Math / Algebra

Question $y$ varles inversely as $x$ . If $x=2$ then $y=7$ . Find $y$ when $x=4$ . $\square$ $y=$ Submit Question

Studdy Solution

STEP 1

What is this asking? If $y$ changes inversely with $x$ , and we know one pair of $x$ and $y$ values, what will $y$ be when $x$ is a different value? Watch out! Inverse variation means as one variable goes up, the other goes down, but not by simple addition or subtraction!
It's all about multiplication.

STEP 2

1. Set up the inverse variation equation.
2. Find the constant of variation.
3. Solve for the new y value.

STEP 3

Alright, so we know that $y$ varies inversely with $x$ .
What does that actually mean?
It means that their product is always the same, a constant!
We can write this relationship as $y \cdot x = k$ , where $k$ is our constant of variation.

STEP 4

We're given that when $x = 2$ , then $y = 7$ .
Let's plug those values into our equation: $7 \cdot 2 = k$ .

STEP 5

This gives us $k = 14$ .
So, our constant of variation is $\textbf{14}$ !
Our equation is now $y \cdot x = 14$ .

STEP 6

Now, we want to find $y$ when $x = 4$ .
Let's plug in $x = 4$ into our equation: $y \cdot 4 = 14$ .

STEP 7

To solve for $y$ , we need to divide both sides of the equation by $4$ : $\frac{y \cdot 4}{4} = \frac{14}{4}$ This simplifies to: $y = \frac{14}{4}$

STEP 8

Now, we simplify the fraction.
Both the numerator and denominator are divisible by $2$ , so we get: $y = \frac{14}{4} = \frac{7}{2}$ So, when $x = 4$ , $y = \frac{7}{2}$ !

STEP 9

When $x = 4$ , $y = \frac{7}{2}$ .

Was this helpful?

Question $y$ varles inversely as $x$ . If $x=2$ then $y=7$ . Find $y$ when $x=4$ . $\square$ $y=$ Submit Question

Studdy Solution

STEP 1

STEP 2

1. Set up the inverse variation equation.
2. Find the constant of variation.
3. Solve for the new y value.

STEP 3

Alright, so we know that $y$ varies inversely with $x$ .
What does that actually mean?
It means that their product is always the same, a constant!
We can write this relationship as $y \cdot x = k$ , where $k$ is our constant of variation.

STEP 4

We're given that when $x = 2$ , then $y = 7$ .
Let's plug those values into our equation: $7 \cdot 2 = k$ .

STEP 5

This gives us $k = 14$ .
So, our constant of variation is $\textbf{14}$ !
Our equation is now $y \cdot x = 14$ .

STEP 6

Now, we want to find $y$ when $x = 4$ .
Let's plug in $x = 4$ into our equation: $y \cdot 4 = 14$ .

STEP 7

To solve for $y$ , we need to divide both sides of the equation by $4$ : $\frac{y \cdot 4}{4} = \frac{14}{4}$ This simplifies to: $y = \frac{14}{4}$

STEP 8

Now, we simplify the fraction.
Both the numerator and denominator are divisible by $2$ , so we get: $y = \frac{14}{4} = \frac{7}{2}$ So, when $x = 4$ , $y = \frac{7}{2}$ !

STEP 9

When $x = 4$ , $y = \frac{7}{2}$ .

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.

Questionyyy varles inversely as xxx. If x=2x=2x=2 then y=7y=7y=7. Find yyy when x=4x=4x=4. □\square□ y=y=y= Submit Question

Studdy Solution

STEP 1

STEP 2

1. Set up the inverse variation equation.2. Find the constant of variation.3. Solve for the new *y* value.

STEP 3

Alright, so we know that yyy varies inversely with xxx.What does that *actually* mean?It means that their product is always the same, a **constant**!We can write this relationship as y⋅x=ky \cdot x = ky⋅x=k, where kkk is our **constant of variation**.

STEP 4

We're given that when x=2x = 2x=2, then y=7y = 7y=7.Let's plug those **values** into our equation: 7⋅2=k7 \cdot 2 = k7⋅2=k.

STEP 5

This gives us k=14k = 14k=14.So, our **constant of variation** is 14\textbf{14}14!Our equation is now y⋅x=14y \cdot x = 14y⋅x=14.

STEP 6

Now, we want to find yyy when x=4x = 4x=4.Let's plug in x=4x = 4x=4 into our equation: y⋅4=14y \cdot 4 = 14y⋅4=14.

STEP 7

To solve for yyy, we need to divide both sides of the equation by 444: y⋅44=144 \frac{y \cdot 4}{4} = \frac{14}{4} 4y⋅4​=414​ This simplifies to: y=144 y = \frac{14}{4} y=414​

STEP 8

Now, we simplify the fraction.Both the numerator and denominator are divisible by 222, so we get: y=144=72 y = \frac{14}{4} = \frac{7}{2} y=414​=27​ So, when x=4x = 4x=4, y=72y = \frac{7}{2}y=27​!

STEP 9

When x=4x = 4x=4, y=72y = \frac{7}{2}y=27​.

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.

Question $y$ varles inversely as $x$ . If $x=2$ then $y=7$ . Find $y$ when $x=4$ . $\square$ $y=$ Submit Question

1. Set up the inverse variation equation.
2. Find the constant of variation.
3. Solve for the new y value.

Alright, so we know that $y$ varies inversely with $x$ .
What does that actually mean?
It means that their product is always the same, a constant!
We can write this relationship as $y \cdot x = k$ , where $k$ is our constant of variation.

We're given that when $x = 2$ , then $y = 7$ .
Let's plug those values into our equation: $7 \cdot 2 = k$ .

This gives us $k = 14$ .
So, our constant of variation is $\textbf{14}$ !
Our equation is now $y \cdot x = 14$ .

Now, we want to find $y$ when $x = 4$ .
Let's plug in $x = 4$ into our equation: $y \cdot 4 = 14$ .

To solve for $y$ , we need to divide both sides of the equation by $4$ : $\frac{y \cdot 4}{4} = \frac{14}{4}$ This simplifies to: $y = \frac{14}{4}$

Now, we simplify the fraction.
Both the numerator and denominator are divisible by $2$ , so we get: $y = \frac{14}{4} = \frac{7}{2}$ So, when $x = 4$ , $y = \frac{7}{2}$ !

When $x = 4$ , $y = \frac{7}{2}$ .