8. Famous Curve The graph of the pear-shaped quarticb2y2 = x3(a − x), a, b > 0is shown above.(a) Explain how you could use a graphing utility to graph thiscurve (b) Use a graphing utility to graph the curve for various valuesof the constants a and b. Describe how a and b affect theshape of the curve.

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: 2/3 Example 2: Find the length of the curve y= from x-0 to x=2.

A:

Q: Question 70 please

A: Given: The equation of parabola The slope of parabola is 4 at x = 1 and -8 at x = -1. The parabola…

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A: Topic:- calculus

Q: curve Y = √x closest to the point (5,5

A: The given curve is y=x.

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A: we have been given a quadratic function y=x2-12x+11 is intercepted at right angles at the point…

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A:

Q: 1. Two control towers are located at points Q(-500, 0) and R(500, 0), on a straight shore where the…

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Q: 3Keth curve ,Orienlation, regtangular equation. X = t-1 1-7

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A:

Q: Show COMPLETE SOLUTION of the curve and sketch. Solve only the intercepts, asymptotes, critical…

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Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through…

A:

Q: Find the equation of the tangent plane to the graph of S(x, y) = In (4x² – y²) at the point (1, 1).…

A:

Q: Determine the missing coordinates of the points on the graph of the function. 2 y = arctan x -3 3…

A:

Q: 3. 4 te (-0, 0), solves x' = -2 Show that x(t) = e2t 2 2 -2 and sketch the graph of the (oriented)…

A:

Q: 5.2 Consider the curve that passes through the point (0,10) and is such that the slope of the…

A: We have to find the curve that satisfies the given conditions of the problem.

Q: find constants a and b so that the minimum for the parabola f(x)=x2+ax+b is at the point (6,7)

A: Minimum for function can be found using second derivative test

Q: Find the equation of the tangent line to the curve y=5x /1+x^2 at the point (4, 20/17) The equation…

A:

Q: 5.) y = x²(x – 5)²

A:

Q: A curve passes through the point (0,5) and has the property that the slope of the curve at every…

A: Slope of the curve is given by dy/dxdy/dx is twice the y coordinate. So, dy/dx=2y

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A: Given, The directrix of the parabola x = 5  Vertex of the parabola = 0, 0 We have to find the…

Q: 6. A quadratic function y = x2 – 12x + 11 is intercepted at right angles at the point (3, –16) by…

A: A quadratic function y=x2-12x+11 intercepted at right anglesat the point (3,-16) by another curve…

Q: 4. Use §4.4 guideline to sketch the curve: y = x - 4x¹/³ A). Domain, Symmetry, Asymptotes,…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

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Q: 1. Use calculus techniques to sketch the curve y Vr-1

A: Given: y=x2-13 To find:  Graph of the function using calculus techniques. Concept: To sketch the…

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A: To obtain closest point on the given curve from the pont (4,0) Firstly we construct a graph of the…

Q: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

A: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

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A: a)  we need to find all the points of the graph that have a horizontal tangent line For that, let…

Q: Two circles of radius 6 are tangent to the graph of y squared =4x at the point (1,2). Find equations…

A:

Q: Graph and calculate the relation of the equation x2/4+y2/16 = 1 using the points calculated in the…

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Q: Two circles of radius 8 are tangent to the graph y^2=4x at the point (1,2) Find equations of these…

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Q: Calculate the length of the curve defined by Vy(y-3)on the interval 1 < y < 9. x =-

A: Solution: Consider the given curve: x = 13yy-3 on the interval 1≤y≤9 Since we know that the arc…

Q: passes through the points (-2, -9) and (4, -6)

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: =1 at the point Find the slope of the tangent line to the ellipse 36 (x. y). slope = Are there any…

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Q: Determine the constants a, b, c and d so that the curve defined by y = ax³ + bx² + cx + d has a…

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Q: ) Find equations of the tangent line and normal line to the given curve at the specified point.  y =…

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Q: 2-x )Use the guidelines of this section to sketch the curve y3x-12VX.

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: and PrinciPle value maximum

A: A harmonic function is  a function of two variables such that, its value at any point is equal to…

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A:

Q: 5. How many lines are tangent to both of the parabolas y = -1-x² and y = 1+ x?? Find the exact…

A:

Q: Question 33 please

A: Equation of curve is as below.

Q: 4)) >〇 impending y= 言 メ= Curve, x=0 and Colculote the orea af the regien between the lines by the…

A:

Q: 1. Find the equation of the family of curves whose slope at any point is 6x. Find also the equation…

A:

Q: 5-x 8. Find the family of the curve whose slope at any point is y-3 passes through the point (2, 1)…

A: Given that slop of curve is (5-x)/(y-3) We know slope is dy/dx . Some formulas  (i). Integration of…

Q: 8) About the y-axis (0, 2) л y = 2sin (x) ;0< x≤ π X X

A:

Q: 25) Find the point on the curve y = Inx that is closest to the point (2, 3) with two digits accuracy…

A: So the point (2.731,1.0046) are closest to the curve y = ln (x)

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A: G1=+7% G2=+4%Station of PVI=6+300Elevation of PVI = 230mStation of PVC=PVI-L2=(6+300)-L2Elevation of…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.