Question

Consider the relationship 3r+2t=18

Answer 1

Answer:

A) $f(t)=6-\frac{2}{3}t$

B) The value of f(-3) is 8

C) The value of t is 6

Step-by-step explanation:

* Lets explain how to solve the problem

- The relation is 3r + 2t = 18

- To change the relation as a function of f(t) you must to find r in terms

  of t that means put r in one side and the others in the second side

A)

∵ 3r + 2t = 18

- Subtract 2t from both sides

∴ 3r = 18 - 2t

- Divide each side by 3

∴ r = 18/3 - 2t/3

∴ r = 6 - 2/3 t

- Change the equation to a function by using the function notation

∵ r = f(t)

∴ $f(t)=6-\frac{2}{3}t$

B)

- To evaluate f(-3) substitute t by -3 in f(t)

∵ $f(t)=6-\frac{2}{3}t$

∴ $f(-3)=6-\frac{2}{3}(-3)=6-(-2)=6+2=8$

∴ f(-3) = 8

* The value of f(-3) is 8

C)

- Solve f(t) = 2 means find the value of t when r = 2

∵ $f(t)=6-\frac{2}{3}t$

∵ f(t) = 2

∴ $2=6-\frac{2}{3}t$

- Subtract 6 from both sides

∴ $-4=-\frac{2}{3}t$

- Multiply both sides by 3

∴ -12 = -2t

- Divide both sides by -2

∴ t = 6

* The value of t is 6

Answer 2

Answer and Explanation:

Given : Consider the relationship $3r+2t=18$

To find :

A.  Write the relationship as a function r=f(t)

B. Evaluate f(-3)

C. Solve f(t)= 2

Solution :

A) To write the relationship as function r=f(t) we separate the r,

$3r+2t=18$

Subtract 2t both side,

$3r=18-2t$

Divide by 3 both side,

$r=\frac{18-2t}{3}$

The function is $f(t)=\frac{18-2t}{3}$

B) To evaluate f(-3) put t=-3

$f(-3)=\frac{18-2(-3)}{3}$

$f(-3)=\frac{18+6}{3}$

$f(-3)=\frac{24}{3}$

$f(-3)=8$

C) Solve for f(t)=2

$\frac{18-2t}{3}=2$

$18-2t=6$

$2t=12$

$t=\frac{12}{2}$

$t=6$