Question

Two variables p and q are related by the equation p=3q+2/q . Given q increases at a constant rate of 4 units per second, find the positive value of q at the instant p is increasing at a rate of 10 units per second . Just to double check my working
@ganeshie8 @jhonyy9

Answer 1

do you think

p = (3p +2)/q
or
p = 3p + (2/q)

how is correct ?

Answer 2

Hey!

Answer 3

\[p =3q+\frac{ 2 }{ q }\]

Answer 4

Hey @ganeshie8 :)

Answer 5

so than p = (3q^2 +2)/q

- q increase 4 unit/sec. so this mean that p increase p = (3*16 +2)/4 = 25/2 = 12,5 unit/sec
- but you need to calculi the positive value of q at the instant p is increasing at a rate of 10 unit per sec.
so than you can writing

10 = (3q^2 +2)/q
- solve this quadratic for positive value of q and will get the right answer to your exercise
sure

- hope so much that this will help you and that this is understandably - good luck

Answer 6

i did like this...Hope i'm right..\[p=3q+\frac{ q }{ 2 }\]\[p=3q+2q^{-1}\]\[\frac{ dp }{ dq }=3-\frac{ 2 }{ q^2 }\]\[\frac{ dp }{ dt }=\frac{ dp }{ dq }\times \frac{ dq }{ dt }\]\[10=(3-\frac{ 2 }{ q })\times4\]\[\frac{ 5 }{ 2 }=3-\frac{ 2 }{ q^2 }\]\[\frac{ 2 }{ q^2 }=\frac{ 1 }{ 2 }\]\[q^2=4\]\[q=\pm \sqrt{4}\]\[q=2,\cancel{q=-2}\]

Answer 7

so for you can being secure in your result you can making the prove for this q=2
so substituting in place of q inside this formula

p = 3q +2/q

10 = 3*2 +2/2

10 = 6+1

10 = 7

- so this mean that not is right

ATTENTION !!!

Answer 8

@MARC above you have wrote p= 3q + (q/2) but in the text of your exercise there you have wrote p = 3q + (2/q)

- can you deciding please how is exactly sure correct this text of your exercise ,please ???

Answer 9

i'm sry @jhonyy9 it was an typo error...
but the equation is\[p=3q+\frac{ 2 }{ q }\]

Answer 10

@jhonyy9

Answer 11

@MARC so than p = 3q +2/q is right that you can correct your calculi because yu have doit them with p = 3q + q/2

please check it and correct your calculi for you can giving the right answer

Answer 12

alright,let me correct it back again :)

Answer 13

This is my working..\[p=3q+\frac{ 2 }{ q }\]\[p=3q+2q^{-1}\]\[\frac{ dp }{ dq }=3-\frac{ 2 }{ q^2 } \]\[\frac{ dp }{ dt }=\frac{ dp }{ dq }\times \frac{ dq }{ dt } \]\[10=(3-\frac{ 2 }{ q })\times4 \]\[\frac{ 5 }{ 2 }=3-\frac{ 2 }{ q^2 } \]\[\frac{ 2 }{ q^2 }=\frac{ 1 }{ 2 } \]\[q^2=4 \]\[q=\pm \sqrt{4} \]\[q=2,\cancel{q=-2} \]

Answer 14

@MARC_ so check it please above i have doit the prove of q=2 and you dont give p=10
so what mean that this is something wrong in your calculi

Answer 15

is it q=3.120 and q=0.214 ? @jhonyy9

Answer 16

so than you need make the prove of these results and check that you will got p=10

ok ? check for what result of q will get p=10 sure ?

Answer 17

p = 3*3 + 2/3
10 = 29/3 what not is right sure --- yes ?

Answer 18

\[10\neq \frac{ 29 }{ 3 }\]

Answer 19

yes so this mean that q=3 not is right root of equation

Answer 20

q=0.214 is also not the right root of equation

Answer 21

than this mean that your calculi are wrong

Answer 22

can u show me your working pls.. :)
so that i can know where i'm wrong

Answer 23

10 = 3q + 2/q so this a very easy quadratic

you dont know solve it right ??? --- why ?

Answer 24

how you have got it here ?

Answer 25

\[3q^2+2=10q\]

Answer 26

yes

Answer 27

\[3q^2-10q+2=0\]

Answer 28

yes this the quadratic what you need to solve it right

Answer 29

\[q=3.120~and~q=0.214\]

Answer 30

sure ?

Answer 31

That's the value i get from the calculator but it seems that i'm not getting p=10 when i substitute the value of q into the equation p=3q+(2/q)..

Answer 32

why ? this mean that there are some mistaque ?

Answer 33

3q^2 -10q +2 =0
discriminant = ?

Answer 34

is it \[b^2-4ac>0\]

Answer 35

please you write here your calculi for i can checking where are you doit wrong

Answer 36

sry,i don't get u
r u asking me solve the equation using the b^2-4ac>0 ?

Answer 37

yes - you get for discriminant 76 - yes so what not is a perfect square

Answer 38

i'm not sure
can u tell me @jhonyy9

Answer 39

3q^2 -10q +2 = 0
D = 76

q1,2 = ?

hope you know formula to sole it - yes ?

Answer 40

to solve it

Answer 41

what formula ?

Answer 42

formula how you calculi the roots of a quadratic with discriminant greater than zero

Answer 43

\[b^2-4ac>0\]\[(-10)^2-4(3)(2)>0\]\[76>0\]

Answer 44

yes but this is how you calculi the discriminant so what mean that the discriminant is greater than zero ?

Answer 45

so this mean that this quadratic has two different real roots - yes ?

Answer 46

yes

Answer 47

so continue calculi these roots of

Answer 48

formula for ?

Answer 49

\[3q^2-10q+2>0\]

Answer 50

q1,2 = (-b+/- sqrt(discriminant) / 2a

yes ?

Answer 51

you dont know this formula ?

Answer 52

u mean the quadratic formula

Answer 53

what i have wrote there above now

Answer 54

for q1,2

Answer 55

\[q=\frac{ -b~\pm \sqrt{b^2-4ac} }{ 2a }\]\[q=\frac{ -(-10)\pm \sqrt{76} }{ 2(3) }\]\[q=3.120~and~q=0.214\]

Answer 56

so than you substitute 3,120 you get p=10 ?

Answer 57

i got p=10.00102564

Answer 58

so this will be right ?

Answer 59

but now i have a different idea for you can solve it

Answer 60

using the rule of 3 simple

do you know it ?

Answer 61

no :/

Answer 62

when q increase 4 unit/sec so than you make the calculi you get p= 12,5 unit/sec

q p

4 u/sec 12,5 u/sec

x 10 u/sec
-------------------------------------

x = (10*4)/12,5 = 3,2 u/sec

x = 3,2 u/sec

- do you like this method ? do you understand it ?

Answer 63

so but i think that your result of 3120 will be more exactly like this 3,2

yes ?

Answer 64

but when u put q=3.2 into the equation p=3q+(2/q) it does not get p=10.

Answer 65

yes i understand you but above how you have got this 10,0001... result for p for what substituted root of q ?

Answer 66

i think 3,120 - yes ?

Answer 67

This has been a long conversation! MARC_ : What do you still need to know, at this point?

Answer 68

when u substitue q=0.214 u will also get p=10 when u round off
but the question say that find the positve value of q..
so q can't be two values right?

Answer 69

@mathmale your opinion please ?

Answer 70

The topic for this question is differentiation

Answer 71

the answer is 2. as you posted above

Answer 72

thank you @ganeshie8 so i have a question please - than you see above where Marc have got q=2 have made these calculi for equation when p= 3q + q/2
- after he have said that correct this equation wann being p = 3q + 2/q

- what is your opinion about this ,please ?

Answer 73

Thnx @Zarkon

Answer 74

@jhonyy9

"p = 3q +2/q

10 = 3*2 +2/2"

here,
p is not given as 10, dp/dt is = 10.
thats what confused you.
MARC's work is fine.

Answer 75

Thnx @hartnn