Evaluate the following. Show your complete solution. S. (2w² - 5w+3)dw 4.

Q: [6] Find the Fourier integral representation of f(x) = { 02 0 1.

A: Fourier integral representation

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A: In this question, the expected value is to be determined.

Q: no of edges for a tree with number of vertices 10 is

A:

Q: (c) Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially,…

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Q: e²x -{8²² 0 [8] Find the complex Fourier integral representation of f(x) = |x| < 1, |x| ≥ 1.

A: The given problem is to find the complex Fourier integral representation of the given function.

Q: 1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then An B = 0 and…

A:

Q: 1. Use de Moivre's theorem to find all solution to 25 +32 i = 0. Give the solutions in polar form…

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Q: Use mathematical induction to prove that for all integers n ≥ 1, 6" 1 is divisible by 5.

A:

Q: At 8 a.m., you place a certain amount of bacteria on a slide. Every hour, the area covered by the…

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Q: after t seconds. A particle undergoing straight line motion has velocity v = (t²+1)² where the…

A: given velocity of the particle v=4tt2+12 where 't' is in seconds

Q: Solve the following equation using bisection method to find the root between x₁=1 and x2=5, make 5…

A: We have to solve the following equation using bisection method to find the root between x1 =1 and x2…

Q: -losed E

A: Volume enclosed by hyperboloid z=1+x22+y22 under the plane

Q: By using the e- & definition, show that lim 2² + X 4 = 1.

A: By the €-δ definition of limit,

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A:

Q: 32. Model With Mathematics In order to take a panoramic photograph, a camera must have a hyperbolic…

A: From given data we can conclude that, By Standard equation of hyperbola :y2a2-x2b2=1

Q: Use Stokes' theorem frotF. ds to evaluate F(x, y, z) = (x + tan¯¹yz)i + y²zj + zk, S is the part of…

A:

Q: [1] Find the Fourier series: (a) f(x) = 3 sin(2x) - 5 cos(7x) + cos(8x) (b) f(x) (c) f(x) = cos²…

A:

Q: if f is any closed Set of X Such that D≤f then F=X 3 if Bx is a base of x Space, then UnD $ $U<B 47…

A:

Q: You may find this question challenging. Given the three points A-[1,6], B-[-1, 1] and C= [4,6],…

A:

Q: A bar of chocolate consists of n ≥ 2 connected pieces. A component is a portion of the original bar…

A: Let us assume that Mn be the number of breaks required, here n≥2 are the number of connected pieces.…

Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

A:

Q: What is the negation of the proposition/statement: 10 > 14 ?   10 < 14   10 ≥ 14   10 ≤ 14   10…

A: Given, proposition/statement is 10 &gt; 14  We have to find negation of the given…

Q: (c) f(x) = cos² (3x)

A:

Q: Use Cartesian coordinates to evaluate Jff ² av where D is the tetrahedron in the first octant…

A:

Q: 2x - 3y = 6 6x - 9y = 10 Use substitution method

A: here We use substituion method

Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: Solution Now, Given height (h) = 7 cm radius (r) = dh 1 Formula: volume of cylinder volume (₁1) =…

A: Given that Height h=7 cm Radius r=10 cm And dhdr=1 Now, the formula for the volume of the cylinder…

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Given equation :      z2=4+4r2As we know that r2=x2+y2..............(polar form→cartesian form)So we…

Q: A study examining the relationship between pre-diagnosis physical activity and cancer enrolled a…

A: Given: A study examining the relationship between pre-diagnosis physical activity and cancer…

Q: 2. (a) How many lines of symmetry does a regular octagon have?

A:

Q: 4. Solve the following 2nd-order OPES (5 Steps) day - (22) + (4-1) dy dx² Y(0) = 4 , y(0) = 1 y cas…

A: We can solve this using euler method of second order differential equation

Q: Q4: Let X be a discrete random variable with probability mass function given in the following table:…

A: 1. Value of C For a discrete random variable X the sum of the probability mass functions is 1 That…

Q: On the plans for a treehouse, a beam represented by QR has endpoints Q9-6, 2) and R(-1,8). A…

A: Given endpoints of beam QR are -6,2 and (-1,8) and endpoints of beam ST are -3,6 and -8,5.

Q: The diagram below shows the graph of y = √√x and y = x. Consider the region bounded by the two…

A:

Q: M

A: Polynomial algorithm for finding an optimum  2RDF (or W2DF) of proper interval graph. So yes, there…

Q: Given the two series: 1+2n4 (1) Σn=1√√³+6 In(n) and (II) Σ+% Using the limit comparison test (LCT)…

A: I Given series is ∑n=1∞1+2n4n5+6. We have to check whether the give series is converges or diverges.…

Q: 7. The coin is tossed twice. Which of the following is the correct representation of the sample…

A: ans 7  (a) {HH, HT,TH,TT} Ans 8 (d)   36 (6 into 6)

Q: = Solve the recurrence relation an 7an-1 12an-2 for all integers n ≥ 2, a₁ = 1 and a₁ = 6.

A:

Q: 1 Function on the interval (-3,3) and has n=5. Draw the graph. 2 x +1 Determine the approximate area…

A: By trapezoidal rule .∫abfxdx= Δx2​fx0 +2fx1+2fx2+2fx3+⋯+2fxn-1+fxn       where    Δx=b-an    By…

Q: ked to calculate the specific heat of water at 61°C. The specific heat of water is given as a nction…

A: We can solve this using given information

Q: 6. A rectangular classroom has length that is 1 meter more than 2 times the width. Find the…

A: Let assume  Width  of rectangular classroom = W=    x Length of rectangular classroom =L=    2x+1…

Q: Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a…

A: The anser is l = 8

Q: (c) The figure shows two similar prisms, if the volume of Prism 1 is 40 cm³, find the volume of…

A: To find the volume of the Prism 2.

Q: 8. Prove or disprove the following: (a) The yz-plane is a subspace of R³. (b) The set of n x n upper…

A: This question from topic subspaces of vector space.

Q: All statements below are false. Provide a counterexample of f and g each. (a) If f + g and fg are…

A:

Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: [(x² - 2xy)dx + (x²y+3)dy ans: Verify Green's Theorem in plane for c of the region defined by y² =…

A:

Q: Evaluat -3.x²

A: We have to find the volume of the solid bounded by z=1-2y2-3x2 and the xy plane.   The volume of the…

Q: Integrate f(x,y,z) = x + √y-2² over the path from (0,0,0) to (4,16,4) given by C₁: r(t)=ti+t²j,…

A: Solution :

Q: Ev 2y² Use tri

A: We have to find the volume of the solid bounded by z=1-2y2-3x2 and the xy plane.   The volume of the…