4 The gradient of the tangent line to the graph of f(x) = 3x2 - 2kx-9 at x = 1 is 10. Find the value of k.

Q: Recall that a function is odd if f(-x) = -f(x) and even if f(-x) = f (x). Which of the six…

A: 6 Trigonometric functions are sinx, cosx, tanx, cotx, secx, cosecx

Q: Consider the matrix A [1 2-2 1 36 -5 4 48-75 Find a basis for the null space of A. What is the…

A:

Q: Facebook has a revenue function of R(q) = 5q2 -10q + 600 and a cost function of C(q) = 3q2 + 200,…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: 3. True or false For each part, determine if you believe the statement is true or false, and justify…

A:

Q: Design a circuit from a description of the circuit in English. The output is 1 if exactly two of the…

A: Option (A)      Let, f(x, y, z) = xyz     Then, f(x, y, z) = 1 => xyz = 1 iff all three of x, y…

Q: Find the slope of the tangent line to the curve 2x²-3xy + y² = 96 at the point (-2,4).

A:

Q: (c) h1,1+h3,1 12,1 5h3,1 h1,2+h3,2 h2,2 5h3,2 h1,3 +h3,3 112,3 5h3,3

A: Given: H=h1,1+h3,1h1,2+h3, 2h1, 3+h3, 3h2, 1h2, 2h2, 35h3, 15h3, 25h3, 3 We have to express each…

Q: Consider the sentence (3xP(x) ^ 3xQ(x)) 3x(P(x) ^ Q(x)). Which of the following is true? A. The…

A: Let P(x) : x is such that x ≡ 1 (mod 3)         Q(x) : x is such that x ≡ 2 (mod 6)    Then,…

Q: 3. Compute the surface integral ff G(r) dA if G(r) = r²z, and the surface S is given by S the…

A: The given surface integral is ∬SGrdS where Gr=x2z. The given surface S is x2+z2=1, 0≤y≤2, z≥0 .…

Q: 1. a. 37 b. 38 For the given triangle, use one of the reciprocal ratios to determine to the nearest…

A:

Q: Problem 1.6 L(a). (a) a = a*b (b) a = a + b* For each regular expression a, list three words that…

A: Given regular expressions are: (a) α=a*b (b) α=a+b* To Do:List three words in Lα.

Q: Generate a fractal (random, of any size) from a matrix using linear transfromation with concepts…

A: Ans- One way to generate a fractal using linear transformations is through the use of an iterated…

Q: Consider the following equations. f(x) = √x + 6 g(x) = x + 6 Sketch the region bounded by the graphs…

A:

Q: 4. This project is related to the Lyapunov 2nd method, linearization technique, La Salle's…

A: Ans- a) To find the equilibria of the system, we set all the derivatives to zero: $\dot{x}_1 = -x_1…

Q: Find the function f (x) if f" (x) = -2 + 12x12x² and f(1) = 5, f' (-1) = 2.

A: As Per Bartleby Answering Guidelines We Solve Only First One Problem  Given that the differential…

Q: a. The necessary and sufficient conditions for a non- empty subset W of V(F) to be a subspace are…

A: (a)Suppose W is a subspace of a vector space V(F). Then if β∈W⇒-β∈W∴ α∈W, -β∈W⇒α+(-β)∈W     (∵ W is…

Q: Let f(x) = sin(x) + 15x. We can check easily that f (0) = 0. Explain using the Mean Value Theorem,…

A:

Q: The graph of f(x) is shown (see figure). 9x² x²+2 f(x). (a) Find the following limit. L = lim f(x) =…

A:

Q: (4) It is given that f(t)= find the Fourier series of f(t). cost, when 0 ≤tsa 0, when ≤t≤ 2m;

A:

Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) 1 = 2…

A:

Q: Consider the graph G with • V(G) = {2,3,6} e(G) = {a, b, c, d, e, f, g} • E(G) = {(a, [2,2]), (b,…

A:

Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+5yιι =yι2   →1Let yι =u →Adydx=ud2ydx2=dudxd2ydx2=dudy×dydxd2ydx2= ududy →Busing Aand B in…

Q: State the Domain of f, i.e., the largest set on which the function f(x,y) = √√√x² + 6y² − 42 is…

A:

Q: Compute the inverse Laplace transform of the following functions. -2s 2s³+3s²+2s+27 (s²+9) (s²+1)

A:

Q: Given that W(x) = (ex - 11nx + 340x5)/(7x3 - 32ex +5lnx). State the rule and explain three(3) steps…

A:

Q: I don't understand why the double integral of z dA over region D turns into…

A: Given information: Cylinder: x2+y2=4. Ellipsoid: 4x2+4y2+z2=64 To explain the steps: ∫∫D z…

Q: Sketch the graph described by the following cylindrical coordinates in three-dimensional space. 2…

A: Given: Cylindrical coordinates: r≤z≤25-r2We need to sketch the graph described by the given…

Q: A choreographer is working with 15 dancers for a new Broadway musical.  For one routine, the…

A: Given that a choreographer is working with 15 dancers for a new Broadway musical. The choreographer…

Q: (3) We look at the matrix "a" found with the Matlab commands >> a = ones(100) >> for i= 2: 100 for j…

A: Answer : This MATLAB code generates a 100x100 matrix "a" with all elements set to 1, and then it…

Q: A cylindrical tank standing upright (with one circular base on the ground) has radius 1 meter. How…

A: Given that cylindrical tank standing upright has radius 1 meter. To determine how fast the water…

Q: Solve the system of linear differential equations: x₁ = 3x₁ + x₂ x₂ = -2x12x₂ + x3 x3 = -2x2 + 3x3

A:

Q: 1. Given the first derivative of a Conference function is h'(t) = -8t + t2 - 9, where t represents…

A:

Q: 15. The angle of elevation from the ground to the top of a flagpole is measured to be 53. If the…

A:

Q: 1 bat (= {0, das 29,65, 19, 4, 65, La, b, c, d, 25, bes, x5 be a toroligy on X=(², B₁3e5 (2) List…

A: 1. The neighborhoods of e are the sets that contain e in their interior. From the topology T, we see…

Q: List all possible equivalence relations on the set (1,2,3,4) without repetition up to isomorphism.…

A: Introduction: An equivalence relation is a binary relation on a set that satisfies three properties:…

Q: Find the complex conjugate eigenvalues and the corresponding eigenvectors of the matrix. 0-7 7 0

A: The given matrix 0-770. To find the eigenvalues and the eigenvectors.

Q: a. Define a relation R on Z as follows: For all integers m and n, mRn ⇒ m = 2n. Then 3R6 (A) True…

A: Given: A relation R on Z define as ∀ m , n ,mRn⇔m=2n To Find: Whether the following are true or…

Q: For the data in Problem 7, generate the following LSE regression curves: y = ao + a₁x (linear), y =…

A: Ans- In the predator-prey model with logistic prey growth, we have the following differential…

Q: Find inverse of the matrix or show that it doesn't exist 1 -2 1 4 -7 3 -2 6 -4 (a) [₁ 1 2 4 7 (b)

A:

Q: Consider the sentences Vx3yP(x, y) and 3yVxP(x, y). Are these sentences true or false under the…

A:

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A:

Q: Suppose po = 1. Find n such that Pn - p ≤ 10-10.

A:

Q: 2. Determine the present value of the annuity which provides a payment of $750 every t an interest…

A: Formula for the annuity is  PV=R1+in-1i We are given R=$750n=5×4=20 quartersi=3.25400 (since 1 year…

Q: Prove: If f is a polynomial on C, then the zeros of f' are contained in the closed convex hull of…

A: Given: f is a polynomial on C.To prove: The zeros of f' are contained in the closed convex hull of…

Q: Minimize c = 3x + 3y subject to x + 2y ≥ 38 2x + y ≥ 38 x ≥ 0, y ≥ 0.

A:

Q: dy - +(1+x)y=e*; y(1) = 0 X- Solve dx

A:

Q: A woman buys a house for a $340,000. She pays $40,000 down and takes out a mortgage at 5.7% for 20…

A: Value of house=340000 Down payment = $40000 So, Amount left for mortgage = 340000 - 40000 = 300000…

Q: The matrix 5 0 -5 0 0 0 -10 -10 0 0 15 15 has two distinct real eigenvalues X₁ < A₂. Find the…

A:

Q: A rectangular storage container with an open top is to have a volume of 14 cubic meters. The length…

A:

Q: L.P. Model: Maximize Subject to: Z = 1X + 10Y 4X+3Y ≤ 36 2X+4Y ≤40 1Y 28 X,Y 20 1.) Plot and label…

A: