Math Challenge? Click to see? Part 3?

Question

Q:20) y is directly proportional √x and y = 4 when x = 16 find the equation connecting x and y

a) If P is inversely proportional to q, and p = 8 when q = 5,
find y when x is 10.

b) Given that y varies inversely as x^2.
i)What is the effect on y if x is multiplied by 2
ii)What is the effect on x if y is divided by 9?

! __________- _________ - _________ - ________- ________ !

Answer 1

Q:20) If y is directly proportional to √x,
then y = k√x, where k is a constant.

We can now find this constant
because we are given y = 4 when x = 16.

Substituting gives: 4 = k * √16.
Therefore, k = 4 / √16 = 4 / 4 = 1.
I'm keeping it simple, so I'll just use the
positive value. As you know, √16 = ± 4.

Now that we know k = 1,
the equation is : y = √x.

a) p inversely proportional to q, means p = k / q.
Substituting the known values gives : 8 = k / 5
Therefore, k = 5 * 8 = 40
and the equation is : p = 40 / q.
I think you mean "find p when q is 10".
p = 40 / 10 = 4.

b) In this problem, yn means "the new y"
and xn means "the new x"
.
y = k / x^2, because y varies inversely as x^2.

i) If x is multiplied by 2, then :
yn = k / (2x)^2 = k / (4x^2) = (k / x^2)(1 / 4) = y / 4.
The effect on y is that it is divided by 4,
or 4 times less than the original.

ii) The original equation is y = k / x^2.
We need to turn it around to find x.
Therefore, x = √(k / y).
Now, if y is divided by 9, then :
xn = √[k / (y / 9)] = √(9k / y) = 3√(k / y) = 3x.
(Notice I used only the positive value of √9.)
The effect on x is that it is multiplied by 3,
or 3 times more than the original.

Answer 2

1. y=k√x where k is 1

a)
pq=k where k is 40

xy=40
y=40/10=4

b)

yx^2=k

x is multipled by 2; value of y decreases by 4 times
y is divided by 9; value of x increases by 3 times

Answer 3

20) y=square root of x
a) Cannot tell from information given
bi) y is divided by 2
bii) x is multiplied by 9.

Answer 4

y2=x y=4 y increase x decreases

Answer 5

y=sqrt(x) or x^2=y

y=4

b)
i) it will divided by 4
ii) it will multipliyed by 3