Question

I need someone to look over 5 questions. Can someone please help me? I will fan and medal.

Answer 1

Sure!

Answer 2

wooh @Ms-Brains is here

Answer 3

Lol. @boldjon Yup! :P

Answer 4

Okay. This is the first question out of five:
I think it is 5.

Answer 5

@Miss.Rose: please show your work, so we'll know why you think the correct answer choice is 5. Thank you.

Answer 6

This is just a guess. So I don't know how to solve this. @mathmale

Answer 7

I appreciate your admitting that. Let's learn how to solve "direct variation" problems.

If y = k*x, then y increases when x increases, and y decreases when x decreases. This is the meaning of direct variation. Our job is to find the value of the "constant or proportionality," which is "k".

Answer 8

choose an (x,y) pair from the table now, please. Any one you pick should be fine.

Answer 9

(x) 4
(y) 20

Answer 10

Great. Now, substitute y=20 and x=4 into the equation y=kx. Show your work. Our goal is to solve for k.

Answer 11

Re-write y=kx subbing 20 for y and 4 for x.

Answer 12

20=k4

Answer 13

Great. Now, solve for k.

Answer 14

How do I solve for k?

Answer 15

Isolate k. To do this, divide both sides of the equation by 4.

Answer 16

20div4=5
k4div4=k1
I am not sure, is this how I do it?

Answer 17

\[\frac{ 20 }{ 4 }=k \frac{ 4 }{ 4 }\]

Answer 18

Reduce that. 20/4=? 4/4=?

Answer 19

20/4=5
4/4=1

Answer 20

Right. k=5.

Re-write y=kx, this time subbing 5 for k.

Answer 21

20=54?

Answer 22

First, Miss.Rose, type y=kx. Just copy this formula.

Answer 23

y=kx
20=5*4?

Answer 24

Your y=kx is correct, as is your example.

However, I would like for you to type y=kx

and then type the same thing, substituting 5 for x.

Please do that now.

Answer 25

y=5k

Answer 26

exactly. THAT is the direct proportion relationship we wanted.

Answer 27

k is the "constant of variation." What is k in your equation, above?

Answer 28

4

Answer 29

How so? You got 5 before.

Answer 30

Sorry, I thought you said what is x.
k=5

Answer 31

Now look at the four answer choices. Which one is correct?

Answer 32

5?

Answer 33

Right. Congrats.

Answer 34

Thank you, can you help me with 4 more?

Answer 35

One more. My goal is to help you learn how to solve those problems yourself. Choose a hard one.

Answer 36

I am going to give you the choice of the 3 I think are hard. Look at them and then decide which one is the hardest, and then help me solve it.

Answer 37

Look carefully at question #5. What do you already know about solving this type of question?

Answer 38

Nothing. I missed out on a lesson at school, and I asked my friend for her notes, it turns out her notes were useless.

Answer 39

so sorry.

That happens.

that's why I prefer to lead you through all of the problem solving steps.

Answer 40

Thank you.

Answer 41

the most important words here are "varies directly." This also describes the previous problem we worked on. We got y = 5 x, remember? k is the "constant of proportionality."

Answer 42

Yes, I remember.

Answer 43

The dependent variable is C, which represents the number of Calories consumed.

C varies directly with the time spent exercising.

Answer 44

Again, C is your dependent variable; its value depends on the value of t.
t is your independent variable; it represents how many hours are spent exercising, and varies from zero to whatever.

Answer 45

k is just the constant of proportionality, which was 5 in the previous problem.
Give this a stab: Write a "direct variation" equation with C as dependent variable, t as independent variable, and k as "constant of proportionality."

Answer 46

By all means review our previous discussion if y ou wish.

Answer 47

C=tk

Answer 48

I'd write that as C = k t, but otherwise your result is fine!

Answer 49

Okay.
C=kt

Answer 50

Cool

Answer 51

Do both of the remaining 2 problems yourself. Msg me when you're done.

Answer 52

Wait... The answers only have C=800t...
Is that what the answer is?
@mathmale

Answer 53

Ooops. We didn't find the value of k.

Pick any one pair (t, C) from the table given.

Answer 54

It says that after this guy walks 4 hours, he has burned 800 calories. Agree with that?

Answer 55

Yes.
So would it be:
C=800t

Answer 56

Not quite. WRite C = k t.

Now let C = 800 cal and t = 4 hr. Find k, the constant of proportionality.

Answer 57

C=kt
800=k4
So we divide 800 by 4 which is 200.

Answer 58

so k=200.

re-write C = k t, subbing 200 for k.

Answer 59

C=200t?

Answer 60

right. very good! done.
sorry I asked you to get info from a table; there's no table for this problem!

Answer 61

Which of the four answers is the correct one?

Answer 62

C=200t

Answer 63

Done.

Answer 64

Okay. I am not really sure how to solve number 3, can you help?

Answer 65

Have to excuse myself now, but I'll be lurking in the background if you need me. You're doing well. Please at least try #3 on your own first. When you've done that, tell me what you know about solving it and what you're unsure of.

Answer 66

Okay.

Answer 67

So... I tried solving it myself and I got:
y=2/5x
I got this because I divided 10 by 4 and got 2.5 and turned that into a fraction. Did do that right, and get the correct answer.

Answer 68

First, the problem states, "y varies directly with x." You should take that as an order to write the appropriate direct variation equation. We've done that several times before. Can you remember this direct variation equation?

Answer 69

Recall y = k x. This is the general equation of ":direct variation."

OK. Problem states: "y=10 when x=4." Can you re-write y = k x using that info?

Can y ou then find the constant of variation, k?

Answer 70

y=kx

Answer 71

right. you are told that y=10 when x=4.
substitute these values into y = k x.

Answer 72

10=k4

Answer 73

Now divide both sides of the equation by 4 to find the value of the proportionality constant, k. Please show all your work.

Answer 74

10/4=2.5
4/4=1

Answer 75

So... then I turn 2.5 into a fraction, right?
\[\frac{ 2 }{ 5 }\]

Answer 76

Divide 10 = k (4) by 4.... we get (10/4) = k. Note that 10/4 is greater than 1.

10/4 = 5/2. either is OK, 5/2 is better. 2/5 is the reciprocal of 5/2, and is not ok.

What is your new k value?

Answer 77

5/2

Answer 78

\[y=\frac{5 }{2 }x\]

Answer 79

right. k = 5/2. Now, as your last step, write the equation of direct variation in the form

y = (k) x. Yes. You have it.

Answer 80

congrats!

Answer 81

Thank you. How do you solve number 2? I have no clue what the first step is.
Again, THANK YOU!

Answer 82

Look at y = 40x. Borrowing from previous experience, what kind of variation is modeled here?

Answer 83

constant

Answer 84

Actually, that 's "direct proportion" or "direct variation." Important terms.

You are given y = 40x, which has the same form as y=kx, which we used earlier.
In this case, k=40 is the proportionality constant.

Answer 85

Now re-read Question 2. Which answer do you think is correct?

Answer 86

40?

Answer 87

Right. You 'borrowed' that from y = 40 x. That's absolutely correct!

Answer 88

Thank you sooooo much for ALL of your help!!!!!!

Answer 89

'Twas great working with you. I appreciate your enthusiasm. Hope to work with you again. Bye for now!