Q/ What is the relationship between the two lines ( L23L, ) where L1:x = 1+ 4t , y = 3 – t, z = 1+t L2:x = -3t , y = 1 – t, z = 2 - 2t

Q: a particle moves along a curve y = (2x² + 5x)°, calculatey (0) and what is the interpretation of the…

A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

Q: 5. Find the slope of the tangent line to the curve y + 2yx3 - x-5y3 = 0 at (0, 5). %3D

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 5  where the tangent line is horizontal. (x,…

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Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

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Q: What is the equation of the tangent line and the normal line to y = x2 – 4x + 2 at (4,2)…

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Q: Compute for the interval [2, 3], where y = 6x – 1. Дх Ду 6 Ax What is the slope of the tangent line…

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Q: Determine the equation of the line tangent to the curve (x+y)^7 = x^7 + y^7 (x+y)  at (−1,1).

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Q: What is the equation of the Tangent Line to the curve y = 3 x – 4 x ² at (-2, – 22)? 19 x - y = 60…

A: Equation of tangent line

Q: Find the orthogonal trajectories for the family of curves (enter your solution as an equation)…

A: Nothing

Q: Perpendicular to y + x = 0; (2, 0) on line

A: To find equation of a line ,which is perpendicular to line y+x=0,and point (2,0) lies on line.…

Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: 3. What is the equation of the tangent line to the curve x3 + x² = y which is parallel to the line…

A: Given the equation of the curve y=x3+x2 and the tangent line is parallel to 3y+x-5=0

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

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Q: 2. Estimate the slope of Ix) at the point: a) where x = 3 b) where x = 2 YA fx) 4 3 2 1 2 3 4 5 6 1.

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Q: See image below

A: Given function is

Q: 4) Find the slope of the tangent line to the curve 4 y = 3(х3 — 2х2 + 3х — 5) at the point (2,) Give…

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Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Compute y / x for the interval [2, 5], where y = 4x - 9. What is the slope of the tangent line at x…

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Q: At what point of the curve y = x* is the normal line parallel to 2x + y = 3? 2 16 ㅇ (, ) (뚜 든) 이 o…

A: To find  The point of the curve y=x^4 is the normal line parallel to 2x+y=3.

Q: b. y = 2x2 when x = 6 %3D 3.

A: Consider the curve: yx=2x23 at x=6. Find the gradient of the curve at x=6.

Q: Suppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x,…

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Q: Find the equation of the tangents: y=x² + 6x² + 10x + 8 parallel x-y= 2. to the line А.…

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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: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: Find the interval on which the curve y = - -∞, 6 dt is concave upward. (Enter your answer using…

A: We have to find out

Q: There is a tank in the shape of a paraboloid:   Water is being pumped into the tank at a constant…

A: Water is being pumped into the tank at a constant rate of 2π cubic inches per minute. If y denotes…

Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: what point/s (x,y) on the graph of f has/have the property that the line tangent to f at (x,y) has…

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Q: A researcher collected data on ( X , Y ), and wanted to test if the true relationship is linear.…

A: To test whether true relationship is linear or not, consider Lack of fit F-test. H0: There is no…

Q: The equation of the line with gradient 3 which passes through the point (1, -4) is: O y = 7x – 3 O y…

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Q: Find the equation of the line that is tangent to y = 2log3(x + 1) and is perpendicular to the line y…

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Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: Find the equation of the normal line to the curve y= 2x -x+4 at point when x=1.

A: The solution is given as

Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С.…

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is…

Q: Compute for the interval [2, 7], where y = 3x - 3. Ay Ax Ду Дх What is the slope of the tangent line…

A: we have y= 3x-3at x=2y=3×2-3 =3at x=7y=3×7-3 =18so,∆y∆x = change in y over the intervalchange in x…

Q: At what point on the curve x = 3t2 + 4, y = t³ – 6 does the tangent line have slope ? (x, y) = ( 3,…

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Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: We will find value of function inside integral and then find end points of interval .At end will…

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: determine the gradient and equationof the tangent to the curver f(x,y) = 0 in the point (a,b) for…

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Q: Hw: Al-z,0), B(210), (slope of Am) - (slape of Bm) = -, what's the trajeebory of m?

A: Given, A (-2, 0) and B (2, 0) (Slope of AM)*(Slope of BM) = -1/2 Let's assume, The coordinate of…

Q: The equation of the tangent line to the curve x2 + y? = 64, at (5,-13) is. 13 (x – 5) + 13 y = y =…

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Q: 2. What is the slope of the line tangent to the curve 8x³ - y² = 4 at the point (1,-2)? 3. What is…

A: In 2 we need to find the slope of the line tangent to the given curve at a point.  in 3 we need to…

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: What is equation of the line normal to graph of y = x^3 + 3x^2 + 7x - 1 at the point where x = -1? O…

A: Solving the problem by finding the normal of the given equation.

Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

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

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