TutorMe homepage
Subjects
PRICING
COURSES
SIGN IN
Start Free Trial
Jonathan X.
Tutor for 2 months
Tutor Satisfaction Guarantee
Pre-Calculus
TutorMe
Question:

Find the vertex of the parabola y=2x^2-8x+7

Jonathan X.
Answer:

We have that x=-b/2a=-(-8)/(2*2) = 2, and then y = 2(2^2)-8(2)+7=-1

Calculus
TutorMe
Question:

Use implicit differentiation to find dy/dx for the given expression 3xy-2x^2*y = 1

Jonathan X.
Answer:

First take the derivative of 3xy using the product rule in which (3xy)' = 3y+3x*dy/dx and then take the derivative of (2x^2y)' which equals 4xy + 2x^2*dy/dx so the following derived expression equals (3y+3x*dy/dx)-(4xy+2x^2*dy/dx) = 1. Next, I need to combine any like terms and isolate a few variables in which I need to isolate mainly dy/dx in which we are solving.

Differential Equations
TutorMe
Question:

Determine the characteristic polynomial of the given ODE and find the roots, 3y"+2y'+2=0.

Jonathan X.
Answer:

In order to determine and translate the given ODE into a characteristic polynomial, we must first consider the expression y=er^x. Next, take both the first and second derivative and then substitute both the expressions back into the ODE. Once that is done, the er^x is factored out and canceled out in which the characteristic polynomial is displayed as 3r^2+2r+2=0. From there, I have to solve for r and since this is the second order, I either go ahead and factor regularly or take the quadratic formula into consideration. Once that is all processed, I should receive my values.

Send a message explaining your
needs and Jonathan will reply soon.
Contact Jonathan
Ready now? Request a lesson.
Start Session
FAQs
What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Session" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.