A. Evaluate the number. P(9, 6) = ____   B.  Evaluate the number. C(6, 5) =____   C. Evaluate the number. C(96, 93) =______

Q: Convert the equation x² + y² = 36 to spherical coordinates and write in standard form, solving for…

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Q: Find the value of the line integral of f(x, y) = -3x - 10 over the curve C parameterized by x(t) =…

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Q: Evaluate each integral. *x+y ["ya [ y dz = *x+y [*** Jx-y y dz dy = • JL.Y [y dV, where E = {(x, y,…

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Q: 3.9 Obtain lower and upper bounds for Y, (G).

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Q: Question Three (a) Prove that F(x, y, z) = (y² cos x+z³)i+(2y sin x-4)j+(3xz+2)k is a conservative…

A: First question is wrong. F is not conservative.

Q: Let f(x), x ≥ 0, be a non-negative continuous function. 5T If f'(x) cos x ≤ f(x) sin x, V x ≥ 0,…

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Q: A produce buyer for a juice company is buying pears. He makes a choice of either Wisconsin,…

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Q: Let f(x)=x²-3x²+6Vxe R and g(x) = max. f(t); x+1≤t≤x+2,-3≤.

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Q: Refer to the study by Carter et al. [A-9], who investigated the effect of age at onset of bipolar…

A: Solution: We have to find or investigate the effect of age at the onset of bipolar disorder on the…

Q: Solve the differential equation: y − 3y = 4e5t at y(0) = 6 Oy=4e-3t2e-5t Oy=-4e- Oy=4e³t+2est O…

A: the given differential equation is of the form of first order linear differential equation.

Q: Convert the point (p, 0, ) = (3, 6 decimals to at least one decimal place. (x, y, z) = 2π 3 to…

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Q: How many WAYS can you make P17 using only P10, P5 and P1 coins? SHOW the different ways.

A: Solution:   Given : P10, P5 and P1    And we have to make P17. Now,        P10 P5 P1   Total 1…

Q: Compute the distance between the following vectors: V = W =

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ∞), where a > 0. b > 0 , c > 0 Find the condition if…

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Q: Describe and sketch the following set of points defined by the following conditions. (x + 2)² + y² +…

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Q: 1 f 1 + then vu Select one: O a. O b. O C. 1 O d. 1 u+v f v=u+f 1_ƒ+v fv u 1 UV u f+v fv

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Q: x and y intercept of the function

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Q: 2. Assume f(t) is a function for which points along the t-axis are measured in hours (hr for short)…

A: Given that ft is a function for which points along the t-axis are measured in hours and function…

Q: 3. Let be the Euler phi function. (d) If mn, show that o(m) (n). (e) Let (n) denote the sum of the…

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Q: Let f(x) be a differentiable function and g(x)=(ƒ(x))³ – 3(f(x))² + 4f(x) + 5x + 3sin x + 4cos x V x…

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Q: Example 6: Consider (x³ −7) € Q[x]. Let ae C be a root of (x³ -7) (in C). Find (1+ a)-¹. Q[x]…

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Q: Let A E BL(H). Then A is called normal if A*A = AA*, uni- tary if A*A = I = AA*, that is, A* = A−¹,…

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Q: Let S = {a+bx+cx²: {V₁, V2, V3} and T and = {w₁, W2, W3} be two bases in the vector space P₂ a, b, c…

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Q: Suppose you are invited to play a game in which you bet $1 on any number from 000 to 299. If your…

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Q: Alejandro wants to adopt a puppy from an animal shelter. At the shelter, he finds six puppies that…

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Q: Suppose sn and tn are sequences such that |sn| ≤ tn for all n and lim tn = 0. Prove that lim sn = 0.

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Q: In a survey of 282 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58…

A: A set is the mathematical model for a collection of different things; a set contains elements or…

Q: LL' is the latus rectum of the parabola y² = 4ax and Pl a double ordinate drawn between the vertex…

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Q: Express the function 0 { f(t) = = in terms of unit step functions and hence determine F(s), the…

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Q: A*(x) = n(t, Un)un, x≤ H. Since for all x H, A* (A(x)) A(A*(x)) = Σkn(A(x), Un)Un = Σ|kn|²(x, Un)Un,…

A: Kindly refer to Step 2 for the solution.

Q: or else explain why the Either find the limit of=1 sequence diverges. Write your answer in the…

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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: 9x² + y² - 54x - 6y +81=0 (4.) 9x² + 4y² + 324. +3826

A: We have to standardize the equation to find center vertex and orientation of ellipse . Then draw…

Q: Find the maximum value of the function f(x, y) = xye-(²x+3) in the first quadrant.

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Q: 7. Use a double integral in polar coordinates to find the area of the region inside both the…

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Q: (1) Give an example of perfect groups (i.e. the group equals to its own com- mutator subgroup). (2)…

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Q: Donald owes the bank $9450. To repay his debt, he paid a fixed amount back to the bank each month.…

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Q: without being a unitary operator. For example, let H = ² and for x = (x(1), x(2),...) in H, let C(x)…

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Q: Solve x643 = 27 (mod 800). Solve 343 = 7 (mod 900).

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Q: Write the form of a particular solution to y(3) - 3y" - y = 2e without determining the coefficients…

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Q: - Using the € – d definition of continuity, show that the func- tion ƒ : R³ → R² defined as f(x, y,…

A: Given a function f:ℝ3→ℝ2 defined by, fx, y, z=xyi^+z3j^ We are asked to show that the given function…

Q: Lemma 8.1. Let pn be the n-th prime. We have

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Q: Let/(x)=sin³ x+A sin² X

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Q: Sy". (y" + 2y' + 5y = 0 y(0) = -1 y'(0) = 0

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Q: Exercise 1 A popular text on simulation theory states that if U~ U(0, 1), then log (U) (6) has an…

A: Given U~U0,1 Let U be the random variable having standard uniform distribution with probability…

Q: Convert the point (r, 0, z) = = 5п " 6 decimals to at least one decimal place. (x, y, z) = 1) ₁ to…

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Q: Solve part b. of question 2.

A: 2) Given differential equation is y" + 2y' + 2y = h(t) , y(0)=0 , y'(0)=1

Q: 5. Write the form of a particular solution without determining the coefficients given that yh=…

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Q: 1) Find the vector and parametric equation of the line in R³ through the point P = (1, 2,-4) 5…

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

Q: Q#12 Please prove that cos(a− ß) cos(a+ß) = (cosa cos 6)²-(sina sin 6)²

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