An object moves along a horizontal line according to s (t) = 5t° – 2t², when is V increasing and when is it decreasing? An object moves along a horizontal

Q: If the position function of a moving object is S(t) =t - 3t + 2 meters from zero in t seconds, then…

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Q: 34. Find the slope of the curve x^2 - 3xy y^2 - 4x + 2y + 1 = 0 at the point (1,-1 O 1/5 1/6 O 1/4 O…

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Q: Find the slope of the line tangent to the curve at the given point. y = 7 cos x ; x = 4 C. - 7V2 7V2…

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Q: The temperature in Edmonton, over the course of a year, can be approximated using the sinusoidal…

A: The given sinusoidal function is: Tx=16.11sin0.51x-1.75+9.14   ......(1)where T is the temperature…

Q: Determine the speed as a function of time t for a particle having position function r(t) (t, 10t2,…

A: We have  r(t) = <t,10t2, t4>  Speed = ||r'(t)||

Q: find the directions in which the functions increase and decrease most rapidly at P0 . Then find the…

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Q: y = −2x4 + 4ax³ - 5x² - 8x + 1

A: Solution:-

Q: Find the COORDINATE POINT(S) of the extrema by using the Second Derivative Test. M needed for these…

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Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

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Q: 2. A particle is moving along a horizontal line such that its velocity is given by v(t) = 3t2 –…

A: Topic:- application of derivatives and integration

Q: Q1)a) Find line that are tangent the curve x2 + xy – y² = 1 at the point (2,3)

A: Explanation of the solution is given below...

Q: The curve y=ax^2+bx+c passes through the point (1,9) and is tangent to the line y=3x at the origin.…

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Q: Find an equation of the tangent plane at the given point: F(r,s)= 2r3(1/s0.5) - 2(1/s4), (2,1)

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Q: A particle is moving along a horizontal line such that its velocity is given by v(t) = 3ť² – 24t+36,…

A: Let's find.

Q: Find an equation for the line tangent to the graph of 4x f(r) = I + 8| at the point (2, 0.8).

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Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

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Q: Find the slope of the line tangent to the graph of y = cos 3xat x = 13π/6.

A: The slope (m)  of the line tangent to the graph y=f(x) at point (x1,y1) is given by:

Q: he path of a total solar eclipse is modeled by f(t)=0.00295t2−0.448t+25.485​, where​ f(t) is the…

A: Given: The path of a total solar eclipse is model is: f(t)=0.00295 t2-0.448 t+25.485 Where f(t) is…

Q: At time t=0, a driver jumps from a diving board that is 25 feet high. Because the drivers initial…

A: Given, Position function, h(t) = -16t2+15t+25 a) When the diver hit the water, h(t)=0…

Q: Let f(x) = 4x + 7 – 17e². Then the equation of the tangent line to the graph of f (0, -10) is given…

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Q: The position function of a particle is given by  s = t3 - 4.5t2 - 7t, t > 0.(a) Find the velocity…

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Q: The position function of an object is given by s(t) = -t + 2t. For t > 0 and s(t) = 0m, the velocity…

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Q: given the position function for an object in motion  is s(t)=-4t3+4t2-1 then the accelaration at t=1…

A: Differentiate the position function with respect to time t.

Q: The point (2,1) is on the graph of x2 . y3 + 5· x² = y² + 23. Find the slope of the line tangent to…

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Q: 5. Find the slope for f(x, y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: To find the slope for function f at point P in the direction of the line from M to N.

Q: A particle is moving along a straight line, whose directed distance from its origin is given by the…

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Q: Q2\Find the point at which the tangent to the curve y = v4x2 + 1-2 has its slop 2

A: Given: y=4x2+1-2 Slope = 2 We know that slope of tangent to a curve y is defined as dydx

Q: A ball is dropped from a 200 foot cliff. If gravity is 32 ft/sec2, find the position function of the…

A: Given :- Initial height of ball (S0)= 200 feet Accelaration due to gravity(g) = 32 feet/sec2…

Q: If s = 3t – 16t-², when will acceleration be zero? An object moves along a horizontal line according…

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Q: The position function of a particle is given bys = t3 -4.5t2 -7t         t≥0(a) When does the…

A: Given the position function of a particle is s=t3-4.5t2-7t, where t≥0. (a). We know that velocity of…

Q: A ping-pong ball is caught in a vertical plexigiass column in which the air flow alternates…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The position function of a particle is given below. s(t) = 3 + 6t2 - 61t, t > 0 When does the…

A: Velocity function is the derivative of the position function. So differentiating s(t) with respect…

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

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Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t - 3 mis over…

A: Given velocity of particle is vt=4t-3. To find the dispalcement of particle over time interval 2,5.…

Q: 5. Find the slope for f(x,y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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Q: Find an equation for the line tangent to the graph of f(x) = 7re %3D at the point (a, f(a)) for a =…

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Q: Q2\Find the point at which the tangent to the curve y = v4x² +1- 2 has its slop 2

A: 1

Q: The position function of a particle is given by = t3 – 10.5t2 – 2t, t > 0 When does the particle…

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Q: Suppose you are standing in a field near a straight section of railroad tracks just as the…

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Q: Let f(x) = 8x + 10 – 3e². Then the equation of the tangent line to the graph of f(x) at the point…

A: The given function is: f(x)=8x+10-3ex

Q: At the point (a, b) the curve æ = t2 – 4t, y = t2 + 2t, teR has a tangent line having slope 2. What…

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Q: The position function of a particle is given below. s(t) = t3 + 3t2 - 6t, t 2 0 When does the…

A: The velocity function of a particle is given byv(t)=ddts(t)

Q: Find y' and the slope of the tangent line to the graph of (3x - 4y)7 = 2y2-7 at the point (3,2).…

A: The slope of equation is defined in terms of m=dy/dx

Q: Consider a particle with a position function given by s(t)=48t-3t^2. When will the the particle…

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Q: O Find the equation of tne curuve at cvery point that passes through the point C0-1) and which the…

A: The equation of the curve which passes through point (0, -1) and which the normal line at point (x,…

Q: A particle moving on a line is at position x(t)=t3−9t2+24t−5 at time t where t is in seconds. At…

A: The given function for position of an object is where t is the time in seconds. Now, to find points…

Q: Q2: Find the slope of the curve r = -1 + cos 0 0-T/2

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Q: h(x) * |4x + 1 %3D a) Find the equation of the line tangent to the graph of fx) at x = 2.

A: 8). Given function is hx=4x+1. To find: (a). The equation of the line tangent to the graph of fx at…

Q: Q2: Find the points on the curve y 2x3 -3x2 -12x + 20 where the tangent is a. perpendicular to the…

A: y=2x3-3x2-12x+20