At time, t, in seconds, your velocity, v, in meters/second, is given by v(t) = 1+t? for 0

Q: find the equation of the tangent line at x=-6 for f(x)=x^3/2. write the answer in the form y=mx+b

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Q: Q5: Does any tangent to the curve y vx cross the x-axis at x--1 If so, find an equation for the line…

A: It is required to find if any tangent to the curve y=x cross the x-axis at x=-1. First find the…

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: If a ball is thrown straight up into the air with an initial velocity of 55 ft/s, it's height in…

A: i) Answer(i): 15 ft/s

Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

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Q: Suppose that an object is moving along a vertical line. Its vertical position is given by the…

A: Suppose that an object moving along a vertical line . Its position is given by the equation…

Q: For which value(s) of x does f(x)=2x33−2x2+4x+14 have a tangent line of slope 2? Select all correct…

A: we have to find value of x at which slope of f(x) is 2means f'(x)=2

Q: A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over…

A: A particle is moving along the y-axis its position is given by y(t)=t3-6t2+9t      at…

Q: If a ball is thrown straight up into the air with an initial velocity of 40 ft/s, it height in feet…

A: Given initial velocity u= 40 ft/s The height in feet after t second is given by  y=40t−16t2 for t= 2…

Q: (b)Using any suitable root-finding technique, estimate the fastest time for the velocity to achieve…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If a ball is thrown straight up with a velocity of 40 ft/s, its height (in ft) after t seconds is…

A: y=40t-16t2

Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

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Q: If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given…

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Q: Find all values of x at which the tangent line to the curve 2x + 11 is perpendicular to the line y =…

A: Graph and tangent line

Q: Find an equation of the tangent line to the function y 5x at the point P(1, 5). Solution

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Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: a car move with an initial velocity of * 50 m/s to the right, determine its position when t=15 s, if…

A: This is a problem related to newton's law of motion. Based on the general formula and concept we…

Q: If a ball is thrown in the air with a velocity 42 ft/s, its height in feet t seconds later is given…

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Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

A: Given that: To find:

Q: 1. For the function f(x) = 2x? + 7x – 3, - (a). Find the slope of the tangent line at x = 2. [1Mark]…

A: The answers are : (a)  15  (b) y = 15x - 11   The detailed solution is as follows below:

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

A:

Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: Find an equation of the tangent line to the graph of h(x)= 2x-x'at the point (-2, 4). Write the…

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Q: 3. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A: Consider the given position function. st=-t3+3t2-6 Find the double derivative of the position vector…

Q: The volume, Vm³, of liquid in a container is given by V = (3h² + 4) ³ - 8, where h m is the depth of…

A: Solution

Q: 4) Find a formula for the line tangent to the curve at the point (4,4).

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Q: Find an equation of the tangent line to the curve

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Q: What is the slope of the tangent line to the curve y=v(x-2) at the point (6,2)? 1/2 (E) None of the…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: (b) If a rock is thrown upwared on the planet mars with a velocity of 12ms, its height in meters t…

A: The height of the rock is given by: y(t)=12t-1.92t2 To find the average velocity over the interval…

Q: In the given question as follows, assume the accleration of the object is a(t)= 32 feet per second…

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Q: The period T of a simple pendulum is given by T=2π√L/g where L is the length of the pendulum and g…

A:

Q: For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is…

A: As per given by the question, the patient's temperature is given by; . Now, First finding the…

Q: he velocity v(t) in the table above is decreasing, 2 raveled, find O An upper estimate = units

A: Here we have,

Q: Find h'(-3) if h = f o g, f(x) = 8x? – 2 and the equation of the tangent line of g at -3 is y = -3x…

A:

Q: Assume a particle's position is given by f(t)=3/t,where t is measured in seconds and f(t) is given…

A: Assume a particle's position is given by ft=3t ,where t is measured in seconds and ft is given in…

Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: If a rock is thrown upward on the planet Mars with a velocity of 12 m/sec, its height (in meters) t…

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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: 2. Find the slope of the curve r = e® at the point with 0= t/2.

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Q: D. Now that you know the equation of the line of best fit, use the equation to estimate the BMI of a…

A: Use EXCEL to determine the regression equation.   EXCEL procedure:   Go to EXCEL Go to Data&gt;Data…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 0. If the…

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Q: 6. The acceleration of a body moving in a straight line is given in terms of timet by a(t) = 8-6t If…

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Q: The graph of the acceleration a(t) of a car measured in ft/s is shown. Use the Trapezoidal Rule with…

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Q: The volume, Vm³, of liquid in a container is given by V = (3h² + 4) - 8, where h m is the depth of…

A: Given, V=(3h2+4)34-8 Where V m2 is the volume at any depth h m.

Q: please explain the whole question

A: The general form of Simpson’s rule is

Q: For what value of x is the tangent line to the curve y= x2 -6x+5 horizontal? A) none of the given…

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Q: 1. For the function f(x) = 4x? + 6x – 6, (a) Find the slope of f(x) at x = 4 (b) Find equation of…

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Q: According to B. F. Visser, the velocity v of air in the trachea during a cough is related to the…

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Q: Where on the curve of 1 does the tangent have the greatest positive slope? y = 1+ x? O 1) 3 3 O 2) 3…

A:

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.