TutorMe homepage

SIGN IN

Start Free Trial

Dillon M.

Engineering Student at SDSU

Tutor Satisfaction Guarantee

Pre-Calculus

TutorMe

Question:

Find the zeros of the following polynomial function. $$F(x) = x^3 +7x^2 +12x$$

Dillon M.

Answer:

First, see if any of the components of the problem share a variable. In this situation they all share an x, allowing it to be factored out. $$F(x) = x(x^2 + 7x+ 12)$$ Now, try to factor out the exponents. $$F(x) = x((x+4)(x+3))$$ Based off of this factoring, one can distinguish that -4, -3, and 0 are all zeros because: 0 = -4 -4 0 = -3 -3 0 = 0 - 0 zeros = -4, -3, 0

Mechanical Engineering

TutorMe

Question:

A hook is drilled into a wall and has two cables attached to it pulling away from it. If one cable pulls away from the wall 300N at an angle of 40deg from the horizontal of another pulls 200N -25deg from the horizontal, what is the magnitude and direction of the resultant vector. If the cement it is drilled into has a critical strength of 500N, does the system fail?

Dillon M.

Answer:

By starting both vectors at (0, 0), one can use Cartesian vector combination by deriving the x and y components of each vector and adding them: $$ F1 = (300cos(40))i + (300sin(40))j$$ $$F2 = (200cos(25))i - (200sin(25))j$$ here you combine the i components and combine the j components to create one vector $$ F(r) = [300cos(40) +200cos(25)]i + [300sin(40) - 200sin(25)]$$ $$ F(r) = 411.1i + 108.3j$$ $$\mid F(r) \mid = \sqrt{411.1^2 +108.3^2}$$ $$\mid F(r) \mid = 425.2N$$ $$\Theta = tan(108.3 / 411.1)$$ $$\Theta = 27deg$$ F(fail) < F(r), therefore the system does not fail

Calculus

TutorMe

Question:

Solve the given integral. f(x) = $$\int_0^{\pi/3}xcos(4x)dx$$

Dillon M.

Answer:

The first step to this problem is identifying that you are going to use the integration by parts method for solving this problem. You know to do this because the x outside of the cosine function makes u-substitution impossible. For integration by parts, one must determine which part of the function one wants to be the "u" and which to be the "dv". The basic rule is the more complicated of the two should be the dv and this stands true in this problem: $$u = x, dv = cos(4x)$$ Once these pieces have been identified one must solve u for du and integrate dv for v: $$u = x$$ $$dv = xcos(4x)$$ $$du = dx$$ $$v=(1/4)sin(4x)$$ With these pieces solved for one can insert them into the integration by parts equation and solve: $$\int_a^b{u} dv = uv - \int_a^b{vdu}$$ $$\int_0^{\pi/3}xcos(4x)dx = [x(1/4)sin(4x)]_0^{\pi/3}-\int_0^{\pi/3}(1/4)sin(4x)dx$$ $$ = [(x/4)sin4x ]_0^{\pi/3}+[(1/16)cos(4x)]_0^{\pi/3}$$ Next, plug the limit values in for x in the form of $$ f(b) - f(a) = f(x)]_a^b$$ f(x) = $$ =(\pi/12)sin(4\pi/3) + (\pi/48)cos(4\pi/3)$$ ...and solve $$f(x) = (\pi/12)(-\sqrt3/2) + (\pi/48)(-1/2) $$ $$ f(x) = (-\pi\sqrt3/24) - (\pi/96)$$

Send a message explaining your

needs and Dillon will reply soon.

needs and Dillon will reply soon.

Contact Dillon

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.

Made in California

© 2019 TutorMe.com, Inc.