There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and the x-axis into two regions with equal area. What is the slope of that line? Preview

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

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 the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: Find the area of the surface formed by revolving the portion in the first quadrant of the graph of…

A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

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

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Q: Find the minimum distance from the point (3, 0) to the circle x2 + y2 = 4.

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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 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 slope and y-intercept of the line through the point (9,5) that cuts off the least area from…

A: Equation of line : Y - y = m(X-x) If this passes through point(9,5) Y-5 = m(X-9) Y = m(X-9)+5 X…

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 exact length of the curve. y=3+8x3/2, 0 less than or equal to X less than or equal to 1.

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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: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal 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 parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

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

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Q: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

A: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

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

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

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Q: Find the area of the segment of a sphere formed by revolving the graph of     y = √(9 − x2) , 0 ≤ x…

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

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: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

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Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: The region in the first quadrant bounded above by the line y = 6, below by the curve y = √6x, and on…

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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: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

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: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: What is the equation of the normal line to the parabola y = 2x? – 5x + 1 at the point on the…

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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<…

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

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

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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: 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: A gutter is to be made from a piece of sheet metal that is a inches wide by bending up pieces of…

A: Width of the metal sheet = a inches We bend up x inchs on both sides.  So width of the gutter is =…

Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

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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: A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it will…

A: We will find the area and cost.

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

A: To Find