eNotes Homework Help is a way for educators to help students understand their school work. Our experts are here to answer your toughest academic questions! Once it’s posted to our site, your question could help thousands of other students.
Popular Titles
Showing
in
Math

MathThe man sold 400 shares with a face value of Rs. 20 paying 5% at a price of Rs. 18 and invested the proceeds in shares with a face value of Rs. 10 shares paying 7% which he could buy at a price of...

MathWe have to rationalize the denominator in sqrt 3/ ( 5  3*sqrt 3) This can be done by multiplying the numerator and denominator by (5 + 3*sqrt 3). Using the relation (a  b)(a + b) = a^2  b^2...

MathWe have to rationalize the denominator in 7 / ( 3* sqrt 6 + 2) This can be done by multiplying the numerator and denominator by (3* sqrt 6  2). Using the relation (a  b)(a + b) = a^2  b^2 gives...

MathThe question asks us to rationalize the denominator in the expression 1 divided by 1 + sqrt 2. => 1/(1 + sqrt 2) * (1  sqrt 2)/(1 sqrt 2) => (1 sqrt 2)/( 12) => (1  sqrt 2)/1 =>...

MathWe have to find the angle ABC given the points A( 1,2,3), B(5,4,3) and C(2,1,2) This can be done by using the law of cosines. First we need to determine the length of AB, BC and CA. The length of...

MathFor any two vectors, the dot product is a scalar. We have to show that a.b = (1/4)(a + b)^2  (1/4)*(a  b)^2 (1/4)(a + b)^2  (1/4)*(a  b)^2 factorize (1/4) => (1/4)[ (a + b)^2  (a  b)^2]...

MathTo find the magnitude of 3A + 2B, we need to add 3A and 2B. The angle between A and B is given as 120 degrees. The component of 3A in the direction of 2B is given by 3A* cos 30. So we have 2B ...

MathThe remainder function is an easy way of determining whether a term ( x  a) is a factor of a polynomial P(x). Whenever P(x) is divided by (x  a), the value of P(a) is the remainder that P(x)...

MathThis question has been previously asked and answered. Please see the link below, and thank you for using eNotes!

MathWe are given that log(x+1) (x^2+3x14)=2. We know that log(a) b = c => b = c^a log(x+1) (x^2+3x14)=2 => x^2 + 3x  14 = (x + 1)^2 => x^2 + 3x  14 = x^2 + 1 + 2x => x = 15 The required...

MathWe have to ind the derivative of f(x)= 1/x^2  1. We use the formula for derivative of f(x) = x^n, f'(x) = n*x^(n) f(x)= 1/x^2  1 => f(x)= x^(2)  1 f'(x) = 2*x^(3) => 2/ x^3 The...

MathThe slope of tangent to a curve y is given by the value of y' at any point on the slope. For f(x)= 4x^3 +30x^2 + 48x36 f'(x) = 12x^2 + 60x + 48 The tangent is horizontal when the slope is 0. =>...

MathThe xintercepts for a function are the points where the graph of the function meets the xaxis. Here the value of f(x) is 0. For the given equation of the parabola: y = x^2 + 4x  3, we find the...

Math232 in base 5 notation is equal to 2*5^2 + 3*5^1 + 2*5^0 => 2* 25 + 3*5 + 2 => 50 + 15 + 2 => 67 in decimal notation Similarly 43 => 4*5^1 + 3*5^0 => 4*5 + 3 => 23 in decimal...

MathThe sum of the roots of a quadratic equation is 8 and their product is 12. What is the quadratic...Let's assume the roots of the equation are r1 and r2. We have (x  r1)(x  r2) = 0 => x^2  x*r1  x*r2 + r1*r2 = 0 => x^2  x( r1 + r2) + r1* r2 = 0 The sum of the roots is given as 8 and...

MathAs 2x + 3, x + 4 and 3x  4 are terms of an AP, they have a common difference. We can write this as: (2x + 3)  (x + 4) = (x + 4)  ( 3x  4) => 2x + 3  x  4 = x + 4  3x + 4 => x  1 = 2x...

MathYou need to solve the integral:`int (x^2 dx)/sqrt(25  x^2)` You need to write the integral such that: `int x*(x/sqrt(25  x^2))*dx` You may use integration by parts such that: `u = x=gt du = dx`...

MathWe have to find the area of the triangle with vertices A(1, 3, 5) , B(2, 3 , 4) and C(0, 3 , 1). The length of the sides are: AB = sqrt [( 1 + 2)^2 + ( 3 + 3)^2 + (5 + 4)^2] => sqrt ( 9 + 36...

MathYes, roots means the values of x for which f(x) is equal to 0. The roots represent points where the graph of the function crosses the xaxis. To find the roots of f(x)= 2x^2 + 3x 20, we equate it...

MathThere are three measures of central tendency. Mean, median, and mode. The mean is a typical average. You add up all the numbers then divide by how many numbers you have. In this problem: 83 +...

MathWe see that the dimensions of the box are 8 inches * 2 inches * 6 inches. All the three sides are multiples of 2. So it is possible to fill the entire volume of the box with 2inch cubes without...

MathSteven walks from town A towards town B at 100m/min. Jason walks from town B towards town A at 80m/min and Melvin walks from town B towards town A at 75 m/min. Let the distance between A and B be...

MathThe man in the passenger train is travelling at 72 km/h. He observes a goods train travelling in the opposite direction at 54 km/h. The relative speed of the goods train to the passenger is 72 + 54...

MathWe have to solve the equations: (x1)^2  (xy)(x+y)  (y2)^2 =  59 ...(1) 2x = 64  5y...(2) (x1)^2  (xy)(x+y)  (y2)^2 =  59 => x^2 + 1  2x  x^2 + y^2  y^2  4 + 4y = 59 => 56...

MathWe have the equation of the tangent at the vertex equal to x + y = 1. x + y = 1 => y = x + 1 The slope of the tangent is 1, the slope of the line perpendicular to the tangent is 1. This line...

MathYou have provided the following information: a = 2^(1/3) + 1, b = 2^(1/3) 1. We need to determine the value of ( a^2  b^2)^3 ( a^2  b^2)^3 => [( a  b)(a + b)]^3 => [(2^(1/3) + 1  2^(1/3)...

MathWe have to find m from the equation: 2^x + 2^x + 1 = m*2^x + 2 As the information provided is not sufficient I assume x takes on integer values only. 2^x + 2^x + 1 = m*2^x + 2 => 2*2^x  1 =...

MathI'm not going to round all the numbers you have provided. I'm going to give you an idea of the rules you should follow with two of them: 2.095: This is rounded off to 2.1 5.058: This is rounded off...

MathThe arithmetic mean of a series of terms is their sum divided by their total number. The arithmetic mean of the terms we have is: (31+35 + 27 + 29 + 32 + 43 + 37 + 41 + 34 + 28 + 36 + 44 + 45 +...

MathThe equation of a line with a yintercept of c and a slope of m is given as y=mx + c. The line we have to determine is parallel to the line 2x  3y = 7. This is possible if they have the same...

MathWe have to solve: (x+y)^2 = (x1)(y+1) (x+y)^2 = (x1)(y+1) => x^2 + y^2 + 2xy = xy + x  y  1 => x^2 + y^2 + xy  x + y + 1 = 0 As there are two variables x and y but only one equation, we...

MathThe equation you gave is : 16^2 + (7=x)^2 = (22 (2x/5)^2 I think it should be 16^2 + (7  x)^2 = 22  (2x/5)^2, the appropriate changes have been made. 16^2 + (7  x)^2 = 22  (2x/5)^2 => 16^2...

MathWe have the variables x and y which have to be determined using the given equations 4x^2 + 6x + 2 = 0 ...(1) x + 6y = 0 ...(2) Using (1), we find x. 4x^2 + 6x + 2 = 0 => 4x^2 + 4x + 2x + 2 = 0...

MathYour question is incorrect as the diagonals of a rectangle are equal. I am changing the question to the lengths of the sides being equal to 14 and 21. The area of a rectangle with sides 14 and 21...

MathFor two vectors: a = (ax)i + (ay)j + (az)k b = (bx)i + (by)j + (bz)k a + b = (ax + bx)i + (ay + by)j + (az + bz)k The cross product of two vectors is the product of their magnitude and sine of the...

MathFor three vectors: a = (ax)i + (ay)j + (az)k b = (bx)i + (by)j + (bz)k c = (cx)i + (cy)j + (cz)k, a.b = (ax)(bx) + (ay)(by) + (az)(bz) and b.c = (bx)(cx) + (by)(cy) + (bz)(cz) a + (b.c) is the...

MathFor three vectors: a = (ax)i + (ay)j + (az)k b = (bx)i + (by)j + (bz)k c = (cx)i + (cy)j + (cz)k, a.b = (ax)(bx) + (ay)(by) + (az)(bz) and b.c = (bx)(cx) + (by)(cy) + (bz)(cz) a.(b.c)= a....

MathGiven f(x) = 2x^2 + 3x  20 We need to find the roots of f(x). Then, we need to find x and f(x) values such that f(x) = 0 ==> 2x^2 + 3x 20 = 0 We will use the roots formula : ==> x1= = (3 +...

MathHi ibrohi! The three main measures of central tendency are mean, median, and mode. 1) The mean, also referred to as the average, can be found by adding together the scores of each exam, and then...

MathTwo lines which are not parallel to each other are intersecting. As your question mentions line segments there could be a possibility that they don't intersect but if they are extended to form...

MathLet the amount of money that is divided be C. It is divided in the ratio 10 : 7 : 5 among X, Y, Z. This can be written in another way as X gets 10/ 22 of the amount, Y gets 7/22 of the amount and Z...

MathThe question asks for the solution of sec x = tan x + cot x in the interval [0,2pi]. => sec x = tan x + cot x => 1/cosx = (sin x/cos x )+ (cos x/ sin x) => (sin x) (cos x) [1/cos x] = (sin...

MathWe have to express the following with a rational denominator: (sqrt 5 + 4) / 2*sqrt 3 multiply the numerator and denominator by sqrt 3 => [(sqrt 5 + 4)* sqrt 3] / [2*sqrt 3* sqrt 3] => (sqrt...

MathWe have to express the following with a rational denominator: (3  sqrt 2) / sqrt 2 multiply the numerator and denominator by sqrt 2 => [(3  sqrt 2)* sqrt 2] / [sqrt 2 * sqrt 2] => (3*sqrt 2...

MathWe have to express the following with a rational denominator: 2*sqrt 3 / 3*sqt 10 multiply the numerator and the denominator by sqrt 10 => (2*sqrt 3* sqrt 10) / (3*sqt 10* sqrt 10) => 2sqrt...

MathGiven that xy = 12 and 1/x 1/y = 3, we are to find x*y. => 1/x 1/y = 3 => [xy/1] [1/x 1/y] = 12 => (y  x) /xy = 3 => 3xy = y  x => 3xy = x  y => 3xy = 12 =>...

MathWe have to find x for which cos 4x = cos 2x we use the relation cos 2x = 2(cos x)^2  1 cos 4x = cos 2x => 2(cos 2x)^2  1= cos 2x => 2(cos 2x)^2  cos 2x  1 = 0 => 2(cos 2x)^2  2cos 2x...

MathSince the directions to solving a Rubiks Cube are so long and are difficult to explain without actual pictures, I have included a few websites below that provide detailed stepbystep instructions...

MathThe magnetic force is given by FM = I*B, where I is the charge multiplied by the velocity of the charged particle. I = 4.0*10^6*1.6*10^19 The magnetic field is equal to 0.2 Tesla directed in a...

MathWe have the two equations x^2 + 8y^2 + 4 = 0 and 4x^2 + 4x + 1 = 0 to solve. 4x^2 + 4x + 1 = 0 use a^2 + 2ab + b^2 = (a + b)^2 => (2x + 1)^2 = 0 => x = 1/2 substitute in x^2 + 8y^2 + 4 = 0...