(c) Calculate the population of a spherical cloud of locusts which lies in the ball æ? + y? + (z – 1)2 < 1 if the population density is A(x, y, z) = 100z², in locusts/m³.

Q: 1- find m n x., min. and saddle points for the following functions : * f = 4x - 6 xy +5y" -20x +26y ...

A: We shall find the maximum, minimum, saddle points for the given functions Consider f=4x2-6xy+5y2-20x...

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Q: Consider the function f : {1,2, 3, 4, 5} → {1,2,3, 4, 5} given by 2 3 4 5 f = 1 3 2 5 3 a. Find f(2)...

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Q: b) For the matrix -2 5 A = 3 \12 3 -2 -1 -5/ (1) (ii) Determine the characteristic equation and the ...

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Q: Consider the function f : [–1,2] → R defined by f(æ) = x² – 1. On the interval [-1,0] the maximum va...

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Q: [8] Write a negation for each of the following statements: Jim is inside and Jan is at the pool. Jim...

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Q: Choose the correct ordered pair that makes the inequality true. 1. ? + 2? ≥ 8           (4,2), (−2,...

A: We have to check one by one, which ordered pair satisfies the given inequality.

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Q: Find the sum of the infinite geometric series. (If an answer is undefined, enter UNDEFINED.) 9(0.4)"...

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Q: 1. Given the following complex numbers: z1 = 2 - j, z2 = -3+ j4, z3 = -5 - j6, z4 = 2 + j3 Determine...

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Q: Question 7 8e 3 Evaluate, 2/30° express your answer in exponential form. O 4e O 4ei 4ei ion O 4e No ...

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Q: Q5)Poles Apart purchased snowboards at a cost of $345 and marks them up by 35% of the selling price....

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Q: Let B = {(1,0, 0), (0,4, –3), (4, 0, 3)} be a basis for R³. Applying Gram-Schmidt process on B, we g...

A: Given basis  B=1,0,0,0,4,-3,4,0,3

Q: 1 -11 B = 1254 2 46 2 10 A = -1 1 3 7 45 %3D Let obtain B A

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral L{f{t)} ...

A: Given function is f(t) = cos(t),0 ≤ t &lt; π0,t ≥ π

Q: 2. Is the following statement true or false? Explain your reasoning. If Si is a rectangle with area ...

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Q: 3. As cars travel on gravel roads, the roads erode and take on a "washboard" look due to the formati...

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Q: Calculate the value of D in detail D3 – 2D2 + D – 2 = 0

A: The given equation is D3-2D2+D-2=0 One root of D is D=2  Use synthetic division  1    -2    1   -2  ...

Q: e. f(x) = 2* DA. O(x²) B. 2(x²) Oc. O(x²) . f(x) = [x][x] (floor of x times ceiling of x) DA. O(x²) ...

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Q: 1. Let R be a region bounded by the by the curves: y-xr' and y=2x-x and x and y non- negative. Calcu...

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Q: Let I be the moment of inertia of the plate with density p =1 bounded by y = e" ,y = e, x = 0 about ...

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Q: Note: Show your work for theses problems. However, you may use a computer for matrix arithmetic. 1. ...

A: Use the slack variables to convert the inequality into an equation.

Q: (b) The rank of the matrix A is 2. (2 4 2 A =1 k 3 1 2 2/ (1) (ii) For this value of k, is A inverti...

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Q: 1 3 -1 5 9. Let A = -1 0 -2 -2 1 1 1 3 (a) Find a basis for the row space of A. (b) Find a basis for...

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Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = In(x), a = 1 Gr...

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Q: 3. Use the binomial theorem to find the coefficient of x° in (x+2)3 2. Use the L theorem to find the...

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Q: Find the interquartile range of the data set. {-4, -6, -9, -3, -2, -4, 0}

A: Introduction: Median is a measurement of central tendency of a given statistical data. When we arran...

Q: The general solution of the given differential equation y" – 4y" + 4y' = 0 is %3D

A: The auxiliary equation is D3-4D2+4D=0 solve for D DD2-4D+4=0D=0,D2-4D+4=0D2-4D+4=0D-22=0D=2,2, D=0  ...

Q: a The number of directions (unit vectors) in which the directional derivatives of f(x v) = xe-xy at ...

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Q: t is the minimum number of nonzero terms of the Maclaurin series for In(1 + x) that you need to use ...

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Q: a differential equation that models the given situation. The stated rate of change is with respect t...

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Q: Part A Which number in the equation indicates the growth rate? O 300 e O 0.75 O time Part B Calculat...

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Q: Find the values of the unknowns using any method applicable. 5а + 2b — 6с+ 4d — е %3D 6 2а — b — с —...

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Q: cos ( - i ln3) is equal to, COS O 4/2 O 5/2 4/2 2. O 5/2 6. 4/2 23,

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Q: Evaluate f(15) and f(35), given the following data. 10 20 30 40 50 y 46 66 81 93 101

A: The given problem is to find the functional values at given points f(15) and f(35) from the given da...

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Q: G0o Suppose the random variable has the cdf 0, x < -3 F(z) = 12-3 <I<: -3<I<

A: Introduction: A random variable has two types of the distribution functions. These are the probabili...

Q: whose

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Q: Find Vlax| for the series. 00 k k Σ k + 12 k=0 (Express numbers in exact form. Use symbolic notation...

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Q: Evaluate, 8e 3 2230° express your answer in exponential form. 2x O 4e 4e 3 O 4e O 4e 4e공

A: First we write 2&lt;30°in exponential form then we will write the final answer.

Q: Ex: 1. Let (an) and (bn) be two diverge sequence show that whether (an + bn) is converge or diverge ...

A: Multiple :    Let , an  ,  bn are two divergent sequence. We need to check that whether an + bn dive...

Q: Assume that, below, A is row equivalent to B. Find bases for Nul A and Col A. 11 2 -3 6 1 10 1 11 A ...

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Q: Graph the solution set of the following systems of linear inequalities. {5? + ? ≤ −6 2? − ? ≥ −1

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Q: 2 3) (6-1)°(st3)

A: We find inverse laplace transform of given problem.

Q: Is there a sequence of continuous functions: fn : [0,1]-->R that is pointwise convergent but the lim...

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Q: 2- find the absolute max.and min.of the function P : x*+y on the closed triangle Plate bounded by th...

A: Given function is f=x2+y2  is bounded by closed triangle plate bounded by lines x=-2, y=-2 and y+2x=...

Q: . f(x) = 2* DA. O(x²) DB. Ω(x) Dc. O(x²) f(x) = [x][x] (floor of x times ceiling of x) DA. O(x²) DB....

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Q: Write down the Euler-Lagrange equations associated with the following Lagrangian L(t, x, y, x°, y°) ...

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