Question

y varies directly as the square of x. When x = 2, y = 40. Find x when y = 640.

a. x = ±6

b. x = ±8

c. x = ±12

d. x = ±20

Answer 1

ans will b B.x=±8

Answer 2

thank you, if you dont mind can you explain to me how you got that?

Answer 3

"y varies directly as the square of x" implies:\[y=kx^2\]where k is some constant

Answer 4

it means y = k x^2 (for some constant k) => y1/y2 = (x1/x2)^2 here y1= 40,x1 =2 and y2 = 640, x2= ?

Answer 5

you are then given: When x = 2, y = 40

Answer 6

so if you plug those values into that expression, then you can calculate the value of k.

Answer 7

\[40=k\times(2)^2=4k\implies k=10\]

Answer 8

so now you know that:\[y=10x^2\]

Answer 9

you should be able to solve from here.

Answer 10

okay, i see what you did. Thanks again
640 = 10x2
so i just solve from there?

Answer 11

yes

Answer 12

what @mysha did was use a short-cut method that avoids having to calculate the value of k. I can explain that method further if you want?

Answer 13

sure, i would appriciate that

Answer 14

but the method was right wasn't it?

Answer 15

ok, the initial values that you were given were "When x = 2, y = 40"

this can be generalised to: \(x=x_1, y=y_1\)

(yes mysha your method was correct)

Answer 16

so, if we take the generalised initial values, we get:\[y_1=kx_1^2\]do you understand so far?

Answer 17

@bombshellbri nw u can do it asnaseer has helped u so far alot! try it

Answer 18

here I am using \(y_1\) in place of 40 and \(x_1\) in place of 2

Answer 19

if you are not too familiar with this type of approach then we can stick to numbers and say:\[40=k\times(2)^2=4k\]

Answer 20

ok?

Answer 21

this is the same step as we did above but we do not now go on to solve for k.

Answer 22

yes, i understand everything you have told me. thank you @asnaseer and you too @mysha

Answer 23

yw :)

Answer 24

haha n.p :) credit goes to @asnaseer more ;)

Answer 25

thx @mysha :)