4. An arch is to be constructed so that its shape follows the curve y=-÷x²+10x, where x measures the horizontal distance along the ground and y measures the vertical height of the arch above the ground, both in units of feet. The general graph of this arch is shown below. (a) Based on this equation, what is the height of the arch at the turning point? Show the work that leads to your answer. (b) If a second arch was to be created that had the same height, but only half the width, determine an equation for this arch based on our work in this lesson.

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: 1 ) Find the equation of the curve for which   y” =  6x – 4 and which passes through (1,2) and (-2…

A:

Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

A:

Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x + 12. (-2,6) (2,-6) (-2,-6) (2,6)

A: We have to find point of inflection of given function.

Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: t this problem?

A: Consider the given parabola:

Q: The slope of the curve y=ax3-bx2-cx-3 at x=2 is 5. If the point of inflection of the curve is at…

A: The slope of the curve y=ax3-bx2-cx-3 at x=2 is 5. If the point of inflection of the curve is at…

Q: 12. Determine the y-intercept of a line with a slope of -2 that is a tangent to the curve: y =…

A:

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: Find an equation for the line perpendicular to the tangent to the curve y = x°- 16x + 6 at the point…

A: Given: y=x3-16x+6, 4,6 we know that equation of line which perpendicular to tangent at given point…

Q: 1) What is the slope of the graph y = 5e³x at x = 1?

A:

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

A:

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: The slope of the curve defined by the equation y-x + x =-2 at the point (-1,0) is %D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

A:

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: Find the equation of the family of curves whose slope at any point (x,y) is 3x2+4

A: To find: the equation of the family of curves whose slope at any point (x,y) is 3x2+4  We know that…

Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

A:

Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

A:

Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: For the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to solve the problem

Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

A:

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: B. Find the slope of the curve at the given point. 1. y = 4 – 3x2 at (-1, 1) 2. y = x2 – 5 at (1,…

A:

Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

A:

Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

A:

Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

A:

Q: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy =6z-…

A: We have to find y

Q: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

Q: Find the slope of the curve at the given point: 1. ( X+2y)^2 =x+10 at (-1, 2)

A: Here I am attaching image so that you understand each and every step. slope of the curve given at…

Q: 11. What is the slope of the tangent line to the curve y = 3x2 - 5 at point (-1,-2)? а. -5 b. -6…

A:

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

A:

Q: 6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a…

A: Given: x-intercept at  y = 2 y-intercept at x = -1 slope at (-2,-2) is 5. (-2,-2) lies on the curve…

Q: The curve is given by 2 + 1), 0<x<3. 3

A:

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: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

Q: or the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: For the curve y = ax³ + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: A seismological station is located at ( 0, -2) , 2 km away from a straight shoreline where the…

A: From the given data, If the earthquake was determined 5 km from the station, that means it could be…

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

A:

Q: -4 The number of tangents to the curve of y=- x³ + 6x? which have a slope of 8 is:

A:

Q: 2. Find the slope of the curve y = 3x +1 at the point (-0). Draw the graph of the curve.

A: GIVEN y2=3x+1 at(-1/3,0) we need to find the slope of the curve and graph the curve

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y + 1)/(x +1) and which…

A: We have to find the equation of line when given slope and passing through the point

Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

A:

Q: 4. Find the equation of a curve whose slope at any point is equal to x + + and which passes through…

A:

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: Two is the slope of the curve y = 4x + x2 at what point?

A: Slope of a curve is given by m=dydx  Use this formula to solve above question.

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.

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.