Problem #7: There is a line through the origin that divides the region bounded by the parabola y = x – x² and the x – axis into two regions with equal area. What is the slope of that line?

Q: find an equation for the level surface of the functionthrough the given point. ƒ(x, y, z) = ln (x2 +…

A: Given: To Find: The equation for the level surface of the function through the point (-1,2,1).

Q: Problem 3. Find the shortest distance between the point P (0, 1,0) and the line l given by x = 1-t,…

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Q: Problem 1: At what points is the function y = form. 2x²+10x+12 x²-5x continuous? Write your answer…

A: In this question, we want to know the points (in the form of interval) at which the given function…

Q: Problem III. For the bounded and shaded region, find the coordinates of the centroid. y= - 20

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Q: Let R be the region in the fourth quadrant bounded below by the parabola y=x²-3 and above by the…

A: Use double integral

Q: Find the equation of the family of curves whose at any point (X, Y) is 1. 3x? + 4 2. * y X+1 3. y-1…

A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

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Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: Figure out formulas for three level curves with levels 0, , 2 respectively. y = 0, 2y² x? = 1, 2y? +…

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Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: #10

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Q: QUESTION 7 Write your own quadratic functions that opens up and takes minimum value of 4.

A: Explained below

Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

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Q: by eliminating the arbitrary constants "A" and "B" from the family of curves Ae³x y = + Be-7x O None…

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Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z =x^2 +3y^2,…

A: z=x2+3y2 , x=1 at the point (1,2,13)

Q: Problem 1 Evaluate the line integral / 2* ds, where C is the line segment from (3,0) to (0,4) in the…

A: Given line integral ∫Cx2ds, line segment (3,0) to (0,4)

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

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Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: 1. Find the domain and two level curves of f(x,y) = /25 – x² – y2

A: As per guidelines, we will solve the first question only. 1. Given function is   f(x,y)=25-x2-y2

Q: Question 5 Suppose that you want to create a rectangular animal enclosure using 80 linear feet of…

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Q: х-у+2z (2,0, – 3) 2x + у-z'

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Q: An equation for the level surface passing through the point (2,0, - 1) is z =

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Q: B In Problems 31-40, find the intervals on which the graph off is concave upward, the intervals on…

A: Given, fx=x4-2x3-5x+3 Formulas used, ddxxn=nxn-1ddxCfx=Cddxfx            C is constantddxconstant=0…

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: Question 4 It has a local/relative maximum when x = A 2 B В) 1 c) o D -2

A: Given, The function  y=fx and the first derivative y' =xx-2 We have to find the relative maximum of…

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: Question 17 Find the point on the parabola y= - x¯ whose tangent line is parallel with y= 3x-5 +4 3…

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Q: II. Open-ended problems. 21. Two lines intersect each other in a circular plane with an equation x²…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: In problems 1 and 2, find any intercepts with the three coordinate axes and sketch a graph of the…

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Q: Problem no. 11 Find the area bounded by the curve 2x2 + 4x +y = 0 and the line y +x = 0. What are…

A: As per the bartleby guidelines we only give first three sub parts question answers.

Q: Question 4. Find the absolute maxima and minima of f (x, y) = e(x² + y²) on the closed triangular…

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? + y =…

A: Given the region bounded by the circle x2+y2=9. The height of the cross-section is 3-x and its…

Q: Given: y² = 2x - 2 bounded by y = x-5. The points of intersection of these two curves are {A}…

A: y2=2x-2 bounded by y=x-5

Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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Q: What will be the axis of symmetry, the line about which a figure or curve is symmetric, reflecting…

A: We have to find the line of symmetry of function and its inverse.

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

Q: Find the exact length of the curve. y = 5 + 8x/2, 0<x<1

A: Topic = application of derivatives

Q: Find the points on the curve y-9x closest to the point (0, 4). ) and (O

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Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

Q: 2. Find the intersection points, if any, of the given pairs of curves: a. x + 4y + 7 = 0; 2x-3y8= 0.…

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Q: Find the length of the curve of y=x³/2 from x=1 to x=4.

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Q: In Problems 1 and 2, find the area enclosed between the given curves, the horizontal axis and the…

A: Take a rectangular strip along the y-axis to calculate the area of the required region.

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: Problem 2 1 4 If f(x,y) = 3 )==x' +¯v' -x² - 3x – 4y – 3, find the local extrema and saddle 3…

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Q: Problem 1. Evaluate x-y+z-2 ds where C is the straight-line segment x = t, y = 1-t, z = 1 between…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.