How many ways can a teacher select Billy and Samantha to be on a committee of 6 people from a classroom of 30 students? O 28 CA O 30 C6 O 30 C2 X 28 CA

Q: g vertices are adjacent to vertex B?

A: Two vertices are adjacent if they are connected by an edge. That is , two edges are adjacent if they...

Q: Question 5 eln (a/e) sec?x - sec²x)° sec(3A – x) What should be the value of A for -dx 'du? ? to be ...

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Q: a) Find the length of the curve y(x) = x3/2/3- x/2, 3 < x < 4. b) Find the area of the surface obtai...

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Q: Find the roots: x5 = 4i

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Q: Find the two values of k for which y(x) = ek is a solution of the differential equation %3D y" – 16y...

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Q: sin x. Complete the table below and sketch Consider the function fix)- its graph. 011/6 11/2 5n/6 7n...

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Q: The slope of the tangent line at any point (x, y) on a curve is 2,r. If the point (9, 3) is on the c...

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Q: Use Stoke's theorem to evaluate the integral curl F dS where S is the surface given by e1-a -y – 1, ...

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Q: Consider the initial value problem y" - 2y' – 8y = 0, y(0) = a, y'(0) = 3 Find the value of a so tha...

A: Given differential equation is y'' - 2y' - 8y = 0 with  y(0) = α , y'(0) = 3

Q: Find the maximum value of f(x,y,z)=y-z subject to x+y+z=1, x^2+y^2=1.

A: Let us consider the function f(x,y,z)  To determine the maxima subjected to g(x,y,z)=0 Find the lan...

Q: Question 32 Given a universal set containing prime numbers between -20 and 20 and composite numbers ...

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Q: 1. Prove that i = (0, 1, 1), 2 = (1,0, 1) and üz = (1, 1,0) form a basis of R. 2. Find the component...

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Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable ...

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Q: dx -= In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) A + - B 6. + 3 D + 6 + -15 -15 -15

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Q: = 0,0 < x < a,0 < y < b dy dx² и(0, у) 3D 0, и(а, у) 3D 0,0 <у <b u(x, 0) = 1, u(x, b) = x, 0 < x < ...

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Q: Find the Laplacian of the scalar field C = e-* sin 0 cos & at the point (1, n/3, n/6)

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Q: Suppose the temperature of a metal plate is given by f (x, y) = the temperature of the metal plate i...

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Q: Associative law for multiplication of complex number ( z1 z2 ) z3 = z1 ( z2 z3 )

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Q: Use the Monotone Convergence Theorem to show that the sequence {an} converges, where +00 an = 1 - n!...

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Q: 21. If f(x) = 2x - 1 an d gx) = 3x + 5, what is f(g(5))? 22. Graph the following equation. 4х - Зу -...

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Q: 22 23. Find the product. (-3x – 7)(5x + 8) 24. What's the equation of a horizontal line through the ...

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Q: (x+x³) (x Tan-'x+ 1) 3 -1 - -is -5 -is

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Q: 3- (2. -6 -5 -4 -3 -2 2. -2 -5 -7 -8- Write an equation for the graph above. f(z) = 4.

A: Graph of the trigonometric function

Q: Solve: t? (dx/dt) + 3tx = t4 In (t + 1), x(1) = 0. %3D

A: Let us consider the differential equation dydx+P(x)y=Q(x) To determine the solution of the equation ...

Q: Determine whether the equation is exact. If it is, then solve it. (e'y + te'y) dt + (te + 2) dy = 0.

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Q: dx = In[F(x)]+C. what is F(/3) if C = 0? For (x+x³) (x Tan-'x + 1)

A: We will integrate the function first.

Q: 12.6 7 S.

A: Concept: Here we shall use the identity,(angle bisector theorem of triangles) QPQR=PSPR

Q: Identify whether each of the following is a polynomial function. Justify your answers. a) h(x) 2- Vi...

A: We have to choose polynomial function for given function.

Q: The wildife department has been feeding a special food to rainbow trout fingerlings in a pond. Based...

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Q: Determine the missing number in the sequence. 35, 40, 50, 65, 85,

A: Given sequence is 35, 40, 50, 65, 85, ___

Q: - sec?x)emG/e sec³x dr e In (a le) What should be the value of A for to be integrable using the form...

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Q: Use Stoke's theorem to evaluate the integral curl F. dS where S is the surface given by z = e1-a²-y ...

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Q: Let S be a 2D subspace of R°. Find projs if projs =

A: Given that S is a 2D subspace of ℝ3 projs&lt;2,-1,1&gt;=&lt;0.5, 0.5, 1&gt; So, consider the 2-D pla...

Q: 3x2+3y2-18y+15 F (x. y) = 4- /2x+4y+4 a) Find domain b) Find sign Diagram

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Q: 1. Some Caribbean pirates recently acquired a great deal of treasure, making them the richest (and m...

A: The upper part of the treasure box is a half-cylinder.Whose diameter is 7 mThen, radius = 72 mAnd he...

Q: 37. Which of the following accurately shows the constraint on the daily capacity for the third produ...

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Q: Q1) Determine the gradient of the following scalar field V = e(2x+3y)cos5z Q2) Given f = x²y + 3z + ...

A: Since you have asked multiple question, we will solve the first question for you.  If you want any s...

Q: Match the differential equation with the appropriate slope field. y' = O A) B)

A: Note: We know that, the slope field is a visual representation of the solutions of a first-order dif...

Q: If L(x, y, y') = S 2y(1+ (y/)²)-'dæ what alternative form can the Euler equation Ly – Ly = 0 take? d...

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Q: Consider the experiment of rolling a pair of tetrahedron. a. Find the sample size. b. Find the eleme...

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for y...

Q: Find the specific solution to the following 2nd order non- homogeneous differential equations b) d²y...

A: Given d2ydx2 + y = sin(x)

Q: FIND THE ARG(Z) 0F THE FOUOWING compLEX NUMBERS

A: Solution

Q: 1 2. Let bn = COS and cn = cos for all n e N such that n > 2. Determine whether the given series con...

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Q: 2y + 5z - 3w = 16 2x + 3y + 3z + 4w = 110 2x + 5y -3z + 4w = 74 -x+ 4y + 5z - 2w = 30

A: We will reduce the system in echelon form by using row operations.

Q: Let L(R") be the set of linear transformations T : R" →→ R² with the metric ||T – ||. Recall from Li...

A: We need to prove that for, T∈GLn and r=T-1-1, the r-neighborhood of T in L(ℝn) is contained in GLn. ...

Q: Prove by contradiction: If x is a nonzero rational number and y is an irrational

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Q: Given the orthogonal basis B for R4 and the vector v below, find the Fourier coefficients for v with...

A: Given  we have given the orthogonal basis for R4 and the vector v below  B =1-21-2, 10-10, 4-347, -2...

Q: 3x2+3у2-18y+15 4- /2x+4y+4 F (х. y) %3D a) Find domain b) Find sign Diagram

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Q: Elsa made $374 for 17 hours of work. At the same rate, how much would she make (in $) for 7 hours of...

A: Since the person makes $ 374 in 17 days. Calculate the the amount earned in 1 day.

Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)