Math

Question Find rr given 4r2=r4r-2=r, then calculate 27r27r.

Studdy Solution

STEP 1

Assumptions
1. The equation given is 4r2=r4r - 2 = r.
2. We need to solve for rr.
3. After finding the value of rr, we need to calculate the value of 27r27r.

STEP 2

First, we need to isolate the variable rr on one side of the equation. We can do this by subtracting rr from both sides of the equation.
4r2r=rr4r - 2 - r = r - r

STEP 3

Simplify both sides of the equation to combine like terms.
3r2=03r - 2 = 0

STEP 4

Next, we add 22 to both sides of the equation to solve for 3r3r.
3r2+2=0+23r - 2 + 2 = 0 + 2

STEP 5

Simplify both sides of the equation.
3r=23r = 2

STEP 6

Now, we divide both sides of the equation by 33 to solve for rr.
3r3=23\frac{3r}{3} = \frac{2}{3}

STEP 7

Simplify both sides of the equation to find the value of rr.
r=23r = \frac{2}{3}

STEP 8

Now that we have the value of rr, we can find the value of 27r27r by multiplying 2727 by rr.
27r=27×r27r = 27 \times r

STEP 9

Substitute the value of rr into the equation.
27r=27×2327r = 27 \times \frac{2}{3}

STEP 10

Multiply 2727 by 23\frac{2}{3} to find the value of 27r27r.
27r=27×23=9×227r = 27 \times \frac{2}{3} = 9 \times 2

STEP 11

Calculate the final value of 27r27r.
27r=9×2=1827r = 9 \times 2 = 18
The value of 27r27r is 1818.

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