There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the x- axis into two regions with equal area. What is the slope of that line?

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the slope of the line through the point (12,15) that cuts off the least area from the first…

A: Given: (12,15)

Q: There is a line through the origin that divides the region bounded by the parabola y = 6x x-axis…

A: We will find the slope

Q: There is a line through the origin that divides the region bounded by the parabola y = 5z – 2z and…

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Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

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: There is a line through the origin that divides the region bounded by the parabola y=4x−6x2y=4x-6x2…

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Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x and the…

A: Answer

Q: There is a line through the origin that divides the region bounded by the parabola y = 8z – 32 and…

A: According to question given :There is a line through the origin that divides the region bounded By…

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: Find the shortest distance between the line y - x=1 and the curvex =y.

A: NOTE: Refresh your page if you can't see any equations. . the given line is  compare this…

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: There is a line through the origin that divides the region bounded by the parabola y = 7x – 3? and…

A: The equation of the line passing through the origin is y=mx where m is the slope of the line. The…

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: A rectangle is bounded by the x-axis and the parabola y=9-x². What length and width should the…

A: Solution :-   Given,A rectangle is bounded by the x-axis and the parabola y=9-x2Since, y aixs is the…

Q: What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance =…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: The given equation of the parabola is,

Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

A:

Q: 3. What is the height of the right circular cylinder with greatest volume that can be inscribed in a…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

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: There is a line through the origin that divides the region bounded by the parabola y = 8x- 32 and…

A: Here we have to calculate the slope of the line  It can be calculated by finding the area and then…

Q: A rectangle is inscribed in a parabola y²=8x with one of its vertical side passes through the point…

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Q: A rectangle is bounded by the x-axis and the semi-circle y = √(36 − x^2). What length and width…

A:

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: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 2 –…

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Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

A:

Q: How many square units is the area of the region bounded by the parabolas y = x^2 and y = -x^2 + 4x ?

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Q: What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval…

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Q: The base of a three-dimensional figure is bound by the line x = y² and the y-axis on the interval…

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Q: Sketch the region in the xy  -plane defined by the equation or inequalities. -1 <=y<=3

A: -1≤y≤3

Q: Find the largest possible area of an isosceles triangle with two vertices in the curve y=4-x^2 and…

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Q: There is a line through the origin that divides the region bounded by the parabola y 2x 5x? and the…

A: Shown below

Q: A rectangle is to be inscribed between the parabola y = 4 -x² and the X- axis, with its base on the…

A:

Q: find the length of the curve y = 2x6+1/8x2 from x is greater than or equal to 1 and less than or…

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Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

A:

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

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x- 3x2 and…

A: Given the parabola : y=7x-3x2Let the line through the origin be : y=mx   , where m is the slope of…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

A:

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

A:

Q: Find the slope of the line through the point (12,15) that cuts off the least area from the first…

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 –…

A: Given data: The given equation of the parabola is y=8-x2. The below figure shows a rectangle is…

Q: What is the average distance between the parabola y = 10x(22 - x) and the x-axis on the interval…

A: From the average of a curve to x axis in an interval.

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: The area of the region bounded by the curve y= e2x, the x-axis, the y-axis, and the line x = 2 is…

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y, the…

A: Solution of the problem as follows

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 shaded area shown in the figure is bounded by the line with equation y = 12-7x-x² and the line…

A: given functions are                                              y=12-7x-x2, y=4…

Q: ) Find an equation of the tangent plane to the paraboloid defined by -- 4x² + 5y² at the point (,-2,…

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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