Answer :
Answer:
The function is A = 10√r
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# A is varies directly with the square root of r
- Change the statement above to a mathematical relation
∴ A ∝ √r
- Chang the relation to a function by using a constant k
∴ A = k√r
- To find the value of the constant of variation k substitute A and r
by the given values
∵ r = 16 when A = 40
∵ A = k√r
∴ 40 = k√16 ⇒ simplify the square root
∴ 40 = 4k ⇒ divide both sides by 4 to find the value of k
∴ 10 = k
- The value of the constant of variation is 10
∴ The function describing the relationship of A and r is A = 10√r
Answer:
A = 10[tex]\sqrt{r}[/tex]
Step-by-step explanation:
Given A varies directly with the square root of r then the equation relating them is
A = k[tex]\sqrt{r}[/tex] ← k is the constant of variation
To find k use the condition r = 16 , A = 40
k = [tex]\frac{A}{\sqrt{r} }[/tex] = [tex]\frac{40}{\sqrt{16} }[/tex] = [tex]\frac{40}{4}[/tex] = 10
A = 10[tex]\sqrt{r}[/tex] ← equation of variation