you might need: calculator\nf(t) = \\begin{cases} t^2 - 5t , & t \\leq -10 \\\\ t + 19 , & -10 < t < -2 \\\\…

you might need: calculator\nf(t) = \\begin{cases} t^2 - 5t , & t \\leq -10 \\\\ t + 19 , & -10 < t < -2 \\\\ \\dfrac{t^3}{t + 9} , & t \\geq -2 \\end{cases}\nf(-10) = \\boxed{}\nshow calculator

you might need: calculator\nf(t) = \\begin{cases} t^2 - 5t , & t \\leq -10 \\\\ t + 19 , & -10 < t < -2 \\\\ \\dfrac{t^3}{t + 9} , & t \\geq -2 \\end{cases}\nf(-10) = \\boxed{}\nshow calculator

Answer

Explanation:

Step1: Determine the applicable function

Since ( t = -10 ) and the first piece of the piece - wise function is defined for ( t\leq - 10 ), we use the function ( f(t)=t^{2}-5t ) when ( t = - 10 ).

Step2: Substitute ( t=-10 ) into the function

Substitute ( t=-10 ) into ( f(t)=t^{2}-5t ). We get ( f(-10)=(-10)^{2}-5\times(-10) ).

First, calculate ( (-10)^{2}=100 ) and ( 5\times(-10)=- 50 ), so ( - 5\times(-10) = 50 ).

Then, ( f(-10)=100 + 50=150 ).

Answer:

( 150 )