Solve h(t)=-5t^(2) 20t 18

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

h^{- 1} (t) = - \frac{3 15 t}{30}

Evaluate

h (t) = - 5 t^{2} \times 20 t \times 18

Simplify

More Steps

h (t) = - 1800 t^{3}

In the equation for h (t),replace h (t) with y

y = - 1800 t^{3}

Interchange t and y

t = - 1800 y^{3}

Swap the sides of the equation

- 1800 y^{3} = t

Change the signs on both sides of the equation

1800 y^{3} = - t

Divide both sides

\frac{1800 y ^{3}}{1800} = \frac{- t}{1800}

Divide the numbers

y^{3} = \frac{- t}{1800}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y^{3} = - \frac{t}{1800}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 - \frac{t}{1800}

Calculate

y = 3 - \frac{t}{1800}

Simplify the root

More Steps

y = - \frac{3 15 t}{30}

Solution

h^{- 1} (t) = - \frac{3 15 t}{30}

Show Solution