If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is pi/3.

Q: Find a quadratic equation whose product of roots x₁ and x₂ is X1 x2 equal to 4 and satisfying the…

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Q: BSNL Ein(x) for * * = , 1, 2, ... secd s = l

A: Given     f(x)=sin(x)sin(x)   for  x≠kπ  k = 0,1,2,3,4.....      we know that L{f(x)}=∫0∞e-sxfxdx…

Q: show that erf(- infinity) = -1

A: Kindly refer to Step 2 for the solution.

Q: Given that the Laplace transform of f(t) is s+ 2 s² + 6s +7' F(s) = then the Laplace transform of…

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Q: 6.    Find the answer by using the Pascal’s formula  (a) & b)

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Q: Transform: f(t) = 5t6e4t O F(s): = OF(s) = OF(s) = O F(s) = = O F(s) = F(s): 3600 30 720 (8+4)* 30…

A: Option A is correct. Explanation is as follows.

Q: ttl =cheme, what is the rate for the 5 equivalent effective

A: Here, in the question, Patrick forecasts that interest rates will rise over a 5 year period…

Q: Let A, B E Mn (F) where n is odd and the characteristic of F is not equal to two. Prove that f AB-BA…

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Q: In cartesian product, prove that (A-B)XC=(AXC)-(BXC) A,B,C are sets

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Q: Solve for the function y that satisfies ty' = 2y + 4t³ cos(4t) = 0 {

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Q: what is the answer of question (3)

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Q: if the tangent tangent (x117₁) to the conve of the curve again in (22, 8₂) them proustait me x 1 20…

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Q: Which is/are the correct counterexample to disprove the statement that all perfect squares are even?…

A: We have to choose the correct counter examples to disprove the statement that all perfect squares…

Q: non-negative continuous function. 5 п 3 Let f(x), x 20, be a If f'(x) cos x ≤ f(x) sin x, V x ≥ 0,…

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Q: 6. (Solve by "Trial and Error".) Below is a floor plan of an art gallery. Is it possible to take a…

A: Using hit and trial way can be found which passes through all the gates only one.

Q: Solve the linear programming problem using the simplex method. Maximize subject to OA. The maximum…

A: By simplex method

Q: 1. Express f(t) in terms of the unit step function uc(t) 1, t-1, t-3, 1, f(t) = if t 5

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Q: If F(s): = -38² + 8 + 3 is the Laplace transform of f(t), find the following, correct to three…

A: Given,           Fs=-3s2+s+3s4s2+5s+9.

Q: 1. Let p be prime and let a 0 (mod p). Let b = a 2 (mod p). Show that ab = 1 (mod p). 2. Use the…

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Q: L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides…

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Q: Let n E N. Prove that 2 + 22 +2³+...+2n = 2n+1 - 2.

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Q: Differentiate y=sinx+cosx+tanx

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Q: For the new solution problem at the bottom, how did you get (4^n/2^2n) = 1/4^n. Plus, why does…

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ∞), where a > 0. b > 0 , c > 0 Find the condition if…

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Q: Let A E BL(H). Then A is called normal if A*A = AA*, uni- tary if A*A = I = AA*, that is, A* = A−¹,…

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Q: Let nEN. Prove that 2+2² +2³+244... +2n 2ntl -2.

A: Here we are given a mathematical series and its equation for its sum. We are to prove that the left…

Q: A store specializing in mountain bikes is to open in one of two malls. If the first mall is…

A: Given,  If the first mall is selected then profit = $ 600,000              If the first mall is not…

Q: =o ex) Solve the D.E. (x+y) dx + (x+zy) dy - that satisfies the initial condition y ez) = 3 ?

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Q: For the selected cell create Dantzig's closed path, and specify the maximum amount of goods possible…

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Q: So So So A² sin() ² sin (772)²sin()² dxdydz = 1, (A, a, b, c are all constants) b C Solve the…

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Q: Let (a) Find the reduced row echelon form of the matrix B. rref(B) (b) How many pivot columns does B…

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Q: A particle moves on a straight line so that its position s (in feet) at time t (in seconds) is given…

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Q: 9: The deflection of a beam, y(x), satisfies the differential equation day = w(x) on 0 < x < 1. Find…

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Q: a. k³ k²-k-2÷ (k-2) Remainder b. 648636² +62b-34÷ (6-7) Remainder: given binoma is a factor of the…

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Q: How many WAYS can you make P17 using only P10, P5 and P1 coins? SHOW the different ways.

A: Solution:   Given : P10, P5 and P1    And we have to make P17. Now,        P10 P5 P1   Total 1…

Q: Mean = 63.6 PDF = 45 SD = 18.8 Find the Chebyshev’s inequality

A: Chebyshev's Inequality: If X is a random variable with mean μ and variance σ2, then for any positive…

Q: (88). Find the eigen functions for the boundry valve problem. following x²y" - 13 xy² + (49+ X) y =…

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Q: Prove the statement, or give a counterexample. c) There is no sequence that converges to 3 in metric…

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Q: After graduating with a master's degree, Kamala combined all of her student loans into a single loan…

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Q: Show that the greatest volume of the cyl- inscribed in a right circular cone of height 4

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Q: By transforming to principal axes, reduce the quadratic form x' Ax for 2 2 1 A = 25 2 1 2 2 to a sum…

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Q: The inverse Laplace transform of 4s² + 11s + 151 (s+7) (s² + 2s + 10) ' is: peat + gest cos(wt) +…

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Q: 3 Find the general solution of the third-order ODE y(³) + 6y" + 10y' + 6y = 0, note that m³ + 6m²…

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Q: Let/(x)=sin³ x+A sin² X

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Q: Let f: [2, 7] → [0, ∞) be continuous in [2, 7] a (2,7). Then prove that there exists at least one…

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Q: 5.1 Let (u, v) be the Euclidean inner product on R2 and let u= (1, 1), u =(3, 2) w (0,-1). Compute…

A: (5.1.1) Given, u=1,1, v=3,2, w=0,-1…

Q: Out of 160 students at a first year linguistics stream in college, 87 students study French(F), 17…

A: Given: Total number of students, nU=160 Total number of students who study French, nF=87 Total…

Q: Find the sum 66 + 67 + 68 + · · · + 301. Show work

A: Sum of first n natural numbers which are in Arithmetic Progression is :…

Q: Find -da - C

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Q: Prove or disprove: ne N. If lim xn exists. Let m≥ 2, and let n, yn E Rm for all 0 and lim(rn yn)…

A: Here we take counter example for disprove given statement