Question

HELP! if (x1,y1) and (y1,y2) satisfy xy=k, then x1y1 = y1y2. Find x or y as indicated...........
--> question (x,x) and (5,25)

Answer 1

if xy = k, then the first pair (x,x) would multiply to k and so would the second pair (5,25)

Answer 2

this means that

x*x = 5*25

Answer 3

Wait, ... still confused

Answer 4

from here, you need to solve x*x = 5*25 for x

Answer 5

is that multiplication?
like 5x25 ?

Answer 6

* is multiply, yes

Answer 7

so 5*25 = 5 times 25 = 125

Answer 8

x*x = x times x = x^2

Answer 9

so

x*x = 5*25

turns into

x^2 = 125

Answer 10

then what?

Answer 11

well you need to isolate x fully

Answer 12

so square root it?

Answer 13

yep

Answer 14

x=5?

Answer 15

no

Answer 16

x^2 square rooted is x, and 125 square rooted is 5?

Answer 17

the square root of 125 is NOT 5

Answer 18

you're thinking of 25

Answer 19

use a calculator or you can simplify \(\large \sqrt{125}\)

Answer 20

My bad, so the answer is x=25?

Answer 21

no

Answer 22

I'll show you how to simplify

Answer 23

Ok. But do I have to solve for y?

Answer 24

\[\large \sqrt{125} = \sqrt{25*5}\]


\[\large \sqrt{125} = \sqrt{25}*\sqrt{5}\]


\[\large \sqrt{125} = 5\sqrt{5}\]

Answer 25

so because the solutions to something like x^2 = 4 are x = 2 or x = -2, this means that the solutions to x^2 = 125 are


\[\large 5\sqrt{5}, \ -5\sqrt{5}\]

Answer 26

and that's the answer?

Answer 27

yes, the only two possible values for x

Answer 28

THANK YOU!!!!!!!

Answer 29

you're welcome

Answer 30

I have another problem.... if you care to help?

Answer 31

sure

Answer 32

ok, z varies jointly as x and y and inversely as w. Write the appropriate combined-variation equation, and find z for the given values of x, y and w.
---> problem: z=10 when x=5, y=-2. and w=3; x=8, y=6. and w=-12.

Answer 33

able to get anywhere with this?

Answer 34

all I know is the formula, is y=kxz/w? I think

Answer 35

very good

Answer 36

ok, so how to plug it in is where im struggling.

Answer 37

the first part tells you that " z=10 when x=5, y=-2. and w=3"

plug all this in, and then solve for k

Answer 38

-2=(k*5*10)/3 ?

Answer 39

oh sorry, i misread what you said earlier

Answer 40

the equation should be

z = kxy/w

Answer 41

sorry about that, try it again

Answer 42

10=(k*5*-2)/3 ?

Answer 43

good

Answer 44

now solve for k

Answer 45

ok, so then it would be 10=-10k/3 ?

Answer 46

keep going

Answer 47

k=-3 ?

Answer 48

correct

Answer 49

is that the answer then?

Answer 50

that answers the first part: the part where you need to find the equation

Answer 51

the equation

z = kxy/w

turns into

z = -3xy/w

Answer 52

so the equation is z = -3xy/w and you use this to answer the second part

Answer 53

z=(-3*8*6)/-12

Answer 54

good, now evaluate

Answer 55

z=-12

Answer 56

?

Answer 57

close

Answer 58

what?

Answer 59

the answer of -12 is incorrect, but it's close

Answer 60

positive 12 ?

Answer 61

good

Answer 62

z = 12

Answer 63

so that's the final answer right?

Answer 64

to the second part, yes

Answer 65

whats next?

Answer 66

you're done, you found the equation and the value of z given the values of x,y,w

Answer 67

so when I input my answer, I just have to write z=12?

Answer 68

the problem asks you to find the equation, which is z = -3xy/w (this is part 1 of the question)

then it asks you to find the value of z when x=8, y=6. and w=-12. The answer to this second part is z = 12

Answer 69

ok, thank you

Answer 70

you're welcome