tricky first order differentials questions

1: I have no clue on this one.

https://cdn.discordapp.com/attachments/345181731663642624/754397442337931346/IMG_20200912_184554.jpg

QUESTION 13 BOTH PARTS

My issue here is that it is in the 1st order differentials chapter of my book but as it is a quadratic so it must be 2nd order? There also doesnt seem to be enough information to work from.

Reply 1

mqb2766

21

Original post by Cpt Avocado

1: I have no clue on this one.

https://cdn.discordapp.com/attachments/345181731663642624/754397442337931346/IMG_20200912_184554.jpg

QUESTION 13 BOTH PARTS

My issue here is that it is in the 1st order differentials chapter of my book but as it is a quadratic so it must be 2nd order? There also doesnt seem to be enough information to work from.

It's first order but the derivative is a quadratic function of t.
Is the max value 0.8? If so, it's possible to write it down?

Reply 2

Cpt Avocado

OP

9

im not sure, i guess it must be but the graph isnt very clear

Reply 3

mqb2766

21

Original post by Cpt Avocado

im not sure, i guess it must be but the graph isnt very clear

If guess it is. Can you write the quadratic down?

Reply 4

username5398004

20

Make a tangent to a point to find the gradient, this will help you find out the equation of the graph. Then differentiate it

Original post by Cpt Avocado

1: I have no clue on this one.

https://cdn.discordapp.com/attachments/345181731663642624/754397442337931346/IMG_20200912_184554.jpg

QUESTION 13 BOTH PARTS

My issue here is that it is in the 1st order differentials chapter of my book but as it is a quadratic so it must be 2nd order? There also doesnt seem to be enough information to work from.

Look at the vertical axis. It represents

\dfrac{dM}{dt}

.

So the quadratic is precisely that. You know the two roots of the quadratic, and the maximum value of it, so you can easily write down the ODE.

(edited 3 years ago)

Reply 6

JESSEMFUNDA

3

For question a )Find the equation of the graph, simple. Because its the rate of change to the pumpkin's mass, rate of change=diffrentationFor question b) Use the differential equation to find the maximum mass of the pumpkin by integrating the differential equation to find the original equation or function. the maxima of the cubic graph will equal the maximum mass of the pumpkin.

Reply 7

Cpt Avocado

OP

9

the answer is 0.05t(8-t)
using (4,0.8) as the turning point i got
dm/dt =- 0.05(t-4)^2 0.8
not sure how to get to the answer from that but i may have gone wrong somewhere

edit: made a correction to dm/dt

(edited 3 years ago)

Original post by Cpt Avocado

the answer is 0.05t(8-t)
using (4,0.8) as the turning point i got
dm/dt = 0.05(4-t)+0.8
not sure how to get to the answer from that but i may have gone wrong somewhere

What you have isn't even a quadratic.

All you need to do is construct the equation of a quadratic which has roots at x=0 and x=8, and a max point of 0.8 at x=4.

Reply 9

mqb2766

21

Original post by Cpt Avocado

the answer is 0.05t(8-t)
using (4,0.8) as the turning point i got
dm/dt = 0.05(4-t)+0.8
not sure how to get to the answer from that but i may have gone wrong somewhere

Use the complete the square form together with the root(s) if you want to use the max point directly.

Reply 10

Cpt Avocado

OP

9

yh i got it, thanks for the help

Reply 11

Cpt Avocado

OP

9

Original post by RDKGames

What you have isn't even a quadratic.

All you need to do is construct the equation of a quadratic which has roots at x=0 and x=8, and a max point of 0.8 at x=4.

i made a typo which i have now edited so it is correct now. i got the correct answer too

tricky first order differentials questions

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