Why must n2 r in the notation nCr?

Q: 13. Algebraically find fo g(r) and go f(x) in their simplest form using I+7 f(r) = and g(x) = Vr - 2...

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Q: Define a sequence {a,} as follows: Let a, = 1, and define (an)² + (2n + 3)an + (4n + 3) An+1 An + 2 ...

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Q: 9.) f(x) = (2x + 1)* %3D

A: The given function is: f(x)=(2x+1)4

Q: 1. A committee of 5 shareholders is to be chosen from a larger group of 7 men and 5 women. How many ...

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Q: 4. (а) Find the general (implicit) solution to this differential equation. dy x – 5 (x – 1) dx y²(x ...

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Q: Determine the tension in each cable supporting the given load for each figure. (Assumem, = 2000 lb a...

A: (a) M1 = 2000 lbfor tension in the cable we need to find balancing condition means vertical omponent...

Q: Šubject 1: Gains from Trade Greece and Finland produce and consume two goods, timber (T) and dairy p...

A: A gain from trade is a simple concept - two parties traded and both parties got something out of it....

Q: The domain and range of the following function f (x) =D (-00, -1] U (1,+ 00) O (-00, -1) U (1,+ o0) ...

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Q: siny+ tan y = siny %3D 12. 1+ secy

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Q: Sketch a right triangle corresponding to the trigonometric function of the acute angle 0. Use the Py...

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Q: 1) find the derivative of y = 4x2 – 3x – 2 | | then evaluate f'(x+3)

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Q: Find the solution of the following initial-value problem d²y, dy + 4y = e, y(0) = 1, dr (0) = 2 %3D ...

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliar...

Q: Determine the behavior of the functions defined below. If a limit does not exist or the function is ...

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Q: -1, x0 c. lim f(x), where f(x) =

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Q: Find the equation of the line tangent to the graph of f(x) = (In x)* at x= 5. ... (Type your answer ...

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Q: Find the most general antiderivative of f(x) = -3x – 7xL7. Note: Any arbitrary constants used must b...

A: Topic = Integration

Q: 5. A man takes out a loan of P150, 000 from a credit cooperative, which charges interest at the rate...

A: This is a problem related to simple interest calculation. Based on the general formula available we ...

Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2, 0sys...

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Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: Consider the graph of f(x) given below and compute the limits. 15- 10- -5 -10 -15- 1. lim_ f(x) 2. l...

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Q: Given the function, g(x) x 2 a. Determine the possible points of discontinuity. b. Discuss the conti...

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Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.

Q: Find the exact length of the curve. y = x3/2, osxs 6 3

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Q: 35 1. Determine if the ratios 20 and- 91 form a proportion. 52

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Q: If f(x)=3x^2−x+3​:   A. An estimate of f′(5) using the interval from 5 to 5.1 is___.   B. An estimat...

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Q: certain drug is eliminated from the bloodstream exponentially with a half-life of 36 hours. onsider ...

A: We can use exponential decay function to solve the problem

Q: Find the unit tangent vector T(t) to the curve  at time t.

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Q: 1. The shadow cast by a post measures 6 feet. If the distance from the tip of the shadow to the topm...

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Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: Given the function f(x) = - 2x

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Q: Evaluate 2 sin x cos x dx by three methods: (a) Let appearance of the answers obtained in (a), (b), ...

A: To evaluate: I=∫2 sin x cos x dx

Q: Consider the graph of f(x) given below and compute the limits. 15- 10- -10- -15- 4. lim f(x) 5. lim ...

A: Graph of the function f(x) is given we have to find the given limits

Q: 8. Determine whether v(x) = r'+3|x| even, odd or neither. Discuss its symmetry.

A: Q8) Given: v(x)=x3+3x  

Q: Question 25 What is the volume of the solid formed by revolving region B around y=busing a vertical ...

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Q: Solve the given initial-value problem. The DE is homogeneous. xy2 dy = y3 – x3, y(1) = 4 dx

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Q: 1 dx by Simpson's rule using eleven 3. 5. Evaluate 1 + x ordinates.

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Q: Find the exact length of the curve. + 4х 1 < x < 3 y

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Q: III. Given: ,X(0)= 0 ,0st< 4] X'-2X = G(t) where : ,124 Solve for X(t) IV. Given: X'(t) + 2 Y(t) = -...

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Q: 4. Use the given information to sketch the graph of the function f. (-2,1)u(1,x) all real except X -...

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Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: Find the determinant of the triangular matrix. -2 0 8 7 -7 6 -4 Use expansion by cofactors to find t...

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Q: S(b) - f(a) 12. Find the average rate of change of f (x) = 2r2 + 2 using the formula on b-a the prov...

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Q: Consider the Following matrive A= 2 3 4 a) Find all the egenalues and eigenvecors

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Q: (V- 1)2 Evaluate dx by two methods: (a) Expand (Vx 1) and multiply the result by x-1/2: (b) let u = ...

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Q: Suppose 7x + 2 f(x) ? + х — 2 Then A f(æ) : В х — 1 x + 2 where A = and B =

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Q: x'=x.cot(t)+sin(t) a. find the general solution that satisfies x(1)=3

A: Let us consider a linear differential equation of first order of the form, dy/dx +P(x)y= Q(x) Then i...

Q: х+1 3.) y = х-2

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Q: x²+3x+2 6. limx0 2x2-1 2+3x 7. limx-00 бх-1 2x2-1 8. limx0 7+3x+5

A: Since you have posted multipart questions i can do first three subparts as per our company guideline...

Q: Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each ot...

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Q: - i. Determine whether n=1 is convergent using ratio test. en ton-1 n

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...