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
5. Yes 1,2, or 3 hours
6. No, because the distance will never change and there aren't multiple values
7. Yes, yes or no (a person could be colorblind)
8. Yes, yes or no (a person could be colorblind)
9. Yes: Rap, country, pop, classical, etc
Hmm....
I know that the first answer is a coin, but I'm not too sure about the second one.
Answer:
Given
f(x) = 2x+7
g(x) = x^2-4
h(x) = 5x
a. 4h(x)
= 4 * 5x
= 20x
b. f(x) - g(x)
f(x) - g(x) = 2x + 7 - (x^2 - 4)
= 2x+7-x^2+4
=-x^2+2x+7+4
=-x^2+2x+11
c. f(g(x)) = 2(g(x))+7
=2(x^2-4) +7
=2x^2-8+7
=2x^2-1
d. g(x)h(x) = (x^2-4)(5x)
= 5x^3 - 20x
e. g(x) / f(x) = x2 - 4/ 2x + 7
