Find the area of a triangle bounded by the y axis, the line f(x) = 5 - r, and the line perpendicular to f(z) that passes through the origin.

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: Find absolute maxima and minima of the function f(x; y) = x^2 + y^2 on the closed triangular plate…

A: The points are:

Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

A:

Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: nissile is propelled from the origin of a coordinate system with the x units

A:

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Find the equation bounded by x = 9yeY and x = 3y2, y = 3 and y = 9 %3D %3D Write your answer in two…

A: solution is given below

Q: Find the length of the curve y 2ln(x) from x 1 to x =4. %3D

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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 the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

A:

Q: Find the point on the graph of y = 3x2 − 2x + 5 where the tangent line is perpendicular to the line…

A:

Q: Find the point on the curve y =√ x that is closest to thepoint (3 ,0) .

A: Let (x,y) be the point on the given curve which is closest to the point(3,0) where The distance…

Q: Find the point on the Curve y rx that is closest to the point (2,0)

A:

Q: Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not…

A:

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Find the point on the line y = x closest to the point (1, 0). Hint: It is equivalent and easier to…

A: Distance between two points in xy-plane can be calculated using the distance formula. For two points…

Q: b) Find the shaded area of diagram that shecked by curve y =x² + 2x and the line y

A: The area between curves y=f(x) and y=g(x) on an interval [a, b] where f(x)≥g(x) on the interval is…

Q: Find the length of the curve y = x2 from x = 0 to x = 7.

A:

Q: and the line perpendicular to Find the area of a triangle bounded by the y axis, the tine f(z) - 9 -…

A: We have to find the area of the region bounded by the y-axis, the line f(x)=9-67x, and the line…

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

A:

Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. %3D (x, y) = %3D -

A: Given query is to find the Indicated point .

Q: FIND THE LENGTH OF THE CURVE 9y = x(x – 3)´ from X = 1 to x = 4 %3D 10

A:

Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

A:

Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

A:

Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Find the length of the curve. y = In(secx), 0Sx</4

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Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

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Q: Find the area bounded by the curve y=- 16 A 10 square units B) 16 square units Ⓒ 8 square units (D)…

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Q: Find the length of the curve 3 y = x7 – 2 from x = 0 to X = 4.

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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: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

Q: Find absolute maxima and minima of the function f(x;y) = x^2 +y^2 on the closed triangular plate…

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Q: Find a result by using variable separation for ý=secy b- xý = x + y

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

A:

Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: Find the length of the curve y = x^4 for 0&lt;_x &lt;_1

A:

Q: Find the absolute maximum and minimum values of f(x, y) = x^2 +xy + y^2 - 3x + 3y on the triangular…

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