Solve for x in the figure ALMN is equilateral, and MP bisects ZM. Show all work!

Q: use the inter medicte Value theorem to prove that 2 the equetion V2x+s -4 + x´= 0 has a root in…

A: intermediate value theorem: if the function  is continuous on and if  and  then the function has a…

Q: Find the Ye neral solution of the eguation. 6y"_5y_4 y =o %3D

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Q: Evaluate the integral O 03/20 Ⓒ100 C 87² dx using the two-point Gaussian quadrature rule. 1+16z4

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: .rdx dy Prove that (a) (b) (8)

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Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

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Q: use the definition prove that s d sinZ %3D Tal

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Q: find the funotion with hejp of a indegral meau value betw een 4,1] of g(x)=\xl-2

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Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: The formula in cell B1 is =A$2. auto fill is used by dragging B1's auto fill box across to c1,D1 and…

A: Enter A$2 in cell B1. Then Autofill is used by dragging B1's autofill box across to C1, D1, and E1,…

Q: ハジ nd the exact lkength of the wnve र 4=1n(seccx)),

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Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: Use Euler's method to obtain a four-decimal following: approximation for t (4 y=2Xy, yC)=1; yU5) =?…

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Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

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Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: Use the modified Euler method of Lecture 3, with n 10, to find xt1 = -t, (0) = 0

A: Consider the given differential equation.

Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: In ARST (not shown), mZR 45° and mZS 64°. Find m ZT. %3D

A: Given that, In triangle RST, m∠R=45∘ and m∠S=64∘ To find:

Q: Find the length of the curve r (t) = 3ti + square root of 3t^3 k in [0,1]

A: Given r(t)=3ti+3t3kfirstly, we have to calculate derivative of r(t)r'(t)=3i+9t223t3kNow, let find…

Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: Find length of the cardioid r=a0³from 0 = 0 to 0 = n %3D

A: Length of the cadioid is given by below formulaLength = ∫0πaθ3dθ

Q: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

A: Given, 2x²=1+5y² Here 5y2 is a multiple of 5 ending in digit 5 or 0. 2x2 can end in 1 or 6 But no…

Q: Evaluate the integral 108 - 2y/E+ 4ydzdy, 4 where A is the parallelogram with vertices (0,0), (),…

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Q: Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O…

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Q: Evaluate the integral dx (4x + 14) by making the appropriate substitution: u = dæ (4x + 14)* Submit…

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Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: Use the Trapezoidal Rule to evaluate the integral S |r| x²dx O 2 O -2 O 1 -1

A: Given Intergral ∫-11xx2dx. We have to find the value of it by using the Trapezoidal Rule. The…

Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

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Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

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Q: Find the imaginary part of the analyhc funckon,whose real part is : sxy? 3x²-34?

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Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: State De Moivre's theorem and if z 7+ j4, find z5 using the ( theorem.

A: Given query is to find the value of z5 using De Moivre's theorem.

Q: Solve for x in the figure * AJKL is isosceles with KJ = LJ. K x+3 X-1 J 2х- 5

A: Since, triangle JKL is isosceles, so, we have, KJ = LJ

Q: A space ship travels at 25 miles per hour and traveled continuously for 211 hours. 4 Enter the…

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Q: Use cubic interpolation method with two points to find uz , where a = 0. 6, h 0.1, ɛ = 0.001 and O'…

A: Cubic interpolation method gives the following formula for evaluation, For, μ2=a(∅')-h1+∈ Therefore,…

Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.

Q: The sum of Hthe first S=3n²+4a fFinal+he li mit an is nlmits ofar plogression an arthmctic

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.