A curve passes through the point (2,5) and the gradient of the curve at any point is given by (4-5x). Use integration to find the equation of the curve.

Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

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Q: Sx cos²xdx

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Q: Given the curve x = a² - y² over the interval 0 ≤ y ≤ a/2, find the surface area of the solid formed…

A: Solution is given below:

Q: Sketch the region of integration and evaluate the following integral. 1 SS= -dA, R={(r,0): 0sr≤3,≤0≤…

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Q: 16) .    Find the solution to the initial-value problem. y' = ey − x, y(0) = 0 y =     PLEASE SHOW…

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Q: Solve the equation for exact solutions in the interval [0°,360°). Use an algebraic method. 2 9 sec²0…

A: Given.

Q: Use implicit differentiation in finding y 1. x²³+y³ =18xy 2. x²y + xy² = 6

A: Given, x3+y3=18xyDifferentiate…

Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

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Q: 4. S (x-1)(2x³+2x²+3x+2) dx x³ (x+1)

A: The objective of the question is evaluate the indefinite integral.

Q: Given: x³y - 3x2y" + 6xy' - 12y = 2x + Inx, write the transformed equation in z. A. (D³-6D2 +…

A: Let's transform equation in z.

Q: If sin a = 0.806 and cos ß = 0.718 with both angles' terminal rays in Quadrant-I, find the…

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Q: Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = 7y-3y² and…

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Q: Problem E4 Proof that: cos³x+sin³ x cosx+sinx + cos³ x-sin³ x cosx – sinx = 2

A: Given  cos3x+sin3xcosx+sinx+cos3x-sin3xcosx-sinx=2

Q: Given sphere A₂: x² + y² + z² - 16x + 6y - 4z + 76 = 0 1. Solve for the center and radius of sphere…

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Q: The count in a bacteria culture was 900 after 10 minutes and 1500 after 40 minutes. Assuming the…

A: NOTE: Refresh your page if you can't see any equations. . let the exponential function is in the…

Q: Find the area of the region bounded above by y = -x² + 2 and below by y = x². 4 3 2 & A wit 543-2-11…

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Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

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Q: 18 0-17 ¹8 cos(x¹8+18) Question 6 Find the total differential for the function w = Odw - 262³ y sin…

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Q: Solve the following exponential equation. Express the solution in terms of natural logarithms or…

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Q: y = |3 - x| x-Intercept (x, y) = y-Intercept -10 (x, y) = ( -12 -14 Find any Intercepts. (If an…

A: Given function:- y=|3-x|  To find:- Sketch the graph , x and y intercepts and symmetry

Q: A population of bees are dying at the rate proportional to the size of the initial hive, H(t), where…

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Q: Problem 3.3 Find the equation of the tangent line and normal line to the curve at the given point.…

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Q: (2x-6) ¹² 3. h(x)= (3 + نمو)

A: The objective of the question is evaluate the derivative of the given function.

Q: Use the Ratio Test or the Root Test to determine whether the following series converges absolutely…

A: Let's find series is converges or diverges.

Q: The following chart shows student population in a certain elementary school over a 5 year period.…

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Q: 3) Find the minimum and maximum values y = 2x5 +5x² on the interval [-2,2]

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Q: 7. Using the method of undetermined coefficients, what is the final form for a particular solution…

A: We first find complementary function

Q: dy What is the general solution to √x² + 3 dx 0 y = √√√x² + 3 + C O o y = 2√√√x² + 3 +C 2√x² + 3 +C…

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Q: The base of a three-dimensional figure is bound by the line y = 6 - 2x on the interval [-1, 2].…

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Q: 21)    Use separation of variables to find the general implicit solution to the differential…

A: Answer: The solution is given below:

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

A: This question is related to gradient of Function, we will solve it using given information.

Q: Solve the equation given. Enter all solutions, in degrees, that lie in the interval [0°, 360°). Do…

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Q: Transformation by trigonometric formulas.

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Q: The maximum number of rabbits, R, that an area can support is 100, there are currently 20 rabbits,…

A: A detailed solution is given below.

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: Suppose that the position of a particle is given by s = f(t) = 2t³ + 3t + 9. (a) Find the velocity…

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Q: A region bounded by fly) = y + 1, y = 4, and x = 1 is shown below. Find the volume of the solid…

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Q: Find all solutions of the equation 2 sin² z The answer is - COST- with < < *. 1 in the interval [0,…

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Q: Use the Integral Test to determine the convergence or divergence of the following series, or state…

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Q: Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx d²y/dx² = = x…

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Q: 2 -5 -4 -3 -2 -1 1 2 3 4 est M The function graphed above is decreasing on the interval ] < * < […

A: Function is decreasing when the graph goes downward when we move left to right in the graph.  So,…

Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

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Q: By power series, solve the ODE y' - 2xy = 0.

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Q: Question 3 Find the standard form of the equation of the ellipse satisfying the given conditions.…

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Q: A radioactive isotope has a half life of 1 min. The amount of material, A(t), at t = 0 is 10 kg.…

A: A radioactive isotopte has a half life of 1 min. The amount of meterial, At, at t=0 to 10 kg.To…

Q: Find an equation for the line perpendicular to 2x + 8y = 32 and goes through the point (-7, - 2).…

A: Let's find equation of line.

Q: The following equation is given. Complete parts (a)-(c). x³-5x²-9x+45=0 a. List all rational roots…

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Q: Find the general solution to the differential equation. y' = 2xy2 y =   PLEASE SHOW STEP BY STEP

A: Find the general solution to the differential equation. y' = 2xy2 y =

Q: Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate…

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Q: he cone z^2= x^2+ y^2, for z ≥0, cuts the sphere x^2+ y^2+ z^2= 16 along a curve C. That is, C is…

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