Answer:
A) [tex]f(t) = 2 - \frac{8}{5}\cdot t[/tex], B) [tex]f(-5) = 10[/tex], C) [tex]t = -15[/tex] for [tex]f(t) = 26[/tex]
Step-by-step explanation:
A) Let be [tex]f(t) = r[/tex] and [tex]5\cdot r + 8\cdot t = 10[/tex], the latter expression is a function in implicit form and we need to turn it into its explicit form, where [tex]t[/tex] is the independent variable.
[tex]5\cdot r = 10 - 8\cdot t[/tex]
[tex]r = 2 -\frac{8}{5}\cdot t[/tex]
[tex]f(t) = 2 - \frac{8}{5}\cdot t[/tex]
B) If we know that [tex]t = -5[/tex]. then [tex]f(-5)[/tex] is:
[tex]f(-5) = 2 - \frac{8}{5}\cdot (-5)[/tex]
[tex]f(-5) = 10[/tex]
C) If we know that [tex]f(t) = 26[/tex], then we solve for [tex]t[/tex]:
[tex]2 - \frac{8}{5}\cdot t = 26[/tex]
[tex]\frac{8}{5}\cdot t = -24[/tex]
[tex]t = -15[/tex]
