TutorMe homepage
Subjects
PRICING
COURSES
Start Free Trial
Nima M.
Tutor and Physicist
Tutor Satisfaction Guarantee
Calculus
TutorMe
Question:

Integrate $$\int ln(x)dx$$.

Nima M.

Let $$dv = dx$$ and $$u = ln(x)$$. By integration by parts $$uv - \int vdu$$. So we get: $$xln(x) - \int x \times \frac{1}{x}dx$$ = $$xln(x) - \intdx$$ which is consequently $$xln(x) - x + C$$ where C is an arbitrary constant

Statistics
TutorMe
Question:

The probability of getting an 100% on a test is 3 % , 90 % on the test is 20% , 80 % on the test is 60% and a 70% on the test is 17%. What is the average grade of the test?

Nima M.

Using the definition of average = $$\Sigma_{i} x_{i}p_{i}$$ which results in $$100\times.03 + 90\times.2 + 80\times.6 + 70\times.17 = 80.9$$

Physics
TutorMe
Question:

Explain why mathematically the gravitational pull of a black hole(the mass of the earth) 2cm in diameter is stronger than the Earth's pull at their respective surface.

Nima M.

Using Newton's Law of Gravitation is $$F = \frac{GM_{1}M_{2}}{r^2}$$ Assume inline LaTeX $$M_{1}$$ is 1 Kg and $$M_{2} = 5.972 \times 10^{24} kg$$ where the radii of the Earth and the black hole are $$r = 6.371 \times 10^{6}m, 10^{-2}m$$ Plugging in the formula, Force of attraction of Earth is $$9.81646 N$$ Force of attraction of the black hole is approximately $$3.98 \times 10^{18}$$

Send a message explaining your
needs and Nima will reply soon.
Contact Nima
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.