A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/s. The height of the jumper can be modeled by h (x)=-0.047x+0.361x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch.

Q: Write the equation of the tangent line to the graph of y= 8x^4-7x-1/3-x^2 at x=1 check the…

A: First we find out first derivative at x=1 which is slope of tangent line.then we use equation of the…

Q: Find the equation of the line tangent to the curve y = 3x?(x² – 6x) at x = 2.

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Q: [xsechtx'dx

A: Topic:- integration

Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: -dx х2-1 2,

A: we have to perform some mathematical operations to solve this, then using partial fraction to get…

Q: Find the equation of the line tangent to the graph of f(x) = 3x³ + 6x? – 4x – 3 at x = -6,

A:

Q: Based on the scatterplot predict the value of y when x = 30 %3D

A: The slope of the regression is downward sloping   we can see that As the X increase, the value of Y…

Q: Find the slope m and the equation of the tangent line to the graph of the function f at the point…

A:

Q: An Object moved in horizontal coordinate line according to f(x) = x^3 - 6x^2 , where f is directed…

A:

Q: Find the slope-intercept equation of the tangent line to f (x) = 3x² – 4x + 5 at the point (1, 4).

A:

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: The slope of the tangent line to the parabola y= 4x2 + 2x + 4 at the point (-1, 6) is : ?  the…

A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A:

Q: Find the equation of the tangent to the curve  y = -5x2 + 6x +7 at the point (1/2 , 35/4)

A:

Q: Use the derivative to find the vertex of parabola. y = -2x2 + 12x - 5

A: Given equation of parabola is y=-2x2+12x-5. To find the vertex using derivative. Solution: We know…

Q: a) Use the definition of derivative to determine whether the parabola y = 2x² – 13x + 5, have a…

A: Derivative y with respect to x and then equate it to the given slope to find x coordinate of the…

Q: Find the slope m of the tangent line to the graph of the function at the given point and determine…

A:

Q: If f(x) = 7x2 - x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

A:

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

A:

Q: Find an equation of the tangent line to the graph of the equation 6x - 5x8y7 = 36e6y at the point…

A: In this question, we will compute the equation of the tangent line of the given curve.

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: The rectangles in the figure have been drawn to approximate g(x) dx.

A: Left Rectangle approximation :The left rectangle approximation uses the left top vertices of the…

Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

A:

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: To find the distance between objects when they have same velocity.

Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: b) Write an equation of the tangent line to the curve x² + y - 25 = 0 at the point (3,4).

A: To find an equation of tangent line to the curve x^2+y^2-25=0 at point (3,4).

Q: Find the coordinates of the point other than the origin where the equation x3 + y3 - 72xy = 0 has a…

A: W we have to solve

Q: If f(x) = 9x2 - x³, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A:

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 64x2 +…

A:

Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: a. (t-e-4t)² sec²4t -tan 4t]

A:

Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.

A: Given curve is: (x2 + y2)2 = 5x2 – y2and the given point is (x1, y1) = (1, 1)Equation of tangent…

Q: Use the quotient rule to derive the given equation

A: Given,           ddxcscx=-cscxcotx

Q: Find the equations of the tangent lines to the graph of x2(x2 +y?) = y2 when x =

A:

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

A:

Q: (a) Use the definition of derivative to determine whether the parabola y = 2x2 – 13x + 5, have a…

A:

Q: Find the slope of the curve at the given point. y3= x3/2a-x   at (a,a)

A:

Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A:

Q: Find the equations of the tangent lines to the parabola -x² + 5x – 6 at its points of intersection…

A:

Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: find the slope of the curve at the point indicated. 19. у %3D 5x — Зх?, X =

A:

Q: Solve the given equation by using the variation of parameter. y" + y= sec² (x). %3D

A: The given non-homogeneous differential equation is y''+y=sec2x. The corresponding homogeneous…

Q: If f(x) =3x2 -x3 ,find f ' (1) and use it to find an equation of the tangent line to the curve y=…

A: Our Aim is to write an equation of tangent line to the curve y=3x2-x3 -(i) at the point (1,2).

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 36x2 +…

A:

Q: The pollution level in the center of a city at 4 am is 22 parts per million and it grows in linear…

A: Form a differential equation of first order and simply solve it.

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A:

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

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.