Tushar Chandra
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About
I have formally taught math, physics, and chemistry.
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Recent Activity

Answered a Question in Math
P(x), Q(x), R(x), and S(x) are nonconstant polynomials with integer coefficients. Some such polynomials need to be found such that ` [[P(x),Q(x)],[R(x),S(x)]]^2 = [[1,0],[0,1]] `. First, square the... 
Answered a Question in Math
The demand for any product is dependent on the price at which it is offered to buyers. The relation between the price and the quantity buyers are willing to buy is decided by many factors, some of... 
Answered a Question in Math
In baseball, the batting average is determined by dividing the number of hits by the number of atbats. Harry's batting average before the game starts is 0.262. He goes 3 hits out of 5 atbats in... 
Answered a Question in Business
The demand curve is a function of price (P) and the number of items that buyers will be at that price, Q. The Cost curve is a function C(Q) that gives the total cost of producing a quantity Q. This... 
Answered a Question in Math
The maximum value of `8*27^(log_6x) + 27*8^(log_6 x)  x^3` has to be determined. Let `y = log_6x^3` `y = log_6x^3` `=gt 6^y = x^3` `8*27^(log_6x) + 27*8^(log_6 x)  x^3` `=... 
Answered a Question in Math
The probability of A is given by P(A) = N/M where N is the total number of events favorable to A, and M is the total number of possible events. For instance, consider a box with 5 red balls and 10... 
Answered a Question in Math
The number of eightdigit positive integers whose digits from left to right are strictly decreasing has to be determined. As the digits are strictly decreasing, for any two digits a, b where a... 
Answered a Question in Science
Photosynthesis is the process by which plants and other organisms like cyanobacteria convert energy from light to chemical energy. This allows energy in the form of solar radiation that is received... 
Answered a Question in Science
Consider a block of mass m is suspended from a spring with spring constant k. There are two forces acting on the block, one of which is due to the gravitational force and the other due to the... 
Answered a Question in Math
A cubic block with dimensions n*n*n is made up of units cubes of dimensions 1*1*1. The total number of unit cubes in the cubic block is n*n*n. If the outer two layers of the cubic block are... 
Answered a Question in Science
When a bicycle moves, there is contact made between the wheels of the bicycle and the ground. Rolling friction between the wheel and the ground restricts the motion of the wheel. This force is... 
Answered a Question in Math
The value of `tan^2 20 + tan^2 40 + tan^2 80` has to be determined. We start with the values of `tan 60` , `tan 120` , and `tan 240` . All three equal `sqrt 3` . `tan 60 = tan 3*20 = sqrt 3` `tan... 
Answered a Question in Economics
The increase in average prices in an economy is known as inflation. If price levels were to double in a certain year, there is an increase in price or inflation of 100%. This leads to the... 
Answered a Question in Math
For any triangle with sides of length a, b, c, the inradius `r = Delta/s` where s is the semiperimeter. `s = (a+b+c)/2` `Delta = sqrt(s(sa)(sb)(sc))` `r = Delta/s` r has to be written in terms... 
Answered a Question in Math
For a triangle ABC, where r represents the radius of the incircle and R represents the radius of the circumcircle, the following identity has to be proved: `r = 4R sin (A/2) sin (B/2) sin (C/2)`... 
Answered a Question in Math
The payoffs for winning bets are: 1 to 1 on odd, even, red and black 2 to 1 on a column 11 to 1 on a street 35 to 1 any one number In American roulette, there are pockets numbered 0 to 36, with... 
Answered a Question in Science
There are many ways in which plants can be propagated. One way of classifying this is sexual and asexual. Sexual propagation occurs from the growth of new plants from seeds. Seeds are formed by the... 
Answered a Question in Business
Capital gain refers to the increase in the value of a capital asset. This can be anything like a stock, real estate, a piece of art, and so on. On the other hand, if the value of the asset declines... 
Answered a Question in Chemistry
Magnesium oxide is a compound of magnesium and oxygen with chemical formula MgO. Each molecule of magnesium oxide has one atom of magnesium and one atom of oxygen. To identify the percentage... 
Answered a Question in Math
Sally won $250,000 in a lottery. She bought a new car for $42,000 and new clothes for $650. She invested the rest at 4.9% per annum, compounded biweekly and withdrew an equal amount of money every... 
Answered a Question in Math
Stephanie plans to buy a big screen TV in 2 years. She believes the selling price will be $1,800 at that time. A tax of 13% will be added to the selling price. The total price that Stephanie has to... 
Answered a Question in Math
Stephanie plans to buy a big screen TV in 2 years. She believes the selling price will be $1,800 at that time. Stephanie decides to make monthly deposits into an account that pays 4.8% per annum,... 
Answered a Question in Math
A principal amount, at a rate of simple interest r per annum, after a time period t years increases to `P_f = P+P*t*r` Compound interest refers to the situation where interest in any period is... 
Answered a Question in Math
A principal amount P, at the rate of interest r per annum, after a time period t years increases to `P_f = P+P*t*r` Compound interest refers to the situation where interest in any period is earned... 
Answered a Question in Math
A principal amount P, at the rate of interest r per annum, after a time period t years increases to `P_f = P + P*t*r` Compound interest refers to the situation where interest in any period is... 
Answered a Question in Math
In 3 years Yvonne wants to purchase a 60 inch HDTV for $4,500 including taxes. He deposits $3,100 into a savings plan today that pays 4.2% per year, compounded yearly. The extra amount he needs to... 
Answered a Question in Math
Nicole deposits $350 in an account every month for 10 years. The amount she will have at the end of 10 years for an interest rate of 3.7% per annum, compounded monthly, has to be determined. The... 
Answered a Question in Math
Marisa borrows $4,400 for 6.5 years at a fixed rate of simple interest. At the end of that time she owes $7,500. The annual rate of interest being charged has to be determined. An amount P, at an... 
Answered a Question in Math
Matthew has two options to save money for his retirement. His two best options are 3.95% compounded monthly or 4% compounded annually. A principal amount P at an annual interest rate of r, after N... 
Answered a Question in Math
Jeremy would like to withdraw $750 from his account every six months for the next 5 years. The account pays 3.8% per annum compounded semiannually. The initial amount to be deposited to enable... 
Answered a Question in Math
Jack receives a lump sum payment of $260,000 from the company pension plan which is used to purchase an annuity that gives equal semiannual payments for 10 years. The rate of interest is 8%... 
Answered a Question in Math
Nancy deposits $300 into her savings account at the end of every 3 months for 2 years. The account pays 3.5% per annum, compounded quarterly, and the amount Nancy has after 2 years has to be... 
Answered a Question in Math
The interest earned on a principal of $846.81 invested at an interest rate of 5% over 2 years has to be determined. If an amount P is invested for t years at an interest rate r, the simple interest... 
Answered a Question in Math
An amount of $6.65 is borrowed for 6 years at an interest rate of 10%. It is not mentioned if we need to determine simple interest or compound interest. If simple interest has to be determined for... 
Answered a Question in Math
Let the amount initially borrowed by Amanda be P. The rate of interest at which this is borrowed is 4.36% per annum, compounded quarterly. The present value of an amount P after t terms, borrowed... 
Answered a Question in Math
Alisha plans to attend university next year. Her grandmother wishes to deposit enough money today in an account paying 5.5% compounded annually so that she can make withdrawals of $5,000 at the end... 
Answered a Question in Science
Ka and Kb refer to the acid and base dissociation constants of a compound. These indicate the extent to which an acid or a base dissociates. A strong acid has a large Ka value, and a strong base... 
Answered a Question in Science
The electrolysis of water is given by the equation: `2 H_2O > 2 H_2 + O_2` When the given sample of water undergoes electrolysis, 1.1682 L of gas is produced at a temperature 273.15 K and... 
Answered a Question in Math
The number of pairs (m,n) of positive integers satisfying `1lt=mltnlt=30` have to be determined so that a real number x exists that allows `sin(mx) + sin(nx) = 2` . For the sine function, the... 
Answered a Question in Science
CAR 1, having a mass of 1,200 kg and traveling with a velocity of 23 m/s due east, has a completely inelastic collision with CAR 2, having a mass of 1,400 kg and a velocity of 28 m/s due west. In a... 
Answered a Question in Science
When two objects undergo an elastic collision, both momentum and kinetic energy are conserved. There is no net loss of the total kinetic energy in the collision. A baseball bat of mass of 2 kg... 
Answered a Question in Science
Impulse or the change in momentum is defined as P = F*t, where F is the net average force and t is the time for which the force F acts. For the same impulse, either a small force acts over a long... 
Answered a Question in Math
The prime factorization of the number N = 343,463,270 is 2 x 5 x 1,733 x 19,819. This can be used to determine the odd and even divisors. The even divisors of the number N are 2, 10, 3,466, 17,330,... 
Answered a Question in Math
For the number given N = 343,463,270. First we need to find the odd and even divisors. First, determine the prime factorization of N. 343,463,270 = 34,346,327 × 10 = 2 × 5 × 34,346,327 = 2 × 5 ×... 
Answered a Question in Math
S is a finite set of positive integers. Let there be N integers in the set and the arithmetic mean of all the integers be M. The sum of all the integers in the set S is M*N. When the greatest... 
Answered a Question in Math
A combination refers to the number of ways of choosing a certain number of elements when the order in which they are chosen is not relevant. Permutations on the other hand refer to picking elements... 
Answered a Question in Math
The least possible value of `(xy  1)^2 + ( x + y )` has to be determined. The least value of `(xy  1)^2` is 0, as the square of both negative as well as positive numbers is positive. If either x... 
Answered a Question in Math
The solutions of `cos(pi/2*sin x) = sin(pi/2*cos x)` have to be determined. `cos(pi/2*sin x) = sin(pi/2*cos x)` `=> sin (pi/2  pi/2*sin x) = sin(pi/2*cos x)` `=> pi/2  pi/2*sin x = pi/2*cos... 
Answered a Question in Math
A choir director has to select a group of singers from among her 6 tenors and 8 basses. The difference between the numbers of tenors and basses must be a multiple of 4, and the group must have at... 
Answered a Question in Math
The sum of two natural numbers is 17402. One of these numbers is divisible by 10. If the units digit of this number is erased, the other number is obtained. The difference of the two numbers has to...
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