Find the linear velocity of a point moving with uniform circular motion, if the point coversa distance s in the given amount of time  t     s = 30mi and t = 2  hr

Q: Find an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: What is the graphical interpretation of instantaneous velocity at a specific time t = to?

A: Instantaneous velocity at a specific time t = to is the slope of the tangent to the curve of…

Q: . Find an equation of the tangent line y = e* that is parallel to the line x – 4y = 1.

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Q: What is the slope of the tangent line to the curve y = T I 7 O-2 02 0 - 17/12 01/1/01 O none of the…

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Q: Find equations of the tangent and normal line to the curve x? – xy – 3y2 = -4 at (1,2).

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Q: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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Q: Find the equation of the tangent line to the curve y=2sin(x) at the point (pi/6, 1) in y=mx+b

A: Using equation of tangent formula.

Q: Find the ABSOLUTE VALUE of the gradients of the tangents drawn to the ellipse x^2/4+y^2/93D2 at the…

A: We have to find absolute value of gradient at x=2 for the given function.

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=0 in the given equation So the point satisfies the equation

Q: Find the equation of the tangent line to the curve y = IVI at the point (9, 27). %3D y = 9x(sqrt(27)

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Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: 2e* Y = 1+ et

A: Topic = Application of derivative

Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t=0 tot = 3.

A: A detailed solution is given below

Q: Find the equation of the tangent line to the curve 3 x' + 2 y – 22 = 3 xy – x at the point (2, 2).…

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Q: Determine the slope of the tangent line of the curve y = x+4 at x = 7. O 14 O 28 O 21 0 7

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Plot the "astroid" y = (4 - x 2/3) 3/2 for 0 ≤ x ≤8. Show that the first-quadrant segment of each…

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Q: Find the velocity of Zoe relative to the surface of the water.

A: The velocity of Zoe Vz is 3 km/hr to west. Velocity of the current Vc is 15km/hr to north. So, the…

Q: Find the equation of the tangent line and normal line to the given curve at the specified point. y =…

A: The given equation is,

Q: Find the equation of the tangent line to x? – y + y? = 21 at the point (1,5).

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Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Find the slope of the tangent to the curve y at (2, 1) %3D xy + 6 dy dx (Enter undef if the slope is…

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Q: The equation of the tangent line to the curve z +y = 36, at (2,-19) is 19 y 3= (х — 2) - 19 19 19 y…

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Q: A DVD has a diameter of 4.75 in. and rotates at 360.r/min. What is the linear velocity of a point on…

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Q: Find the equation of the tangent and normal to the curve at the indicated point 2. y = Vx² – 9 at…

A: We have to find the equation of tangent and normal to the above curve.

Q: Find the equation of the tangent line and normal line to the curve r+4.ry +y = 13 at (2,1). %3D

A: Let's find.

Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: The x-coordinate (measured in meters) increases at a steady 10 m/sec. So, dx/dt= 10A point on the…

Q: Determine the point on the curve y 16 a² where the tangent line is horizontal. A (2, 12) (-2, -12)…

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Q: Find the linear velocity of a point on the edge of a wheel rotating 35 times per minute. The…

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Q: Find the rate of change f(r, y) = In(6x² + 10y2) at (V2, v2) in the direction making a (positive)…

A: We have to find divergence of the given function first.

Q: 2y+ In(xy) +z = 6 at the point (4,0.25, 2)

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Q: Find an equation for the horizontal tangent to the curve at Q. y = 1+ v2cscx + cotx

A: To find tangent line , find out the slope of the tangent line Take derivative to find out the slope…

Q: Find the distance from the centre at which the velocity in S. H. M. will be half of the maximum.

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Q: Find the slope of the tangent line to the curve I defined b y 5x²+8xy-4y"= 1B47 atthe point %3D…

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Q: 4. Find the point(s) on the graph of (x – 1)²+ (y +3)² = 16 where the tangents are horizontal.

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Q: Find the linear velocity of a point rotating at 30 revolutions per second on a circle of radius 6 cm

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Q: Find the linear velocity of a point moving with uniform circular motion, if the point covers a…

A: From the data: s=45 cm t=5 sec

Q: Find the equation of the line tangent to xe' + ye = 1 at the point (0, 1).

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Q: Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal. a)…

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Q: Find an equation of the tangent to the curve r + ry + y² = 3 at (-2, 1). %3|

A: First find the slope of the tangent with the help of derivative of the curve than write the equation…

Q: Find the slope of the tangent line to the curve (a lemniscate) 2(a² + y?)' = 25 (æ² – y²) at the…

A: The given equation of the curve: 2x2+y22=25x2-y2

Q: Find an equation of the tangent line to the curve at the given point. y = v x, (81, 9) y = |0

A: y = xdifferentiate with respect to x,dydx= 12xdydx(81,9)= 1281=118

Q: Find the slope of the tangent to the curve y² In(x) + x²y = 4 at (1, 4). %3D Need Help? Read It

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Q: Find the equations of the lines tangent and normal to the curve guen by para- metric equations at +…

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Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

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Q: find the equation of the line tangent to the curve y2+ exy=4 at point (0,2)

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Q: Find the points on the curve y = 2x3 + 3x? – 12x + 9 where the tangent line is horizontal. (x, y) =…

A: we have to find the points on the curve where the tangent line is horizontal. y=2x3+3x2-12x+9

Q: Find the tangent plane to the equation 5e* бу at the point (12, 24, 5) Z =

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Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: Let the particle is at the point (x,y) at any time t in first quadrant where y=x2  Its x-coordinate…

Q: The equation of the tangent line to the curve z? + y² = 49, at (9,-15) is , %3D 15 - (z – 9) + 15 15…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.