What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for −3 ≤ x ≤ 4?

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: What is the shortest distance from the curve x^2+xy+y^2=16 to the origin?

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Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

Q: t this problem?

A: Consider the given parabola:

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

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Q: What is the largest vertical distance between the graphs of the functions y = Va and y x2 in the…

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Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: What is the maximum vertical distance between the line y =x +2and the parabola y =x2 for     -1 ≤ x…

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Q: Find the shortest distance from x²+3y²=12 to the point (4,2).

A: We have to find the shortest distance from x²+3y²=12 to the point (4,2).…

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

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Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

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 length of the curve y= 3/2x^2/3 from x = 1 to x = 8

A: Given,         The length of the curve y=32x23 from x=1 to x=8.We know that,         The length of…

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

A: Definition used -                  Vertical distance is given by -…

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

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Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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

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Q: Find the coordinate of the local maximum for the curve 21 y=2+9x- +2x

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Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

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Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

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Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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

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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 the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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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: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for -1 <x<…

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Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: please show in your solution how to get the pt of intersection between curves  y=(x)^1/3 and…

A: Point of intersection of the curves is the point where two curve intersect .

Q: Find the minimum distance from the parabola: x - y2 = 0 to the point (0,3).

A: x - y2 = 0 x = y2  Let us take a point (x,y)=(y2, y) on the parabola

Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: What is the smallest possible area of the triangle that is cutoff by the first quadrant and whose…

A: Given that the triangle that is cut off by the first quadrant and whose hypotenuse is tangent tothe…

Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

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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: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

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Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

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Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find

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.