find the Vertexfocus. aixis cnd directrix for each of the fottling Paraboles.f 89=x46x+ 17)

Q: Find [E(x-x)] from the following table: 2 3 4 5 P(x) 0.1 0.1 0.2 0.3 0.2 0.1

A: Given The given table is  Apply formula Ex=∑xxfxEx2=∑xx2fx

Q: Q1. [2 (a) Given the matrix A = |7 11 4 -61 show that the matrix (A+ A") is -2 4 Symmetrical Matrix....

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Q: 1- The ring of integer numbers (Z+-) isa subring but not ideal of the ring of real numbers (R +) 2- ...

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Q: 3. Let o denote the Euler phi-function. Recall that for an integer n = pi'p..p, where p1, P2, ., Pk ...

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Q: Q3/ Solve the differential equation using Laplace transforms d2y dr + 16y = 10 cos 4x , given y(0) =...

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Q: Show that the petersen graph is nonplanar.( Hint :show that the graph is contradictible to k5.

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Q: 2. Given f is a homomorphism from the ring (R,+, ) onto the ring (R',+', '), prove that a) if (I,+, ...

A: Definition: Let I be an ideal of the ring R. I is said to be maximal ideal if there is no intermedia...

Q: w: Prave that [ X" Ju Cx)] =x* Ju-1 X)

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Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below, wit...

A: a) The points are A(0,−40, 0) and B (40, 0,⎯20)A0,-40, 0 and B (40, 0,-20) Obtain the distance AB: A...

Q: A curve is defined by parametric equations x = t? +t - 1 and y = 2t2 -t + 2 for all t i. Show that A...

A: See the attachment

Q: 2. Determine if each of the statements below is true or false. If a statement is true then prove it....

A: See the attachment

Q: 5. Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. Not...

A: Assume that there are some sets A and B such that PA=PB but  A≠B.  Since, A≠B there exists some elem...

Q: Q.1 Find a.b and a x b a =i+j+k b= - 5i + 2j– 3k Q2 Find the cosine of the angle between the vectors...

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Q: x – iy Find whether f (z) = is analytic or not. 2 x +y

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Q: Q4) f(x, y) = x"/s –x/ay² Does the function is harmonic ?

A: If a function satisfied Laplace equation then the function is called harmonic function

Q: Let T be a tree with p vertices of degree 1 and q other vertices. Show that the sum of the degrees o...

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Q: If n is not a poime then there exist Some ab€ 7h Such that ab # Itnk fox all

A: Definition: A number which can not be factored as product of two numbers other than the number itsel...

Q: H.W • Find f (x) of f(x)= by using the definition of the derivative. • 1- Find if y=3r-4 and t = Vx ...

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Q: Question 2 The limit: limn takes the form and this limit 2-2 In(x 1) Note: If your answer is a fract...

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Q: The population of Village Ain 1997 was 2600, years later in 2007 the population had grown to 4600. W...

A: Given the population of a village in 1997 was 2600 and years later in 2007 the population had grown ...

Q: faster please

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Q: 3. Determine all solutions in the positive integers of the following Diophantine equations: (a) 18x ...

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Q: Quze O QY Use Gramer's Rule to Find K,y and Z -y-22 = -8 + 32 = 2 7X +y+Z = 0 %3D Q2/ Find the ang l...

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Q: Use Grammar's rule to solve the system -6x + 4y + 3z = 30 -2x + z = 6 Зх — 2у — z %3D 8

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Q: Find the domain of the following function. Make a sketch of the domain in the xy-plane. f(x.y) = /x-...

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Q: what is 6 times 8

A: To find - What is 6 times 8

Q: If tan'o 2tan²ß=1 Show that 2 Cos?-cosB=o

A: Use trigonometric identities to prove given result. 

Q: Sketch the surface z = f(x.y). f(x.y) = - /x² +y?

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Q: Kindly explain the process of this solution:

A: It is problem to integrate the differential 'g' within the limits. In the first step, the resultant...

Q: 1 4 ,5 2-+2 8

A: The given expression is 18-247+256.

Q: 0.8 Use the trapezium rule, with five ordinates, to evaluate [e dx. Correct your answer to three dec...

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Q: f(x)=2x2-7 , (2,1) 2 f(x)=5+2x-x² , (0,5) 3 f(x)=x2+x+1 ,(1,3)

A: Slope of the tangent line of f(x) is f '(x) value at that point.  Slope of the tangent line of f(x) ...

Q: 45°C ->F° 1001

A: Given 1 45°C→°F2 100°F→°C3 110°F→°C

Q: 400 mg of a steroid to kg

A: We have to change 400 mg of a steroid to kg. We know that 1 mg=10-6 kg

Q: Q:00)

A: Here lnx2-1=0Let fx=lnx2-1=0 We need to approximate root till 3rd iteration.

Q: Find all the second-order partial derivatives of the function. r(x.y) = In (2x + 3y) дудх дхду dy?

A: Given that r(x,y) = ln(2x+3y) We need to calculate all the second order partial derivatives. The cal...

Q: The angle between the vectors a=(2,6) and b=(3,-1) is :إختر أحد الخيارات а. 4 b. С. 3 d. 2

A: The required angle is, option (b) π/2 The detailed solution is as follows below:

Q: Let a and b be integers such that b measures a. (a) Prove that –b measures a.

A: Given: b measures a To proof: -b measure a

Q: The current toll for the use of a certain toll road is $2.75. A study conducted by the state highway...

A: Given q=6000e-0.4p When p=2.75, we have q=6000e-0.42,75=6000e-1.1=1997.2265 When p=5, we have  q=600...

Q: Change this LP problem (e.g., money, time, or number of batches), so that it has at least two whole­...

A: Assume x be the number of batches of cakes and y be the number of batches of cookies

Q: 4 2dx x² –6x+10

A: Given The given integral is  ∫242x2-6x+10dx

Q: QY Use Gramer's Rule to Find Kyy and Z -y-22 =-8 %3D + 32 = 2 %3D 7x +y+Z= 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

Q: 4. For r, y E R, let z y if and only if (x- y) E Q. Show that defined as such is an equivale relatio...

A: ~ is defined as : For all, x, y in R, x~y if and only if (x-y) belongs to Q Reflexivity : x~x for al...

Q: find a unit normal vector UN to the curve y = x at the point p(1,3)?

A: The given curve is y = x3, we can write it as x3 - y = 0 = f(x,y,z), where z = 0

Q: one of the eigenvalues of the matrix 0 1 A = -2 1 0 is -20

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Q: The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgag...

A: Assume x be the number of units of special risk insurance and y be the number of mortgages. 

Q: Find the Fourier transform to the function given below: for t<0 for t = 0 for t> 0 1

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Q: у" - Зу' — 4у %3D0

A: Given differential equation is, y''-3y'-4y=0....1 The given equation is second order homogeneous dif...

Q: Using the points given below, calculate the value of f (1.5) using a cubic spline, instead of accept...

A: The given data points are 1,1, 2,2, 3,0, 4,1, 5,3

Q: f Applyth) oroterAunge -kutta to sotve the fotloing Vatue probtem and 1

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.