What does the arc length formula give for the lengthof the line r(t) = ⟨2t, t, -2t⟩, for 0 ≤ t ≤ 3?

Q: Determine arc length of the graph of the equation (y-1)3  = x2 where the interval is [9,11].

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Q: length of the curve r = 4 sin 20 for ÷sos 6 2

A: To find the length of the curve r=4 sin 2θ for π6≤θ≤π2.

Q: How do the paths r1(t) = (cost,sin t) and r2(t) = (sin t, cost)around the unit circle differ?

A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

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 arc length of the curve x = (10 – 2y)³/² ,-3 < x<

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Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find…

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Q: Find the length of the arc of this curve and Sketch the curve y cu. = x sq.  from ( -1,1 ) and ( 8,4…

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Q: 1. The graph of the equation x² = -2 + y + 5 cos y is shown below for y<11. The x-coordinate of…

A: We are given the graph of the equation, x2=-2+y+5cosy is shown below for y≤11. Here, x=-2+y+5cosy.

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

Q: 4. If the length of the curve y=√√x-x² + arcsin√x on [a,1] is 1, find the value of a.

A: We have to find the value of a.

Q: Q: How many intersection points between the following curves 1+ cos(0) and 1- cos(0)?

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.