Sure, let's solve this step-by-step.
Step 1: Define the functions [tex]\( g(t) \)[/tex] and [tex]\( h(t) \)[/tex].
Given:
[tex]\[ g(t) = 2t + 1 \][/tex]
[tex]\[ h(t) = 3t + 3 \][/tex]
Step 2: Evaluate [tex]\( g(t) \)[/tex] at [tex]\( t = 5 \)[/tex].
[tex]\[ g(5) = 2(5) + 1 \][/tex]
[tex]\[ g(5) = 10 + 1 \][/tex]
[tex]\[ g(5) = 11 \][/tex]
Step 3: Evaluate [tex]\( h(t) \)[/tex] at [tex]\( t = 5 \)[/tex].
[tex]\[ h(5) = 3(5) + 3 \][/tex]
[tex]\[ h(5) = 15 + 3 \][/tex]
[tex]\[ h(5) = 18 \][/tex]
Step 4: Calculate [tex]\( g(5) \cdot h(5) \)[/tex].
[tex]\[ g(5) \cdot h(5) = 11 \cdot 18 \][/tex]
[tex]\[ g(5) \cdot h(5) = 198 \][/tex]
Final Answer:
[tex]\[ g(5) = 11 \][/tex]
[tex]\[ h(5) = 18 \][/tex]
[tex]\[ g(5) \cdot h(5) = 198 \][/tex]
