Find the equation of the line through (2,4) that cuts off the least area from the first quadrant.

Q: Find an equation of the normal line to the parabola y= x2 -5x +4that is parallel to the line  x-3y…

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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: Find the equation of the least squares line and use it to predict the elongation when the tensile…

A:

Q: The highway department is planning to build a picnic park for motorists along a major highway. The…

A: We have, The highway department is planning to build a picnic area for motorists along a major…

Q: Find the dimensions of the isosceles triangle of least area that circumscribes a circle of radius r.

A: We have given isosceles triangle that circumscribes a circle of radius 'r'.

Q: Determine the area of the largest possible rectangle whose base is on the x-axis and the top two…

A: The given curve is y=9-x2

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 equation bounded by x = 9yeY and x = 3y2, y = 3 and y = 9 %3D %3D Write your answer in two…

A: solution is given below

Q: Find the area of the region bounded by the graphs of the equations. x² + 8x, y = 0 y 200/3

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Q: Find the exact area of the shaded region: (0, 4) y = 4 - x2 3 (3,-5)

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Q: estimate using the Linear Approximation and find the error using a calculator. 9^1/3 − 2

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Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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

A:

Q: Find the dimensions of a rectangular box of volume 1000cubic inches for which the sum of the…

A: Let x,y,z be the length, breadth and the height of the rectangular boxxyz=1000  and the sum…

Q: find the area of the loop of the curve y^2 = x^3 (1-x)^6

A:

Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given : y = 2x2 + 10, y = 4x + 16 and the lines x = -2 and x = 5.   To find the three areas.

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: Find the area of the region bounded by the x-axis and the lines x =- 2 and y =- 4x + 20.

A: It is known that area of region bounded by the curves is given by the integral, A=∫abf2(x)-f1(x)dx…

Q: Find the area of the region bounded by y=square root of 2x, y=3x-4, and y=0

A: Recall: Area between the curves:      If f(x) and g(x) are two continuous functions and f(x) ≥g(x)…

Q: Find the areas of the regions enclosed by the lines and curves, y = x² - 2x and y = x yx728 3

A: Given curves are y = x2 - 2x and y = x

Q: Find the area of a triangle bounded by they axis, the line f(x) r, and the line perpendicular to…

A:

Q: Find the area of the shaded region 10x) = 8x - 2x - x, g0x) = 0

A:

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

A: Given : Point (6,6)

Q: Find the average value of(x,y)=2x^2y^2 over the rectangle R with vertices (−6,0),(−6,2),(6,0),(6,2)…

A:

Q: Find the areas of the regions enclosed by the curves and lines y2 = 4x, y = 4x - 2

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find an equation of the normal line to the parabola y = x 2 - 5 x + 4 that is parallel to the line…

A: Given:       y=x2-5x+4 is parallel to the line x-3y=5.

Q: A farmer wants to construct a fence around an area of 6936 square feet in a rectangular field and…

A:

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: y = 4x,_y = 4x – 2

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: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: How many square units is the area of the region bounded by the two curves y = x^2 - 4x and y = x^3 -…

A:

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: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: What is the standard linear approximation?

A: A linear approximation is an approximation of a general function using a linear function. They are…

Q: Find the area of the shaded region. (9,3) x = y2 (0,0) (9,-3)

A: Using horizonal strip Established double integral

Q: Find the area of the region bounded by y=−4x+ 9, y= 2x^2−11x+ 9, and the lines x=−2 and x= 5.

A: The area of the region bounded by two curves y=fx and y=gx, where a≤x≤b, can be calculated by using…

Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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

A:

Q: Find the region bounded by y=2sqrt(x-1), the x-axis, the line x=5 and the line x=17.

A:

Q: Find regression of line

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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 a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: Sketch the region in the xy  -plane defined by the equation or inequalities. |x|<4 and |y|<2

A: x<4  and  y<2⇒-4<x<4  and  -2<y<2   ∵x<a⇒-a<x<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