Illustrative Examples Table 3. Study and analyze the given examples in evaluating expressions involving permutation. 7! 7! 7.6•5+4.3-2N 7.6.5.4.3•1 2520 1. P(7,5) = 2520 1 (7-5)! 2! 1 6! 6! 6.S 6•1 2. P1 %3D %3| %3D (6-1)! 5! 1 1 4! 4! 4•3•2+1 24 3. PA 24 (4-4)! O! 1 EXERCISES C. Evaluate the following expressions 2 P(6,4) 4. P(10,0) ||

Q: Find the sum of the scries (ii) E (n + 3)x"

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Q: (a) (1, -2,0) and centered at the point (2, -1,3). Find an equation of the sphere that passes throug...

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Q: Qu s) Let f(r) = , and for any t> 3 consider the 3 integral I = | 2 - f(t) dt. %3D a) Find I. Is I a...

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Q: A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P = ...

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Q: 1. A computer shop charges P20.00 per hour (or a fraction of an hour) for the first two hours and an...

A: Given: Charges per hour or a fraction of an hour for the first two hours is P 20. And charges for ad...

Q: Is the function f (x) below continuous on [3, +00)? (0, x > 0 X, 0 3

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Q: 2 + J 3 5- j3 Simplity usingg exponeutical

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Q: B be a real number such that B+ is an integer. Show that Br + is an integer all natural numbers n.

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Q: Find the derivative of the function f(x) = e(z²-3z).

A: We have to find the derivative of the function f(x)=e(x2-3x) .

Q: Problem 3. First verify that y(x) satisfies the given differential equation. Then determine a value ...

A: Introduction: A function yx is the solution of a differential equation if it satisfies the equation....

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Q: 5. Consider the wave equation Ut – a?uxx= f(x,t) for the semi-infinite domain 0< x < ∞ and t2 0 with...

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Q: On which of the following intervals is f(x) = continuous? %3D x-

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Q: for |x|< a 0 for x<a Q4. Determine the Fourier transform of f(x) =

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Q: There exists a power series with interval of convergence [1, 2]U [4, 6]. (If true, please n example,...

A: Statement in (3) is False as the given union is Not an interval. Statement in (4) is also False by d...

Q: Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the grid...

A: 4 Consider the given graph. We have to evaluate g∘f3. We know that g∘fx=gfx Hence, g∘f3=gf3 From the...

Q: Which of the following set can be considered as a universal set? .a z={z:xzis an integer number} .b ...

A: The universal set is defined as the set which contains the whole.

Q: On [-27, 47), f(x) ==Y². Find all values of x. Find the x-intercepts of f(x) on [-27,47).

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Q: Find a value for the constant k, if possible, that will make the function continuous. Skx², f(x) = (...

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Q: Show that d(x y) = √x-y defines a metric on the set of all real numbers

A: We will use the basic knowledge of metric spaces and set theory to answer this question.

Q: F 15 18 13 14 19 E Eulerize the graph above in the most efficient way possible. The weights on the e...

A: We can solve this using euler method

Q: Describe the domain of the function f(x, y)= In(6+x-y). {(x, y): y<x-6} {(x, y): y 2 0} a. {(x, y): ...

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Q: In an apartment complex, there are 5 windows in each apartment, and 9 apartments in each floor. How ...

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Q: 4. n! (read "n factorial") is the product of the first n positive integers, that is 2! = 2 1, 3! = 3...

A: We can solve this by using formula of factorial

Q: Find the the domain, vertical, and horizontal asymptotes of the function: 2+Vx Y= 2-Vx

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Q: e*,g(x) = = e-* in C[-1,1] Q4) For the following functions f(x) find , |IF |I, d(f,g), and then find...

A: given function fx=ex , gx=e-x in C-1,1 inner product is defined as f,g=∫-11fxgxdx find a) f,g b) f c...

Q: Show that : %3D tan 0 tan (0 + 60°) + tan 0 tan (0- 60°) + tan (0 + 60°) tan (0 – 60°) = – 3.

A: Solution is given: Hope the answer is helpful.

Q: *2. (a) If you have successfully solved examples (xix) and (xx) from Problem 1, it should be clear t...

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Q: (3,8, 3) The cross product of the two vectors u = and v-(7, 1,5) is the vector : Select one: w = (37...

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Q: prove that C+Ã +3 = ARC Using the truth table

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Q: (b) Find the area of the triangle whose vertices are A(0,0,0) ; B(1,1,1) and C(0,2,3). 1 (C) Find th...

A: Given (b) The vertices are A0,0,0, B1,1,1, C0,2,3 c(1) y=1x2-1 c(2) y=9-x2

Q: min zd = 2y, - y2 + 3ya 3y - 2y2 + ya = 1 Y + y2 - 2y3 s 2 -Yı +y2 - 5y3s-1 Y, sin rest. ; yz, Y3 S0...

A: To transform a primal problem into dual problem we follow some rule.  If the primal problem is minim...

Q: Find all real singular points of x(x2 –7 x + 10) y" + sin(x) y' +x y =0. {-6, –6} None {5, 2} {4, 3}...

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Q: Exercise Set P.1 page(14-16) 4 In Exercises 67to 78, evaluate the variable expression for x-3, y=-2,...

A: Given the variable expression is  z-2y2-3z312 and x=3, y=-2 and z=-1

Q: Give an example of conditionally convergent series n=1 an and n-1 bn such that En=1(an + bn) converg...

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Q: Graph the parabola. y-(r-3)+1 Piot five points on the parabola: the vertex, two points to the left o...

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Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point...

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Q: RHS x2 -2 x3 $1 82 -4 -2 -62 1/4 -1/2 0 x3 1 1/4 5/2 1 -1/6 1/3 Write the original problem and its d...

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Q: . Prove that |x|+ |x + ;] = |2x| for any real number .

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Q: OLet Faffasb)tairbeR} and + defined on AF as fellows! (asb) +ceod) = (atc,b+d) (arb).ccod)= (ac, bd)...

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Q: How to prove the Regular expression identities: (x + y)* = (x*y)*æ*

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Q: 1. Number of tails when tossing a coin five times 2. Length of electrical wiring on electrical appli...

A: according to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: 1) An arithmetic sequence has a its 5h term equal to 22 and its 15th term equal to 62. Find its 100t...

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Q: Find a particular solution to the differential equation 2y" – ly – ly = -2r² + lt – 5e²". |

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Q: of T2, T-:

A: Consider Tn={n, n2}, where n is an integer. The objective is to find the number of elements in each ...

Q: THEOREM 23. Let K be an integral operator on L2([a, b], a) KS = [°xe K(x, y)f(y) da(y) where T| K(x,...

A: We will use the basic knowledge of functional analysis to answer this question. Recall the definitio...

Q: 5. Suppose you have a set of proposed activities along with start time a, and finish time f, where 0...

A: We will use the basic knowledge of linear programming and optimization theory to answer this questio...

Q: In McLaurin series of common functions, solve the following. 1. cosh x

A: The Maclaurin series for the function fx is given as follows: f0+f'01!x+f''02!x2+f'''03!x3+fiv04!x4+...

Q: Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line pas...

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Q: 3) Suppose plane P, contains the points A(5,0, –1), B(2,3, 2), and C(-2, 1, –4), and assume P, is th...

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