Which one of the following is the gradient of the tangent line at the point (6, -3) on the graph of, x + xy + 2y² = 6? Select one alternative: 1 6 O O O 1 6 1 3 3

Q: 口 38 Which one of the following equations describes the tangent plane to the curve, f(x, y) =…

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Q: Solve the following initial value problem using Laplace transform d'y dy dt -2y = 6e³t; dt² y (0) =…

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Q: 2.) Find the volume of the solid generated by rotating the region enclosed by y = x + 3, y = 0, x =…

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Q: A water tank is in the shape of an inverted cone. The cone is 8 ft tall and 8 ft wide at the top.…

A: Given a cone of 8 feet height and base has a diameter of 8 feet, the cone is inverted. To find the…

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: 12. The graph of y=x² between x=1 and x=3 is rotated completely around the x-axis volume generated.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: temperature function satisfies Tx(2, 3) = 1 and T,(2, 3) = 3. How fast is the temperature rising on…

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Q: 5. 1-cos2y 1+cos2y dy

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Q: To say that x + 5| ≤ 3 is the same as saying is in the closed interval [A, B] where A is: and where…

A: The objective is to find A and B.

Q: Solve the equation. Approximate the solution to four decimal places. e5 — 3x = 10

A: We can Tak ln both side and solve as follows

Q: 1. n² Determine whether the series Σn=13n+1 ln(n+1) is convergent or divergent.

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Q: Use Lagrange multipliers to find the absolute maximum and minimum values of the function z = f(x, y)…

A: The function z=fx,y=x2-xy+y2 subject to the constraint x2+y2=8

Q: Determine the area bounded by y = x³ and y = 4x using a vertical element

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Q: 3. Compute the net area of the following function on the given interval. f(x)=x²-4; [-2,2] -14 <-2…

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Q: Distance Between Two Cars A car leaves an intersection traveling east. Its position t sec later is…

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ = dx 7x +…

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Q: 10. Show that there is a root of cos(x): = in the interval (0,7). TT Do NOT find the root. Explain…

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Q: 50° 60° 70° ?

A: To find the measure of the unknown angle in the following figure.

Q: 8. Find the area bounded by y=ex, y=x² and x=2. a. 3.1 u² b. 4.1 u² c. 5.1 u² d. 6.1 u²

A: Here we have to find the area bounded by the given curves.

Q: Solve the given differential equation by separation of variables. dp = P - p² dt et+c P = _t+c X

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Q: Suppose that f(5) = 1, f '(5) = 7, g(5) = −5, and g'(5) = 8.Find the following values.

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Q: You have a penny, a nickel, a dime, a toonie, and a loonie. How many different (non-zero) sums of…

A: You have penny, nickel, dime, toonie and loonie  How many different sum of money produce

Q: Find the derivative of each of the following functions using any method. 4.) f(x) =…

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Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: 1 A large tank is partially filled with 100 gallons of fluid in which 40 pounds of salt is…

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Q: A Ferris wheel is 57.85 m tall and has a diameter of 54.4 m. What are the dimensions of a scale…

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Q: xdx+sin y ४ (vdx-xdy}=0

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Q: f(x) = 2²3 on (0, ∞) x+3

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Q: x dx 2)√√√27+6x-x²

A: Given, ∫ x27+6x-x2dx

Q: If f(x) is linear, g(x) is linear, and h(x) = f(x)/g(x) What is the maximum number of vertical…

A: fx is linear, gx is linear and hx=fxgx

Q: The speed of sound traveling through ocean water with salinity 35 parts per thousand has been…

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Q: What is the derivative of x² + y² = 9 using mplicit differentiation? dx = xy dy dx = -xy dy dx dy dx…

A: Given query is to find the derivative of the expression.

Q: Show that the following series is divergent using the Test for Divergence. 4k³ - 1 k³ + 5k² + k k=1

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Q: 17 Describe the effect on the function f(x) = √x to g(x)=√x-2. F The graph was a vertical…

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Q: dx It see ax a) x + 1 (cot ax- csc ax) + c 6) x + 1 ( cot ax + μc ax) + c c) x + £ (cut ax + cac ax)…

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Q: L (a) √16-²16-²-² 1 dz dy dx Sketch each of the following: the solid E • the projection of E onto…

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Q: Let f(x) = 2x² - 4x and g(x) = -3x - 1. Find f[g(-4)]. f[g(-4)] =

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Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

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Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line =…

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Please see the below picture for detailed solution.

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: For the next three series, (a) determine the radius of convergence, (b) determine for which the…

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Q: What is the equation of the curve that passes through the point (-2,3) and whose slope function is…

A: Integrating the slope equation gives the curve equation

Q: Find the solution of the given initial value problem. π ty' + 2y sint, y = 1, t > 0 Y || =

A: In this question, we want to find the solution of the given first order non-homogeneous linear…

Q: Question 6c. Consider the region enclosed by the functions f(x) = √√x and g(x) =−x√x+2√x c) Find the…

A: Topic = Area

Q: 9+5d = 35-6 int equation (11) from To - 113 = 9+126 = 77

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Q: rectangular plot (the fourth side is a er and will not require fencing). Find the dimensions of the…

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Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…