There is a line through the origin that divides the region bounded by the parabola y=7x-(2(x)^2) and the x axis into two regions with equal area. What is the slope of that line?

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

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A:

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A:

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A:

Q: A cylindrical gift box, whose top is in the shape of a hemisphere, is to be covered by gift papers.…

A: Volume of cylinder is given by V=πr2h Total surface area of cylinder is given by A=2πrh+2πr2 Where h…

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

A:

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: 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: 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: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

A:

Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

A:

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

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: 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: The area bounded by the parabola y = 4x2, y-axis and the lines y = 1, y = 4 is

A:

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: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

A:

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

A:

Q: Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

A:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: The equation of the parabola is given by y = 4x2.Differentiate y = 4x2 with respect to x as follows.

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

A:

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: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

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

A:

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

A: Area between curves

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A: The given parabola is: y=2x2 The tangent line at (5,50) has the slope: mx=5=dydxx=5          =4xx=5…

Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Given that, The curves are y=x2+5 and y=-x2, the line x=3, and the y-axis. Find the area bounded by…

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

A:

Q: There is a line through the origin that divides the region bounded by the parabola y=6x−2x^2 and the…

A: y = 6x - 2x2 y = 2x ( 3 - x )  Hence, this parabola crosses x axis at x = 0 and x = 3

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 –…

A:

Q: The area of the region enclosed by the parabola y =2 -X and the line y = - xis equal to:

A: Given that that a parabolic equation and a line equation y = -x. And we find area enclosed by…

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 the area of the region bounded by the parabola y = -x² + 4x - 3 and | its tangent lines at the…

A: We have to find the area of the region.

Q: The area bounded by the parabola x² = 2y, and the line x - y = -4 is 18 square units. %3D

A:

Q: What is the area of the region bounded by the parabola y = x^2 and the line y = x?

A:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A:

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

A:

Q: Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola a

A:

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 slope of the tangent line to the graph of the solution of y' = 3√√y + 7x³ that passes…

A:

Q: Find the area of the region bounded by the line y = 2x – 5 and the parabola y = x² – 4x. - -

A: Graph of enclosed region -

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 the area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

A:

Q: Find the area of a triangle bounded by the yy-axis, the line f(x)=10−2xf(x)=10−2x, and the line…

A: Now, from the graph we have the points of intersection of the lines

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.