Alpha particles are deflected along hyperbolic paths when they are directed towards the nuclei of gold atoms. If an alpha particle gets as close as 5 units to the nucleus along a hyperbolic path with asymptote y=3/5x, what is the equation of its path?

Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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Q: Q3// Does the parabola y = 2x2 - 13x + 5 have a tangent whose slope is (-1)? If so, find tangent and…

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Q: A bowl has a shape that can be generated byrevolving the graph of y = x2/2 between y = 0 and y = 5…

A: The Volume of the bowl is given by

Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

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Q: t this problem?

A: Consider the given parabola:

Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

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

A: topic - derivatives and linear equation in two variables

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

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

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Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

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Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: A particle is moving along a hyperbola  xy= 8. As itreaches the point (4, 2) , the y-coordinate is…

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Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: Find the point on the curve 4x

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Q: 2. Find the equation of the horizontal asympto

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Q: In 1911, Ernest Rutherford discovered the nucleus of the atom. Experiments leading to this discovery…

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

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Q: Find the points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

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Q: In order to graph y = 3 cotx, an interval 2 containing one period is found by solving 0 < x< T. An…

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Q: use graphs to find approximate solutions ex = 4

A: we have to use the graph to find the approximate solution of ex=4.

Q: The tail ends are extended indefinitely in both sides, but do not meet the x-axis, although they get…

A: As per our guidelines we are supposed to answer only one question per post so I am solving first…

Q: Find the length of the curve (Sketch and Solve) One branched of the curve 9y2=4x3 from x = 0 to…

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Q: The slope of the tangent line to the parabola y = 3x + 3 + 4 at the point (5, 94) is: 33 The…

A: Equation of parabola y=3x2+3x+4 The slope of the parabola at any point is calculated as  dydx=6x+3…

Q: Find the equation of horizontal asymptote of y=3(0.2^x)+15pi

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Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Find the horizontal and vertical asymptotes of the curve. 6x²+x- - 9 у x² + x - 56 X = (smaller…

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: What is the equation of the function for a parabola that moves 2 units to the right of the origin, 2…

A: Given parent function is f(x)=x2

Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: Find a point on the curve y = x2 that is closest to the point (18; 0)

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

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Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: Suppose that / (3r-x²) dr=Ax³+ Bx+C, for constants A, B, C. What is the value of C if the curve…

A: The given integral ∫3x4-x2dx=Ax5+Bx3+C

Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

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Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

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Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: The equation of a curve is y= 4x²+4lx+12-k, where kis a constant. In the case where k=1, find the…

A: If a line is parallel to the x-axis then its slope will be 0.   Slope of the curve y=f(x) is m =…

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive…

A: The curve is  y =  x3  -3a2x +2a3, where is a positive constant.

Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: The slope of the tangent line to the parabola y=2x^2+2x+7 at the point where x=4 is: slope =…

A: The equation of the parabola is y=2x2+2x+7

Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…