There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2 and the x-axis into two regions with equal area. What is the slope of that line?

Q: The area bounded by the curve y 4x and the lines r = 6 ,x = 10 and a axis is

A: As per guildlines we can solve one question at a time. If you want answer of all please ask them…

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: If a rectangle has its base on the r-axis and two vertices on the curve y = e-", show that the…

A:

Q: Find the three areas of the region bounded by y=2x^2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+16x=−2x=5

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

A:

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 area of the region bounded by the parabola y = 3x2, the tangent line to the parabola at (3,…

A:

Q: Find the slope and y-intercept of the line through the point (10,9) that cuts off the least area…

A: Equation of line in point slope form : (y - a) = m*(x-b)  Where, slope = m and point = (a,b)

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

A:

Q: The area of region bounded by the parabola y2 = 4x and the line %3D y = 2x – 4 is

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4 .

Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: Given,

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: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: What is the area of ​​the region between the parabola y=x^2-1 and the line y+2x=2?

A: The solution is given below in the next step:

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: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

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

A:

Q: A few years ago, there were light sabre battles. What is the distance between two light sabers given…

A: Solution of this question is

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

A:

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

A: -1≤y≤3

Q: Find the area of the region bounded by the parabola y = 2x2, the tangent line to the parabola at (3,…

A:

Q: Find the area of the region bounded by the parabola f(x) = 16-x^2 and the lines  x=0 and x = 4 and…

A: Givenf(x) = 16-x2lines x=0, x=4 and x-axis(y=20)

Q: y = -a(x – h)? +k (-2.1 , 2.9) (1,n)

A: The given curve is y=-ax-h2+k. Here h=-1 and k=11 given. So the curves becomes y=-ax+12+11. Also the…

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 number b such that the line y = b divides the region bounded by the graphs of y = 9x2 and y…

A: To find the number y=b that divides the region bounded by the graphs of y=9x² and y=16 into two…

Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+1 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+1x=-2x=5……1   To find: Area of the region enclosed with the above curve and…

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: Find the area of the region enclosed by parabola y=3-x2 and the line  Y=3-2x

A: We have to find the area of the region enclosed by parabola y=3-x2 and the line y=3-2x. The point of…

Q: Calculate the area described by the equation y= -6x² +24x + 10, bounded by the lines x = 0 and x =…

A:

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

A:

Q: Find the equation of a horizontal line that equally cuts the area bounded by the curves 2y=x^2 and…

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 area of the region bounded by the parabola y = 2x², 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: Find the areas of the regions enclosed by the lines and curves y2 - 4x = 4 and 4x - y = 16

A: Consider a curve: y2-4x=4……1   and line: 4x-y=16……2

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: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

A:

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

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Q: The region shown below is bounded by the curve y = 2x3 and the lines x = 8 and y = 3.

A: Given y=2x13 and lines x=8 and y=3. ax=y38when x=8⇒y=4 when y=3 ⇒x=278 By washer method,…

Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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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

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

A:

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

A: To Find