9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

Q: 5) Find the general solution by using reduction of order method to (x² + 1)y" – 2xy' + 2y = 0 given…

A:

Q: Find the value of the integral x²dx (x² + 9)(x² + 4)² 0-

A: The integral can be solved by first simplifying the integrand by partial fraction decomposition.…

Q: 2. Homogenous DE x²y = 4x2 + 7xy+ 2y²

A: We solve the given homogeneous differential equation

Q: Find дхду of z = In(x² – y)

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Evaluate integral the 6x ..d. (x²+4)(2x-2)

A:

Q: (In 10x+ 41nx) ³dx A Inx B In°x+4 In°x D In 10x+4lnx In 10x+ 4lnx E F None

A:

Q: Consider the problem maxx [-(x - 4)]² subject to x21. Use Thus the Kuhn-Tucker conditions to find a…

A: We are given the following problem.       maxx -(x-4)2       Subject to x≥1 Let us simplify the…

Q: 8) Is (x+3) a factor of x4 + 2x2 + 17x – 48 Drop coefficients onto top line

A: Given,  x4+2x2+17x-48

Q: Differentiate implicitly to find 3xy +4y°z-2x = 3

A: Given query is to find the derivative.

Q: /4y² - 25 -dy

A:

Q: 1. 05x<5 2k ī (x) if (I - x) if sxsI 2 2kx < 1 2

A:

Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

A:

Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

A:

Q: 1. Use the Product Rule to differentiate y = x³(2x + 1)*.

A:

Q: 18x- 2(3x + 1) = 5x – 16; Prove: x = -2 %3D

A:

Q: 3. Divide x+4x-3x-2 by X-2) then divide if CX-2) isa factor of x² t4x-3y-2 why?

A: We have to divide (x3 + 4x2 - 3x - 2) by (x - 2)  Then ,

Q: 2. Find the critical numbers of y =2x² – x4

A: Given y=2x2-x4

Q: 3. Find the coefficient of xy' in (2x + 3y)°.

A: The provided information is we find the coefficient of  x2y7    in (2x+3y)9 Then, (79)*(2x)2*(3y)7…

Q: Divide f (x) = 2x ^ 4 + 3x ^ 2 + 10 by g (x) = 3x ^ 2 + 5x + 1 in Z11.

A: Solution:         To Divide f(x)=2x4+3x2+10  by g(x)=3x2+5x+1…

Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. x-1 А) True B) False

A: We know that algebraic substitution is method in this replace the veriable of integration by a…

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

A:

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: Find the devivative of the fanction from N 2x+3 %3D

A:

Q: 4. Prove that (2x+3y)(4x²−6xy+9y²)+(2x−3y)(4x²+6xy+9y²) is 16x³ equivalent to 1 for x = 0.

A:

Q: (b) lim In(5x2 +3) – In(2r² + 1). -

A: Given :

Q: 7.Find a²z of z = 2x³-5xy² xy

A:

Q: 1. Differentiate: y = 3(x²-1) A. (In 3) 3(x²-1) B. (2x) 3(x²-1) C. 2x (In 3) (3**-1) D. x²(In…

A:

Q: Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions…

A: The complete solutions are given below

Q: 17. Given 2x+4 — 2x+3 = 1, find x.

A:

Q: 1. (18pts) Find / simplify each: V100x*y7 + V54xy2 3 4 1 -2 2y5 2x4 205x V10x2 Rationalize * 3 1…

A: Simplify

Q: what do you get when you expand x+4/xy^2?

A: We can make it easier for you

Q: 4. Evaluate the integral 2x -5x2 d.x

A:

Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

A:

Q: When p (x)=2x + kx +1 is divided by x +1, the remainder 1s the same as when q (x)=3x + kx +2 is…

A:

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: 4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is…

A: The given function is,

Q: Sketchthegraphofy=x2−5x+4.

A: We first make a table for y=x2 −5x+4 x 1 2 2.5 3 4 y 0 -2 -2.25 -2 0

Q: - To show that AADB (бх — 1)° 48 (4x + 25)° EACBD by AAS, what must be the 48 A' D value of x?

A:

Q: 1. Examine (2x - y)15. Explaim coefficient of the x y' term.

A: Consider the binomial expansion of (ax+by) to the power n. The co-efficient of any term xpyq will be…

Q: Find product solution for this PDE: xuy - yuz = 0. %3D

A: Solution of partial differential equation.

Q: 2). when 2x°-3x+Kx-1 is divided by X-1 the remainder is 2, find Ke

A: value of k is 4  see below the calculation and answer

Q: 12x 3 3 15 12 x4

A:

Q: 10. Determine the upper bound on the error in the approximation = x - 16x5 + 256x° if |x| < 0.2…

A: We need to find upper bound on the error.

Q: By applying product rule to find y' 3 (1+x*) x4 - x*

A:

Q: -y=In(5x -2x+1) 3 In n(5x² -2x+1 %3D

A: This is the problem of function.

Q: 5) Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A: Use the procedure of reduction of order to solve the given differential equation as in next step.

Q: Is X4 + 3X2 – 2X +I irreducible in (Z/5Z)[X]?

A: Answer

Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1

A: ∫xdxx-1

Q: Find 2 for all of: 1- y = xvInx 2- y = 3 x(x-2) x²+1

A:

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.