2. What is the radius of the circle defined by x + y² - 6x + 4y - 1 = 0

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A: Simplify given equation in z then  two times partially differentiate z

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A: The objective of the question is determine sizes if possible and evaluate the values x,y and z.

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Q: 36. What is the area of the region bounded by the graph of y = 3x - 4, the y-axis, the lines y = 1…

A: See the details solution in below

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A: Given :Future value =F=$65000Present value =P=?Rate = r=6%=0.06Time=t=5 years

Q: Find ₁²² x²dA where R = {(x, y) | 4x² + 25y² < 100}

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Q: Given f″ (x) = 4x−5 and f′(−1) = −6 and f (−1) = 5. Find f′(x)=  and find f(4)=

A: We have to find f′(x) and f(4).

Q: Consider the given function, h(x) = 3x² - 15x+4. (a) State whether the graph of the parabola opens…

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Q: 3. 31 √ √(²x- (2x - 4y)dydx 1 -1

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Q: Evaluate the definite integral. [*sin5(x) dx Step 1 To solve the integral 6( sin(x) sin³(x) dx,…

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Q: cos θ = 5/13 , θ lies in quadrant IV Find sin 2θ.

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Q: (a) Find a vector equation and parametric equations for the line that passes through the point A(5,…

A: We have to find solution for given questions.

Q: Q1 Pick a number A number is chosen at random from the whole numbers 1, 2, 3, ..., 25. Work out the…

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Q: 3 여 x 3

A: Given: 121-111231X=0-21

Q: 2. Approximate √64.1 by using linearization and use a calculator to compute the percentage error.

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Q: Write a recursive formula for the arithmetic sequence an given below. an= and a1= 10,19,28,37,46,…

A: To write a recursive formula for the arithmetic sequence given below.an=? and a1=?10, 19, 28, 37,…

Q: h'(x) = cosxcot(sin^3x)+cosxsinx ⠀ h(x) = sin(x) -2 (cos(t³) + t)dt

A: Applying Leibniz's rule

Q: xdx

A:

Q: Determine whether S is a basis for P3. S= (3-t, t3, 9t2, 8t + t, -1 + 3t) OS is a basis of P3. OS is…

A: Please see the below picture for detailed solution.

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: y=-3 √9-y² |25−x − y’ dxdy=

A: The given double integral:∫y=-3y=3∫x=-9-y2x=9-y225-x2-y2dxdyWe need to evaluate the above integral.

Q: JI X

A: Given 121-111231X=0-21 Let the matrix X be X=xyz

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Q: Consider two matrices H-29-1-9 and = I = (a) Find a 2 × 2 matrix G satisfying HG = I if possible. If…

A: See this solution in below

Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: Example Two tanks T₁ and T₂ each contain 100 gal of water each. In T₁ the water is pure, whereas 150…

A: AS WE KNOW THE GENERAL FORMULA IS dy1dt=inflowminconcentration of…

Q: No calculators. Find the exact length of the curve. y=2+2x³/2, 0≤x≤1

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Q: Determine whether the series is absolut Σ n = 1 sin(n) 57 O absolutely convergent conditionally…

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

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Q: 5: Find the volume of the solid which is generated by rotating the region bounded by y=√x, y=x-2 and…

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Q: If f(x) = 1/√x, use the definition of the derivative to find f'.   You must show ALL of your work…

A: The given problem is solved below in detail.

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Q: nd the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2 You…

A: Given :limx→21-x21-x2

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral 8 x-6 So ²x+8 dx

A: Use fundamental theorem of calculus to evaluate the integral.

Q: eliminate the arbitraty constats of the differential equation y = C1e^2x + C2xe^2x a. y” + 2y’ + y =…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. Select the…

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Q: 7. The points of inflection are found by solving the first derivative equal to zero. 8. When the…

A: You must have idea about Calculus in order to get the answer for these questions.

Q: Given the ODE (cscy)dx + (cos²x)dy = 0. A one-parameter solution of it is: O cosy + tanx = c siny =…

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Q: I. Use the definition of the Laplace transform, using improper integrals, to find the Laplace…

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Q: • Find f' (-1) for f(x) = (3x + 2)² in each of the following ways: • Create a table of secant slopes…

A: Solution is given below:

Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

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Q: 4. √ (4x²–5x+6) dx

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Q: Part 2. Integration by substitution Solve the following integrals through video presentation. √x+1 x…

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Q: b). Find the equation of the plane that passes by P(1, -2,3), Q(1,0,1), and the Origin O(0, 0, 0)

A: We have to find the equation of plane.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. 8. f(x) = 2³3r² -…

A: In this question we have to find the absolute maximum and absolute minimum.

Q: Find the critical point(s) of the function y = 0-2 cos (0) at 0 € [2, 4]. (Give your answer in the…

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Q: Trig Substitution: For the following integral, which trig substitution is needed? O Tangent Sine…

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Q: 17. Assume that f'(x) = (x - 1)(x - 2)²(x-3)³. (a) Find the interval(s) on which is increasing. (b)…

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Q: Verify that the function satisfies the two hypotheses of Mean Value Theorem on the given interval.…

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