How to solve (7r / 2)/(35 ^ 2)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (7r / 2)/(35 ^ 2) | Equatix

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Question

$$\frac{7r/2}{35^{2}}$$

Evaluate

$\frac{r}{350}$

Solution Steps

Calculate $35$ to the power of $2$ and get $1225$.

$$\frac{\frac{7r}{2}}{1225}$$

Express $\frac{\frac{7r}{2}}{1225}$ as a single fraction.

$$\frac{7r}{2\times 1225}$$

Cancel out $7$ in both numerator and denominator.

$$\frac{r}{2\times 175}$$

Multiply $2$ and $175$ to get $350$.

$$\frac{r}{350}$$

Show Solution

Differentiate w.r.t. r

$\frac{1}{350} = 0.002857142857142857$

Steps Using Definition of a Derivative

Calculate $35$ to the power of $2$ and get $1225$.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{\frac{7r}{2}}{1225})$$

Express $\frac{\frac{7r}{2}}{1225}$ as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{7r}{2\times 1225})$$

Cancel out $7$ in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r}{2\times 175})$$

Multiply $2$ and $175$ to get $350$.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r}{350})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{1}{350}r^{1-1}$$

Subtract $1$ from $1$.

$$\frac{1}{350}r^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{1}{350}\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{1}{350}$$