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

MathWhat you need to find here is (2xy^2y^4 divided by 3yx^1)^2 multiplied by (4xy divided by 2x^1y^3)^2 This can be written as: [(2xy^2y^4) / ( 3yx^1)]^2 * [4xy/2x^1y^3]^2 => [(2xy^2)/...

MathLet the square root of 3 + 4i be x + iy. So (x + iy) (x +iy) = 3 +4i => x^2 + xyi + xyi + i^2*y^2 = 3 + 4i => x^2 – y^2 + 2xyi = 3 + 4i Equate the real and complex terms => x^2  y^2 = 3...

MathThe slope of a line that passes through the points (x1, y1) and (x2, y2) is given by (y2  y1)/ (x2  x1) Here we have x1 = p , y1 = q , x2 = p  4 and y2 = q + 4 So the slope is ( q + 4  q) / ( p...

MathThe multiplicative inverse of 3 + 2i is the number that if multiplied by 3 + 2i gives 1. If the multiplicative inverse is x + iy. (x + iy)(3 + 2i) = 1 => x +iy = 1/(3 +2i) => x + iy = (3 ...

MathWe have 1/(x^2+x). Now this has to be expressed as the sum of two fractions 1/(x^2+x) => 1/ (x + 1)*x Let this be equal to A / x + B / (x +1) => [A(x + 1) + Bx]/ (x^2 + x) [A(x + 1) + Bx]/...

MathFirst let's determine z from i(z1)=2 i(z1)=2 => iz  i = 2 => iz = i  2 => z = i/i  2/i => z = 1  2/i => z = 1  2i / i^2 => z = 1 + 2i Now the absolute value is sqrt (...

MathWe have to find the definite integral of y=3^4x for x=0 to x=1 Now Int y = Int [ 3^4x] = 3^4x / 4* ln 3 Now for x = 1. 3^4x / 4* ln 3 = 3^4/4* ln 3 For x = 0 3^4x / 4* ln 3 = 3^0 / 4*ln 3 => 1 /...

MathWe have to find (cos x)^2, given that sin x / cos x = 2 sin x / cos x = 2 square both the sides => (sin x)^2/ (cos x)^2 = 4 => (1  (cos x)^2) / (cos x)^2 = 4 => 1/(cos x)^2  1 = 4 =>...

MathTo multiply (75i)(7+8i), First open the brackets and multiply all the terms with each other. Then simplify by adding the real and complex terms together. => 7*7 + 7*8i + 7*5i  40i^2 =>...

MathTo determine h(h(1/3)), first we'll have to determine the expression of h(h(x)). For this reason, we'll have to apply the rule of composition of 2 functions. (hoh)(x) = h(h(x)) We'll substitute x...

MathWe'll integrate using parts. Int udv = uv  Int vdu We'll put u = ln x. We'll differentiate both sides: du = dx/x We'll put dv = 1/sqrtx We'll integrate both sides; Int dv = Int dx/sqrtx v = 2sqrt...

MathWe'll multiply by 4 both sides: 4(sin x)^2 = 1 We'll subtract 1 both sides: 4(sin x)^2  1 = 0 We'll rewrite the difference of squares as a product: 4(sin x)^2  1 = (2 sin x  1)(2 sin x + 1)...

MathWe'll integrate by parts. For this reason, we'll consider the formula: Int udv = u*v  Int vdu (*) We'll put u = x. (1) We'll differentiate both sides: du = dx (2) We'll put dv = e^3x (3) We'll...

MathTake a right triangle with the hypotenuse equal to 1. Now let one of the other sides be equal to x. If the third side is s, s^2 + x^2 = 1 => s^2 = 1  x^2 => s = sqrt (1 x^2) Now for the...

MathGiven the lines : 2x  y + 2 = 0 x + y 4 = 0 We need to verify if the lines are parallel. First. we need to rewrite the equations into the slope form y= ax+b ==> 2x  y + 2 = 0 ==> y= 2x + 2...

MathThe vertex of a quadratic expression y = ax^2 + bx + c is given by ((b/2a), (4ac – b^2)/4a) We have y = 8x^2 + 4x – 3 Here a = 8, b = 4 and c = 3 –b/2a = 4 / 2*8 = 1/4 (4ac – b^2)/4a =...

MathWe can find the values of log using tables, but you will not find tables for logs to all bases. Therefore we use the formula to convert the given log which is has a base 7 to a log with base 10....

MathWe have to simply e^ (ln 2 + 3 ln x) Here we use the properties that d^ (a + b) = d^a * d^b e^ (ln 2 + 3 ln x) => e^ (ln 2) * e^ (3 ln x) a log b = log a^b => e^ (ln 2) * e^ (ln x^3) Now for...

MathTo find the LCM and GCF of a set of numbers it is best if we first write them as product of prime factors. Now 27 = 3*3*3 90 = 3*3*5*2 84 = 3*2*2*7 For the greatest common factor GCF take the...

MathIt is given that f(x) = 6x / (3x^3 + 4) Let t = 3x^2 + 4 dt / dx = 6x => dt = 6x dx Int [6x / (3x^3 + 4) dx] => Int [dt / t] => ln t + C replace t with 3x^2 + 4 => ln (3x^2 + 4) + C...

MathThe volume of a cone is given as (1/3)*pi*r^2*h. Now we know h= 8 and the volume is given as 96*pi. Equating the two and substituting the values we have: (1/3)*pi*r^2*8 = 96*pi => r^2=96*3/8...

MathWe have to find the derivative of y = sqrt (cos x) / x^2* sin x Now an easy way to find the derivative here is to use the logarithm. take the natural logarithm of both the sides: ln y = ln [sqrt...

MathThe velocity function of the particle is v (t) = 19t^2 – t. Now the instantaneous acceleration is the derivative of the velocity function. Therefore acceleration is v’ (t) = 38t  1. The...

MathThe equation x + 5y + 3 = 0 can be written as => 5y = x – 3 => y = (1/5) x – 3/5 This is of the form y = mx + c, where m is the slope and c is the yintercept. The slope of x + 5y + 3 =...

MathWe have to express 4x/ (4x^2 – 9) as a sum of fractions. We see that 4x^2 – 9 = (2x – 3) (2x + 3)\ Let A / (2x – 3) + B/ (2x + 3) = 4x/ (4x^2 – 9) => [(2x + 3) A + B (2x – 3)]/ (4x^2...

MathDenoting x^4 – 3x^3 + x – 4 by f(x), according to the remainder theorem if x – 5 is a root of x^4 – 3x^3 + x – 4, then f (5) = 0 Now, f (5) => 5^4 – 3*5^3 + 5 – 4 => 25*25 –...

MathWe have to solve for x and y using the equations: 5x + 3y = 14 … (1) 8x + 13y = 8 … (2) 8*(1) – 5*(2) => 40x + 24y – 40x – 65y = 112 – 40 => 41y = 72 => y = 72/ 41 5x + 3y =...

MathThe point equidistant from (1, 2), (4, 3) and (5, 8) is the point of intersection of perpendicular bisectors between any two sets of points. For the points, (1, 2) and (4, 3) the midpoint is (5/2,...

MathIn this problem we have to determine the point (x, y) that divides the line segment between (4, 2) and (8, 7) in the ratio 2:1 Now the coordinates of the point (x, y) that divides the distance...

MathWe can write the given equation of the circle, x^2 + y^2 – 8x – 6y = 0 as x^2 + y^2 – 8x – 6y = 0 => x^2 – 8x + y^2 – 6y = 0 => x^2 – 8x + 16 + y^2 – 6y +9 = 16 + 9 => (x...

MathIf there is a direct variation between two variables, when one variable goes up so does the other and when one goes down so does the other. If we denote the two variables as X and Y, their relation...

MathSupposing that you want to talk about the convergence of series, I'll emphasize the definition of an absolutely convergent series. A series "Sum an", for n = 1 to n = infinite is absolutely...

MathNo, it is not special, as long as you keep in mind that the complex numbers have the following form, called rectangular form: z = x + iy, where x is called the real part of the number and y is...

MathGiven the center of the circle is ( 4, 3) and the radius is 7. We need to find the equation of the circle. We know that the equation of the circle is given by: (xa)^2 + ( yb)^2 = r^2 where (...

MathY= 2(X4)^2  8 We will expand the bracket: ==> y= 2(x^2  8x + 16)  8 ==> y= 2x^2  16x + 32  8 ==> y= 2x^2  16x + 24. ==> a= 2 b= 16 c = 24 Now we will determine the...

MathThe depth of water is given by the function d (t) = 4sin (pi t/8) + 12. Now, at 6:00, the depth of water beyond the barrier is 12 m and the barrier is visible to a height of 0.5m. For a boat with a...

Mathg(x) = sqrt(3x+1) We need to find the inverse of g(x). First we will assume that y= g(x). ==> y= sqrt(3x+1) Now we need to isolate x on on sides. Let us square both sides: ==> y^2 = (3x+1)...

MathGiven the function : d(t) = 4sin( pi*t/8) + 12 Where d is the depth in metres and t is the time in hours. At the initial time ( 6:00 or t=0) the depth is 12 meters. We need to find the depth at...

Mathy = (2x^2  10x  6) / (2x^2  x  3) We need to determine the xintercept. xintercept is when the curve meets the xaxis. Then, y value will be 0. Then we need to find the xcoordinate. ==> 0...

MathTo find the yintercept of a rational function we need to equate all the x in all the terms to 0 and see what the value of y is. Here y = (2x^2 10x 6 )/ (2x^2  x  3). Substituting x with 0...

MathWe have the functions : g(x)=sqrt x and h(x) = x^3  1. Now we are required to find hog(4). hog(x) = h(g(x)) = h( sqrt x) = (sqrt x)^3  1. Therefore hog(4) => (sqrt 4)^3  1 => 2^3  1 =>...

MathTo notice all transformations,we'll consider the parent function adn we'll identify it in the function g(x)=4(x+1)^2  3. For the beginning, we'll expand the square from the expression of g(x):...

MathState the center and radius..Given the equation of a circle, (x+2)^2+(y1)^2=36, state the center...The standard equation of a circle with center ( a , b) and a radius of r is given as: (x  a)^2 + (yb)^2 = r^2 Now we have the equation of the circle of (x+2)^2+(y1)^2=36 Comparing this with the...

MathWe have to add 3 + 2i + 1 5i. When adding complex and real numbers complex terms can be added with each other only. The same goes for the real terms. So 3 + 2i + 1 5i => 3 + 1 + 2i 5i => 4...

MathThe volume of a gas varies inversely with the pressure applied. Let us denote volume as V and the pressure applied as P. Now as they are inversely related. V = k/P Now for a pressure of 30 pounds...

MathWe have y = 8^cos x. We use the chain rule to find the derivative of 8^(cos x) Now the derivative of a^x is a^x log a and the derivative of cos x is sin x. y' = log 8 * 8^cos x * (cos x)' => y'...

MathThe equation of a circle requires the center and the radius of the circle. We have the center as (2 ,1). For the radius we use the fact that the point (4, 1) is on the circle. The distance between...

MathWe'll express the first principle of finding the derivative of a given function: lim [f(x+h)  f(x)]/h, for h>0 We'll apply the principle to the given polynomial: lim {sqrt [3(x+h)+7] ...

MathTake the independent variable as the mass of the body that causes the beam to bend. The bend in the beam is the dependent variable. Let's denote the mass as m and the bend as b As the amount by...

MathIf the hypotenuse of a right triangle is 10 units and angle B is 70 degrees determine angle A and...We have a right angled triangle and one of the sides given as 70 degrees. Now the second side is 180  90  70 = 20 degrees. Also, the hypotenuse is 10. Let the other sides be a and b. So cos 70 =...