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.

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Question

$$10 g \frac { 1 } { 0.095 } =$$

Evaluate

$\frac{2000g}{19}$

Solution Steps

Expand $\frac{1}{0.095}$ by multiplying both numerator and the denominator by $1000$.

$$10g\times \frac{1000}{95}$$

Reduce the fraction $\frac{1000}{95}$ to lowest terms by extracting and canceling out $5$.

$$10g\times \frac{200}{19}$$

Express $10\times \frac{200}{19}$ as a single fraction.

$$\frac{10\times 200}{19}g$$

Multiply $10$ and $200$ to get $2000$.

$$\frac{2000}{19}g$$

Show Solution

Differentiate w.r.t. g

$\frac{2000}{19} = 105\frac{5}{19} = 105.26315789473684$

Steps Using Definition of a Derivative

Expand $\frac{1}{0.095}$ by multiplying both numerator and the denominator by $1000$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(10g\times \frac{1000}{95})$$

Reduce the fraction $\frac{1000}{95}$ to lowest terms by extracting and canceling out $5$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(10g\times \frac{200}{19})$$

Express $10\times \frac{200}{19}$ as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{10\times 200}{19}g)$$

Multiply $10$ and $200$ to get $2000$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2000}{19}g)$$

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

$$\frac{2000}{19}g^{1-1}$$

Subtract $1$ from $1$.

$$\frac{2000}{19}g^{0}$$

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

$$\frac{2000}{19}\times 1$$

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

$$\frac{2000}{19}$$