Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

Q: (a) Show that for each complex number z ‡ 1, (b) Show that (c) Show that η n Στ k=0 Text Σcos(k0)…

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Q: A conjunt "C" groups 8 topics from the Calculus course.  trying to identify the liking for the…

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Q: If F(s) = -3s² s + 1 is the Laplace transform of f(t), find the following, correct to three decimal…

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Q: Observe the following pattern: 1 + 3 = 22 1 + 3 + 5 = 32 1 + 3 + 5 + 7 = 42  Find the next two lines…

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Q: Find the number of elements in A1 ∪ A2 ∪ A3 if there are 135 elements in each set and if the sets…

A: We have to find the number of elements in A1 ∪ A2 ∪ A3 if there are 135 elements in each set and if…

Q: Expand 3x + 2y)7 using the binomial theorem. Simplify your final result.

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Q: Q2: given that G=40 1=55 C = 0.8Yd + 25 T = 0.1Y+ 10 Calculate the equilibrium level of income(y)…

A: Given: G=40, I=55, C=0.8Y+25, T=0.1Y+10   To Calculate: The equilibrium level of income (Y) To find:…

Q: Given that the Laplace transform of f(t) is S -7 877 s² + 7 F(s) = then the Laplace transform of…

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Q: Problem 4. Let V, W be vector spaces over F, and let U be a subspace of V. Suppose SE L(U, W). Prove…

A: Kindly check Step 2 for the solution.

Q: A= 0 0 0 0 0 1 0 0 0010 0001 Find the cofactor 0 0 01 0-1 0 3 C 1,1

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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

Q: Test the optimality for the following transportation solution and answer the questions below (Note:…

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Q: Use a truth table to determine whether the statements ~p→(~q V r) and (~r^ q)→ p are equivalent.

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Q: Q1- If z₁ =3+2i, and z2 = 1-2i. Fined the real part and imaginary part of the 2z2-z₁+5-i following…

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Q: n theo

A: Here, in the question Given: G be a connected graph of order p≥4. We have to prove that yt(G) = 2p-q…

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

A: The given problem is to find the value of f(5π/3) for the given inequality f'(x) cos(x)< f(x)…

Q: Prove that there are infinity many prime numbers.

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Q: Question 4 Prove or disprove: Let k, m, n E N. If kn and if m/n, then km\n.

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Q: Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0…

A: Given that The graph depicts the standard normal distribution with mean 0 and standard deviation 1

Q: Part 1 a) What can you say about a solution and the behavior of the equation y'= -y2 just by looking…

A: Given differential equation is  Y' = - y2  which is homogeneous.

Q: Example 1 Use Stokes' Theorem to evaluate curlF. ds where F¹ = 2²7 – 3xy + x³y³k and S is the part…

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Q: 7.3 Isomorphisms of Interval-Valued Fuzzy Graphs In this section, we consider various types of…

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Q: 5s The inverse Laplace transform of s² + 81 is A cos(bt), where A and b are constants such that b >…

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Q: Transform: f(t) = 4t² sinh5t O F(s) = O F(s) = O F(s): OF(s) = O F(s) = OF(s) = O F(s) = O F(s) = =…

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Q: equal to 4 and satisfying the relation X1 x2 X₁-1 X₂-1 + = 2.

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Q: Find the order of 5 modulo 2^100.

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Q: Find the bases for the row space and column space of the matrix 1 -2 5 0 3 5 -7 0 -6 3 -2 1 -3 8 -9…

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Q: 1+4=5 2+5=12 3+6=21 8+11=?

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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: Chapter 2, exercise 4.11(a). For an extra challenge, you can try to prove that you only need the…

A: Any permutation is the product of two-cycles/transpositions. We use this idea to show that the…

Q: Find the length of the arc of the curve from point P to point Q. x² = (y-4)³, P(1, 5), Q(27, 13)

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Q: What is the kind of relation between the two commodities ?

A: Relation between the commodities: The relation between the two commodities can be determined by the…

Q: create any mathematical problem and show its solution.

A: A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the…

Q: By using the Bisection method to find the root (only one root) of the function: f(x) = 8x3 – 18x2 +…

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Q: Using the - definition of continuity, show that the func- tion f R³ R² defined as f(x, y, z) = xyî +…

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Q: 1. Taylor Approxmations Use sympy to find the Taylor Approximations to sin x with 1 term, 2 terms, 3…

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Q: Evaluate the following integral in spherical coordinates. SS Se- (x² + y² +2²) ² D 3/2 0 dV; D is a…

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Q: Differentiate y=sinx+cosx+tanx

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Q: 2) B=(4,-√6,-10, 0, 7 Integers A) 4,0 2, 2, 1.7, √ 4 B) 4,-10,

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Q: Proof by contradiction. There is no largest composite number  contradiction

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Q: v +w and v -w are combinations of v and w. Write v and w as combinations of v +wand v -w. The two…

A: To Write: v and w as linear combinations of v+w and v-w.

Q: (3) Let G be the group Sn. Let S be the 3-fold Cartesian product of {1,...,n}. Describe the orbits…

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Q: Use the sample data and confidence level given below to complete parts (a) through (d). A research…

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Q: . State whether the series converges absolutely, conditionally, or not at all. ∞     n = 1(−1)n + 1…

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Q: 2. f(t) = 4t cosh 3t

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Q: Find all extrema and any inflection points for the function f(x)=sec² x-2 tan x on the interval T T…

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Q: A marketing report concerning personal computers states that 650,000 owners will buy a printer for…

A: There are a total of 1,450,000 owners in the population.  Let's call people P if they buy ONLY a…

Q: 2 Points Solve the following 2-dimensional linear programming problem graphically: maximize: 3x1 +…

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Q: X 0 1 123 2 3 4 5 сл f(x) 0 0.5 0.8 0.9 0.941 0.962

A: There doesn't exist any exponential function which transform zero to zero. Here I have considered…

Q: (a) Define the following hyperbolic functions directly in terms of the exponential function (i)…

A: We know the exponential form of all the given hyperbolic functions.  Now the graph are given bellow.