Akash Goyal

Carnegie Mellon University

Tutor

Biography

Tutor with experience on chegg and coursehero

Education

BS Mathematics

Carnegie Mellon University

Educator Statistics

Numerade tutor for 5 years

104 Students Helped

Topics Covered

Unlocking the Power of Functions: Boost Your Programming Skills

Breaking Limits: Unlock Your Potential with Our Expert Solutions

Explore the Power of Continuous Functions: Boost Your Mathematical Skills

Mastering Partial Derivatives: Essential Techniques and Tips

Discover the Best Series to Binge-Watch | Your Ultimate Guide

Akash's Textbook Answer Videos

Vector Calculus

If $z=f(x-y),$ use the chain rule to show that $\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=0$

Chapter 2: Differentiation

Section 5: Properties of the Derivative

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Prove that if $p, q, r(p \neq q)$ are terms (not necessarily consecutive) of an A.P., than there exists a rational number $k$ such that $\frac{(r-q)}{(q-p)}=k$.

Chapter 9: Progressions

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Find the number of terms common to the two A.P.'s $3,7,11, \ldots, 407$ and $2,9,16, \ldots, 709$.

Chapter 9: Progressions

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Prove that there are 17 identical terms in the two A.P.'s $2,5,8,11, \ldots 60$ terms and $3,5,7,9, \ldots 50$ terms.

Chapter 9: Progressions

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

The fifth term of an A.P. is 1 whereas its 3 1st term is $-77$. Find its 20 th term and sum of its first fifteen terms. Also find which term of the series will be $-17$ and sum of how many terms will be 20 .

Chapter 9: Progressions

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Akash's Quick Ask Videos

A gold-colored ring has a mass of 18.9 grams and a volume of 1.12mL. Is the ring pure gold? (The density of gold is 19.3 g/mL.)

Physics 101 Mechanics

An aeroplane is flying with a uniform speed of 100 m/s along a
circular path of radius 100 m. the angular speed of the aeroplane
will be [KCET 2000]
(a) 1 rad/sec (b) 2 rad/sec
(c) 3 rad/sec (d) 4 rad/sec

Physics 101 Mechanics

A stone is tied to one end of a string 50 cm long is whirled in a
horizontal circle with a constant speed. If the stone makes 10
revolutions in 20 s, what is the magnitude of acceleration of the
stone
(a) 493 cm/s2 (b) 720 cm/s2
(c) 860 cm/s2 (d) 990 cm/s2

Physics 101 Mechanics

body moves with constant angular velocity on a circle. Magnitude
of angular acceleration
(a) r?2 (b) Constant
(c) Zero (d) None of the above

Physics 101 Mechanics

A 100 kg car is moving with a maximum velocity of 9 m/s across a
circular track of radius 30 m. The maximum force of friction
between the road and the car is [Pb. PMT 2000]
(a) 1000 N (b) 706 N
(c) 270 N (d) 200 N

Physics 101 Mechanics

The maximum speed of a car on a road–turn of radius 30 m, if the
coefficient of friction between the tyres and the road is 0.4, will be [CBSE PMT 2000]
(a) 10.84 m/sec (b) 9.84 m/sec
(c) 8.84 m/sec (d) 6.84 m/sec

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