Write a polar equation of a conic with the focus at the origin and the given data. parabola, directrix x = 5 X

Q: Ow Find using the appropriate Chain Rule for w=y³-5x²y where x = es and y = e, and evaluate the…

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Q: Determine whether the vector field F is conservative. F(x, y, z) = ye²i + zexj + xe k conservative…

A: We have to check if F is conservative or not.

Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: We have verified that x and x are linearly independent solutions of the following second-order,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

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Q: Consider the following. u = 2i + 6j v = -7i+j+9k Find u x v. Determine if u x v is orthogonal to…

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Q: Assume that the radius r of the cylinder below is decreasing at a rate of 2 m/s, and that its height…

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Q: Question 17 V -2 8- 7 16 16 6 5- 4 3 رها را 2 1 -4 -7 1 > V V 2 3 4 5 Find an equation for the graph…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: Solve the differential equation by variation of parameters. 1 4 + ex y" + 3y' + 2y = 4

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Q: Use Newton's method to approximate the given number correct to eight decimal places. √47 1.89969104…

A: Use Newton's method to approximate the given number correct to eight decimal places.476

Q: etch the region of integration. (Select the correct graph.) In 5 5 [ins T3 124 af In y dy dx

A: Follow the procedure given below.

Q: force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the Give the…

A: This is a problem related to 2nd order differential equation of the newton's law of spring motion.…

Q: I'm still confused on the position vector. The question is Let r(t) be the position vector…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

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Q: Exercise (a) Graph fand the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3,…

A: Here we have to evaluate the given function at given values of x

Q: Write the sum of the two iterated integrals as a single iterated integral by converting to polar…

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Q: Umm can this be answered more clearer, I can't really tell what the answer is, and when I put it in…

A: Let's solve.

Q: Evaluate the iterated integral. 2 . (x+y+z) dx dz dy

A: The given integral is: I=∫02∫08∫01x+y+zdxdzdy   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Exercise (b) Find the slope of each secant line. Step 1 Recall that the slope of a non-vertical line…

A: Since the secant line is passing through another point Q(3,3) Therefore we will substitute x = 3 in…

Q: The population density of a city is approximated by the model f(x, y) = 2000e-0.01(x² + y²), x² + y²…

A: This is a problem related to double integration. Please follow the general procedure given below.

Q: A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is…

A: Basic differential equation is used

Q: Find the radius of convergence, R, for the power series ₁ (−1)n. in=. O R = 0 R = 2/1/2 R = ∞ R = 2…

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Q: Describe a plane vector u 9 Vector Match the vectors p, q, r, s, and t with one of the combinations…

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Q: (x + y) dx + (3x + 3y - 4) dy = 0

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Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: 2. (x+y) dx + (3x + 3y − 4) dy = 0

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Q: Estimate the slope of the graph at the points (x₁, y₁) and (x2, Y₂). At (x₁, y₁), slope At (x, y₂),…

A: We know:- sllope of a line passing through two points =y2-y1x2-x1

Q: 10z +2 (z+1)²(2-3)² S dz

A: ∫10z+2z+12z-32dz

Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: (d) If the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the…

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Q: Why is the Second Derivative Test inconclusive when f"(c) = 0? Explain. Please use clear…

A: This is a problem related to derivative. Please follow the procedure given below.

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. 8u, y = uv x = UV a(x, y)…

A: Given,            x=uv-8u , y=uvTo find : Find the Jacobian ∂x,y∂u,v for the indicated change of…

Q: Consider the following function. 1 x² - 25 Complete the following table. (Round your answers to two…

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Q: Given a = (5, 10) and p = (1, 3), find – ả + 4p. 10 - a + 4p =

A: a→=<5,10> and p→=<1,3>

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Topic = Differential equation

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' 3y = 12ex - 12 y(x) =

A: See  the details solution in below

Q: the function. x+1 f(x)= (a) Find the Inverse function of f. 1-¹(x) = (b) Use a graphing utility to…

A: Please see the below picture for detailed solution.

Q: Osaddle point none of these

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Q: lim x-0 tan x - x .3 X

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Q: Evaluate the iterated integral. ITT 4ze dy dx dz

A: ∫14∫01∫0x34ze-x4dydxdz

Q: Find the derivative of f (x) = 30 6/2x+1

A: Given problem:- f(x)=-302x+16  TO Find:- Deriative of f(x)

Q: Problem 2.1 Find the vertical asymptotes of the function Then graph the function. Y x² +1 3x - 2x2

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

A: simplify the expression and solve the integral

Q: Find the determinant. x² -Ed 2x 5x4 W(x5, x²) = = (x²)(5x4) - (2x)(x5) The Wronskian ---Select---…

A: We need to fill in the blanks.

Q: Write the following equation in logarithmic terms. Do not simplify your answer. e5 = 4.5 Answer ||…

A: we have to write the given function in logarithmic terms . For this, first we should know some…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Y₂ = 1/² { Ур 1+cos 2x D²+1 Уp = Ур { Т Ур - D2+1 y, = + { +++ 1 + +7c0$ 2+} D=+1cos +++cos 2x} -4+1…

A: This is aproblem related to differential equation. Based on concept of particular integral we will…

Q: Evaluate the iterated integral. 2 √4-3²3-8²-12² SS S x dz dy dx 0 -S+x² + y²

A: Given, ∫02∫04-x2∫-5+x2+y23-x2-y2xdzdydx

Q: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

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