Enable contrast version

Tutor profile: Nicholas H.

Inactive
Nicholas H.
College student: Tutor for several years
Tutor Satisfaction Guarantee

Questions

Subject: Pre-Calculus

TutorMe
Question:

Solve the equation $$2\cos^2 3\theta = \cos 3\theta$$ for $$ 0\le \theta <2\pi$$.

Inactive
Nicholas H.
Answer:

$$2\cos^2 3\theta = \cos 3\theta$$ gives $$2\cos^2 3\theta-\cos 3\theta=0$$, so $$(\cos 3\theta)(2\cos 3\theta -1)=0$$. Therefore $$\cos 3\theta=0$$ or $$\cos 3\theta=1/2$$, so either $$3\theta=\pi/2, 3\pi/2, 5\pi/2, 7\pi/2, 9\pi/2, 11\pi/2$$ or $$3\theta=\pi/3, 5\pi/3, 7\pi/3, 11\pi/3, 13\pi/3, 17\pi/3$$. Dividing by 3 to find $$\theta$$, we obtain the solutions $$\theta=\pi/6,\pi/2,5\pi/6,7\pi/6,3\pi/2,11\pi/6$$ and $$\theta=\pi/9,5\pi/9,7\pi/9,11\pi/9,13\pi/9,17\pi/9$$.

Subject: Calculus

TutorMe
Question:

Prove that a infinite sequence .99999...= 1

Inactive
Nicholas H.
Answer:

$$ .999... = \sum_{i=1}^{\infty} \frac9{10^i} = \sum_{i=1}^{\infty} \frac{10-1}{10^i} = \sum_{i=1}^{\infty} (\frac{10}{10^{i-1}} - \frac{1}{10^i}) = \frac{1}{10^0} = 1$$ This proves that .999... = 1

Subject: Economics

TutorMe
Question:

How does the increase of minimum wage affect the economy?

Inactive
Nicholas H.
Answer:

Recent evidence shows that any effects of raising the minimum wage would not be extremely significant, but by raising the minimum wage, it is known that the purchasing power of individuals will increase, and reducing employee turnover, which are both positive effects for the consumers.

Contact tutor

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

Request lesson

Ready now? Request a lesson.
Start Lesson

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 Lesson" 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.