Question

Assistance with College Calculus

Answer 1

Minimize Q=2x^2 +5y^2, where x+y=7

Answer 2

I am a Senior and I'm still in Geometry, could you maybe help me ?

Answer 3

Maybe.

Answer 4

It has to do with SohCahToa.. I am terrible at it

Answer 5

Sorry but I cant help you. I haven't done Geometry in 4 or 5 years.

Answer 6

No worries, thanks anyways!

Answer 7

Hmm, so y would equal 7-x, then you would use that as y and distribute. (I'm working on that part now)

Answer 8

Okay

Answer 9

So after plugging in and expanding

Q = 2x^2 + 5(49 - 14x - x^2) because that's (7-x)^2 factored out.

I guess it's a case of distributing and combining like terms from here

Answer 10

So
-3x^2 +245 -70x

Answer 11

Yep, that's what I got. Then I just divided by -1 to get rid of that negative in front

Answer 12

Okay.

Answer 13

So now its

3x^2 -245+70x

Answer 14

Next I do the first derivative right?

Answer 15

Yeah then set that = to 0, if it's wanting you to find the actual minimum value

Answer 16

Okay. x= -35/3

Answer 17

So that's your X
We can find Y now

7 also being 21/3

Answer 18

y= 56/3

Answer 19

Pearson says both x and y are incorrect.

Answer 20

I may see the problem. Hold on

Answer 21

Does X= 5 and Y= 2 work. If so, I see where we messed up

Answer 22

Or, I atleast

Answer 23

Um let me type it in

Answer 24

Yes x=5 and y=2

Answer 25

Yeahhhhh, I made an elementary mistake

Answer 26

??

Answer 27

I factored (x-7)^2 wrong -_______- lol

Answer 28

Yeah I was going to ask how you factored (7-x)^2 ..

Answer 29

Yeah, Mb about that one

Answer 30

Can you start back over?

Answer 31

Yeah,
So we have those two equations wanting X and Y. So we would first rearrange the second to read y= 7-x.

Now we can use substitution to get

Q = 2x^2 + 5(7-x)^2

Answer 32

Okay.

Answer 33

After foiling (correctly!) We get

2x^2 + 5(49-14x+x^2)

Answer 34

We can now distribute and get

2x^2 + 245 -70x +5x^2

Answer 35

Combining: 7x^2 - 70x + 245

Then derivative time

Answer 36

Okay. Thanks

Answer 37

Anytime