Questions: Given h(t)=-14 t+8 a) Evaluate h(2) h(2)=-20 b) Solve h(t)=190 t=-13 c) Evaluate h(-39) h(-39)=554 d) Solve h(t)=302 t=

Transcript text: Given $h(t)=-14 t+8$ a) Evaluate $h(2)$ \[ h(2)=-20 \] b) Solve $h(t)=190$ \[ t=-13 \] c) Evaluate $h(-39)$ \[ h(-39)=554 \] d) Solve $h(t)=302$ \[ t= \] $\square$

Solution

Solution Steps

Step 1: Evaluate $ h(2) $

Given the function $ h(t) = -14t + 8 $, substitute $ t = 2 $ into the equation: \[ h(2) = -14(2) + 8 = -28 + 8 = -20 \] The result is: \[ \boxed{h(2) = -20} \]

Step 2: Solve $ h(t) = 190 $

Set the function equal to 190 and solve for $ t $: \[ -14t + 8 = 190 \] Subtract 8 from both sides: \[ -14t = 182 \] Divide both sides by $-14$: \[ t = \frac{182}{-14} = -13 \] The solution is: \[ \boxed{t = -13} \]

Step 3: Evaluate $ h(-39) $

Substitute $ t = -39 $ into the function: \[ h(-39) = -14(-39) + 8 = 546 + 8 = 554 \] The result is: \[ \boxed{h(-39) = 554} \]