 1

1. The equation $c = w - 4ay^3$ is a polynomial equation.
2. We need to isolate $y$ on one side of the equation to make it the subject.

STEP 2

1. Isolate the term containing $y$ .
2. Solve for $y^3$ .
3. Solve for $y$ .

STEP 3

First, isolate the term containing $y$ by subtracting $w$ from both sides of the equation:
$c = w - 4ay^3$ $c - w = -4ay^3$

STEP 4

Next, divide both sides by $-4a$ to solve for $y^3$ :
$c - w = -4ay^3$ $\frac{c - w}{-4a} = y^3$
Simplify the expression:
$y^3 = \frac{w - c}{4a}$

STEP 5

Finally, take the cube root of both sides to solve for $y$ :
$y = \sqrt[3]{\frac{w - c}{4a}}$
The expression for $y$ as the subject of the formula is:
$y = \sqrt[3]{\frac{w - c}{4a}}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMake yyy the subject of the formula c=w−4ay3c=w-4 a y^{3}c=w−4ay3

Studdy Solution

STEP 1

1. The equation c=w−4ay3 c = w - 4ay^3 c=w−4ay3 is a polynomial equation.2. We need to isolate y y y on one side of the equation to make it the subject.

STEP 2

1. Isolate the term containing y y y.2. Solve for y3 y^3 y3.3. Solve for y y y.

STEP 3

First, isolate the term containing y y y by subtracting w w w from both sides of the equation:c=w−4ay3 c = w - 4ay^3 c=w−4ay3 c−w=−4ay3 c - w = -4ay^3 c−w=−4ay3

STEP 4

Next, divide both sides by −4a-4a−4a to solve for y3 y^3 y3:c−w=−4ay3 c - w = -4ay^3 c−w=−4ay3 c−w−4a=y3 \frac{c - w}{-4a} = y^3 −4ac−w​=y3Simplify the expression:y3=w−c4a y^3 = \frac{w - c}{4a} y3=4aw−c​

STEP 5

Finally, take the cube root of both sides to solve for y y y:y=w−c4a3 y = \sqrt[3]{\frac{w - c}{4a}} y=34aw−c​​ The expression for y y y as the subject of the formula is:y=w−c4a3 y = \sqrt[3]{\frac{w - c}{4a}} y=34aw−c​​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMake $y$ the subject of the formula $c=w-4 a y^{3}$

1. The equation $c = w - 4ay^3$ is a polynomial equation.
2. We need to isolate $y$ on one side of the equation to make it the subject.

1. Isolate the term containing $y$ .
2. Solve for $y^3$ .
3. Solve for $y$ .

First, isolate the term containing $y$ by subtracting $w$ from both sides of the equation:
$c = w - 4ay^3$ $c - w = -4ay^3$

Next, divide both sides by $-4a$ to solve for $y^3$ :
$c - w = -4ay^3$ $\frac{c - w}{-4a} = y^3$
Simplify the expression:
$y^3 = \frac{w - c}{4a}$

Finally, take the cube root of both sides to solve for $y$ :
$y = \sqrt[3]{\frac{w - c}{4a}}$
The expression for $y$ as the subject of the formula is:
$y = \sqrt[3]{\frac{w - c}{4a}}$