The sum of two positive numbers is 20. Find the numbers if the product of the square of one and the cube of the other is a maximum.show drawing and complete solution.

Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We have to solve  part 1, 2 and 3.

Q: Find the interval of convergence for the given power series. Use interval notation, with exact…

A: We have to find the interval of convergence.

Q: y = f(x) denote the function defined as x²+x-2, if x < 1; f(x) = 1 X, if 1 ≤ x < 2; √x – 1, if x ≥…

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Q: 9² P 2 -2- -N -6 -4 4 6 f (x) above, find the following limits. answer field, in text entry mode…

A: Topic:- application of calculus

Q: True or False: Multiplying a vector by a scalar will result in a collinear (parallel) vector.…

A: 5) Here, the statement is Multiplying a vector by a scalar will result in a collinear (parallel)…

Q: Find the volume generated by revolving about y = 2, the area bounded by y² = x-1 and y = -x +3.…

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Q: A company's revenue from selling x units of an item is given as R = 1200x x². If sales are…

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Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

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Q: The scientific notation of the number 0.0023 is 2.3x10-3 صواب خطأ

A: The given number is 0.0023We need to write the scientific notation of the number 0.0023

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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Q: Given a -5, b=8, and the angle between them 150º, find: ) the magnitude of the vector a +b ) the…

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Q: 5. Given z = arctan (), Find əz/ay

A: We can answer the question as below.

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2. Lim xcosx sin²x 2 x-o

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Q: 2e^xdx-3e^ydy=0   Find y(x) and f(x,y)

A: Follow the procedure given below.

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We have to find the volume.

Q: The length of a rectangle is increasing at a rate of 5 meters per hour and the width is decreasing…

A: The length of a rectangle is 11 meters and the width is 20 meters. The length is increasing at a…

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

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Q: Find the Jacobian ə(x,y,z) / ə(u,v,w) of the transformations below. a. x=3u cos v, y=5u sin v, z=7w…

A: We want to find Jacobian.

Q: 3. The Critical Point of y = xe-*

A: Answer :-  We have to find the critical point of y = xe-x

Q: 3. The Critical Point of y=xe*

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Q: We are interested in the first few Taylor Polynomials for the function f(x)= 7e + 3e-* centered at a…

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Q: 16 The range of the function f (x)=6x-8 is all integers numbers. صواب O خطأ

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Q: If f a system of tow equations in two variables has infinitely many solutions, then it is…

A: Here we have to determine the true and false statements.

Q: y = x² - 6x² + 8x and y = x² - 4x. 2. Find the area bounded by the two curves y:

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Q: 5) -IN 위에 3 2' 2

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Q: show that if y=x/tan(x) then y'=cot(x)-csc(x)

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Q: Find the volume of the region between the planes x+y+2z = 2 and 4x+4y+z=8 in the first octant. ▪▪▪…

A: Given :x+y+2z=2 4x+4y+z=8

Q: g(x) = x²mx, -2, mx+b, if x 1.

A: We can solve this as follows:

Q: (4x+5y=-3 5x+4y=3} x=-3 and y=3 x=3 and y=-3 .B x = -3 and y=-3.0 ( x=3 and y=3 DC Solve this system…

A: we have to find solution

Q: Find the length of the arc of the curve y = (1 + x²) fron the point where x = 0 to the point where x…

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Q: A thermometer reading is 60oF at 3:00AM and a Civil Engineering student takes it outside where the…

A: Given: At 3:00 AM, thermometer reading = 60°F The outside air temperature = 20°F At 3:10 AM,…

Q: 3 If the function u = ln (2³ +2²4-²) then x ou + you is 2e^u e^2u 02 1/2 Other:

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Q: 9. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 4√108…

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Q: Use the following function and its graph to answer (a) through (d) below. Let f(x)= 6-x, x3. a. Find…

A: We have to find out limit

Q: 2. Continuity. Find all points where the function is discontinuous and identify which condition(s)…

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Q: 3) x² + y² + 16x+10y+80= 0 2 CXA6 2 5) x² + y² - 22x+26y +254 = 0

A: Here we have to find the standard form.

Q: II. Solve the following problems. Enclose fina

A: answer is in next step .please give a like

Q: 13. Convert the rectangular equation to polar form. 1+1=2

A: x2 + y2 = 25 is compare with r2cos2θ + r2sin2θ = r2 so here r = 5 tanθ = x/y tanθ= 1 θ= π/4 so the…

Q: NA AN 4 » *K 0

A: We have to graph the hyperbola

Q: {4x + 5y = -3 IS: 5x+4y=3} x=-3 and y=3 A O x=3 and y=-3 .BO x = -3 and y=-3.00 x=3 and y=3 DO Solve…

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Q: The volume of a cylinder of height 12 inches and radius r inches is given by the formula V = 12². dV…

A: Given query is to find rate of change of volume.

Q: 3. Find the inverse of the matrix. SHOW ALL WORK. [120 -1

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Q: True or False: If lim f(x) = 2 and lim g(x) = 4, then lim[3ƒ(x)² – 4g(x)] = −4 *G O True O False

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Q: Find the measures of the angles of the triangle whose vertices are A=(-2,0), B=(3,3), and C=(1,-1).…

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Q: Differentiate the function and simplify the final answer. y = 2xsin x - x^2cosx

A: Given,y=2xsinx-x2cosx

Q: Given the graph of y = f(x), sketch the graph of y=√√f(x).

A: We have to make graph of f(x).

Q: 14. The vectors a and b are given below. Use these vectors to sketch each of the following. za + b…

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

Q: a²z Find of z = In(xy) a²y

A: To find out the double partial derivative with respect to y