Basic Math Examples

$1.1814 = (\frac{1}{y}) \cdot {((0.83333) (1 + 0.2 \cdot y^{2}))}^{1.75}$

Step 1

Simplify

$(\frac{1}{y}) \cdot {((0.83333) (1 + 0.2 \cdot y^{2}))}^{1.75}$ .

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Step 1.1

Simplify terms.

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Step 1.1.1

Apply the distributive property.

$1.1814 = \frac{1}{y} \cdot {(0.83333 \cdot 1 + 0.83333 (0.2 y^{2}))}^{1.75}$

Step 1.1.2

Multiply.

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Step 1.1.2.1

Multiply

$0.83333$ by

$1$ .

$1.1814 = \frac{1}{y} \cdot {(0.83333 + 0.83333 (0.2 y^{2}))}^{1.75}$

Step 1.1.2.2

Multiply

$0.2$ by

$0.83333$ .

$1.1814 = \frac{1}{y} \cdot {(0.83333 + 0.166666 y^{2})}^{1.75}$

Step 1.1.3

Combine

$\frac{1}{y}$ and

${(0.83333 + 0.166666 y^{2})}^{1.75}$ .

$1.1814 = \frac{{(0.83333 + 0.166666 y^{2})}^{1.75}}{y}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Factor

$0.166666$ out of

$0.83333 + 0.166666 y^{2}$ .

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Step 1.2.1.1

Factor

$0.166666$ out of

$0.83333$ .

$1.1814 = \frac{{(0.166666 \cdot 5 + 0.166666 y^{2})}^{1.75}}{y}$

Step 1.2.1.2

Factor

$0.166666$ out of

$0.166666 \cdot 5 + 0.166666 y^{2}$ .

$1.1814 = \frac{{(0.166666 (5 + y^{2}))}^{1.75}}{y}$

Step 1.2.2

Apply the product rule to

$0.166666 (5 + y^{2})$ .

$1.1814 = \frac{{0.166666}^{1.75} {(5 + y^{2})}^{1.75}}{y}$

Step 1.2.3

Raise

$0.166666$ to the power of

$1.75$ .

$1.1814 = \frac{0.04347426 {(5 + y^{2})}^{1.75}}{y}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$y \approx 0.73685674, 2.45446785$

Step 3