The function v(t) =t° -7t +12t, [0,6], is the velocity in m/sec of a particle moving along the x-axis. Complete parts (a through (c).

Q: find an equation for the line in the xy-plane that is tangent to the curve at the point…

A: To find an equation for the line in the xy-plane that is tangent to the curve at the point t = 2…

Q: dy Give the coordinates of the point where y = sin(t)- t³ O (0,0) O (0.535,0) O (-0.535,0) (0, 1) is…

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x-…

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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: t) Find the equation of the tangent plane z = e° + x + x° + 7 at the point (5, 0, 3138). z =|

A: The answer is found in step-2.

Q: d'y Calculate the second derivative dr? for the plane curve defined by the equations #(t) = t and…

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Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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Q: Find the position function of the particle moving along a line that satisfies the a(t)=4 sint-cos t,…

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Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

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Q: dg at t = 2 dt Given g (x, y) = x² + In (xy?}vhere a = t'and y = t³ Find

A: I am attaching image so that you understand each and every step.

Q: 4 dy Given the equation Vx + 6xy + y* = 2, evaluate . Assume that the equation implicitly defines y…

A: The given equation is                                   x2+6xy+y4=2       ......(1) where y is a…

Q: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: c) Use the velocity function v(t)= 2e2m/s to compute the distance traveled by an object over the…

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Q: dy is maximum for the function, dt Give the coordinates of the point where y = sin(t)- t

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Q: The position of the particle at time t is given by s(t) = t² – 18t + 80. %3D The particle is moving…

A: The particle will move from left to right if the velocity is positive

Q: (x = t³ + 7 y = t5 – 3t d²y calculate for a function given parametrically dx?

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Q: Find the point at which the curve Sx=f +19 Ly=d-4t has a vertical tangent. (x, y) = (

A: Given: The curve is given as x = t5 + 19, y = t4 - 4t   To find: The point (x,y) at which the given…

Q: The position of the particle at time t is given by s(t) = t² – 8t + 15. %3D The particle is moving…

A: Concept used particle will move fromleft to right when velocitydvdtbecome positive.dsdt>0

Q: Find the differential of the function. y = V6 - t8 dy %3D

A: Solution: The objective is to find the derivative of the given function

Q: Find the linear approximation to the equation f(r, y) = 4 ln(z – y) at the point (2,15,0), and use…

A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

Q: At time t sec, the positions of two particles on a coordinate line are s1 = 3t3 - 12t2 + 18t + 5 m…

A: To find velocity we have to differentiate the distance s with respect to t.

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Q: A particle moves on a coordi-nate line with acceleration a = d2s/dt2 = 15sqrt(t) - (3/sqrt(t)),…

A: Given:

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: A particle moves in a straight line with acceleration a(t) = 3t2 + et, initial velocity v(0) = 4

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Q: dt F(x) = | 6+ 8t Find the interval on which the curve is concave downward.

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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

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Q: At time t 2 0, the velocity of a body moving along the s-axis is v=t2-7t+6. When is the body moving…

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Q: Find the displacement of an object on the interval 0 ≤ t ≤ 6 if its velocity is v (t) = 4t -√√t

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

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Q: Find the differential of f(x,y)=sqrt(x^2+y^3) at the point (3,2). df = ? Then use the differential…

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Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: Find the directional derivative of the function f(x,y) = 3-6xy+ 10y at the 1 point P (1,5) in the…

A: The given function is fx,y=3x-6xy+10y . Obtain ∇fx,y as follows.…

Q: Find the point on the curve z = 5 sin(t), y = cos(t), - sts. closest to the point (2,0) . (Hint:…

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Pls help ASAP

A: SOLUTION-

Q: Find the equation of the tangent plane to f(x,y)=√2xy+ 1 at the point            (2, 2),and use it…

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Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

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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: Let v(t) = -14t + t² be the velocity, in ft/sec, of an object at time t, in %3D seconds. a) What is…

A: Solution is given below:

Q: Q2: If a body is moving along the coordinate line with velocity of: v(t) = sin(nt) 1-The position of…

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Q: xe" dx+x²ydy Compute e'dr+r'ydy along the curve C: * = 31, y =t² ,0<ISI

A: Topic: application of integration

Q: dy Assuming - 9x³ - 2y - 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Q: 32. In the diagram, VW= 3, WX= 4, and VX= 8. Is WX tangent to OV? W b. yes a. no

A: We will use the property that radius is perpendicular to tangent line.

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.