Find the derivative of: – 7 sin² (4x²). Hint: sin²(x) = [sin(x)]²... ...so use the chain rule (twice!).

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Q: Find the chromatic number of the graph below and prove you are correct.

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Q: Use Matrices and Grammars rule to solve the system of linear equations -x + 2y + 3z = 1 2x +z=0 = 2…

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Q: Problem 2 Solve the nonlinear optimization problem - min f(x₁,x2) = (x₁)² − x₁x2 + (x₂)² − 2x2 s.t.…

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Q: 8. + 10 Graph of f (-1,-2) (1,2) (2,0) (3,-2) The graph of the function consists of three line…

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Q: Consider the following vector-valued function: y : (−π,0) × (−1,1) → R³, y(u, v) = {cosh (v) cos(u),…

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Q: Use the technique of separation of variables to solve the following differential equation: y' + y²…

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Q: The characteristic equation for this ODE is 4= and r₂ = evaluate the solution at t = 0: y(0)= y'…

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Q: a. Find the approximations Tio, M₁0, and S₁0 for ² sin x de and the corresponding errors Er, EM, and…

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Q: Consider the following statement. 3√2-7 is irrational. This statement is true, but the following…

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Q: Find the first partial derivatives of ƒ(x, y, z) = z arctan(\) at the point (5, 5, -3). A. (5,5,-3)…

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Q: Use Laplace transforms to solve the following initial value problem. y' + 3y' - 10y= 0, y(0)= -3,…

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Q: Q 1-A:Solve the following inequality and represent it on Real Line (2) x²- 3x ≤ 4x²-5x (3) 2x x-5x+6…

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Q: What conditions on b₁,b2, b3, b4 make e [1 27 24 25 39 FI 01 b₂ by ba

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Is this my working correct for the part where I have to show it is integrable.

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Q: ) Given two vectors: A = 21-3ĵ+ A = 21-3j+7k 7k 2) B Find 1) B B = 2i+j-2k 3) AxR

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Q: The set of circles centred at the point (-2, 3). More generally, given a fixed point (a, b), what is…

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Q: 4. Let F = {s+t√2 s,te Q}. Show that F is a subfield of R. You may assume that √2&Q.

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Q: 2. Provide a graphical (one combined) solution for the system of linear inequalities below: y + ¾t >…

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Q: If the equation Gx=y has more than one solution for some y in R^n, can the columns of G span R^n?…

A: Please see the answer below.Explanation:

Q: You don't need to find an explicit solution unless you are specifically asked to. Consider the…

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Q: Write an equation for a rational function whose graph has the given characteristic. Graph your…

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Q: 3. We have seen in lectures that, for any integer n > 0, there is a ring homomorphism Pn Z→ Zn…

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Q: Prove the following statement by mathematical induction. For every integer n 20, 1-2¹-n-2+2+2. Proof…

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Q: 09: Let (R.+..) be a ring of real numbers and (M₁2+..) is a ring of 2x2 matrices over R. Let f: R…

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Q: Problem 9. Let R a ring such that a² = a for any a in R (such a ring is called Boolean). Show that R…

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Q: Suppose A is nxn matrix and the wquation Ax=0 has only the trivial solution. Explain why A has n…

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