cos³t and y r sin t parametrize an astroid (Figure 6.84 in the Let r > 0. The equations x = r• text). Draw the graph, and find the length L of the astroid. (Hint: Square roots are nonnegative!)

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A: Explained below

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A: Given- r=-1+sinu To Draw- The graph of the above equation of the limaçon.

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A: Given area from question:

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A: Given: Angleθ=5π6, To sketch: The given angle in standard position.

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Q: QUESTION 18 Solve the equation on the inteval Osx s2n sinx -3=-2 T TTF Paragraph Arial 3 (12pt) EE T…

A: Given : The equation is sin x - 3 = -2 , 0 ≤ x ≤ 2π   To find x.

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Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: refer to Figure 16.. Calculate the projection of −→AC along −→AD.

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Q: Question 11 Let C be the path given by the parametriç equations Xt and y -1from t=0 to t=2 and let…

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Q: -2п a) cos 3 b) cot 45° 3 с) у%3D sin-1 /2 d) y = arccos 2.

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

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A: Let's find.

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Q: "The formula specifies the position of a point P that is moving harmonically on a vertical axis,…

A: The formula specifies the position of a point P that is moving harmonically on a vertical axis is…

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A: Solution of question as follows

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A: we need to find leftmost point on the upper half of the cardioid r = 1 + cos(theta) by plotting in…

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Q: Question 19 of 34 Find the area of the region enclosed by; the cardioid r32(1-sine) A) I DONT KNOW…

A: See the details solution in below

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A: Our objective to find the cartesian equation of the curve.

Q: The graph of one lobe of r = 4 sin(30) is shown below. T/2 2 3t/2 The area of one lobe of r² = 4…

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Q: Consider the following.x = 5 cos(θ)y = 6 sin(θ)-π/2 θ π/2(a) Eliminate the parameter to find a…

A: x = 5 cos(θ)So, cos(θ)= x/5 y = 6 sin(θ)sin(θ)=y/6

Q: from Equation (3). Then find the length of the indicated portion of the curve. 11. r(t) = (4 cos t)i…

A: The arc length is, 5π/2   The detailed solution is as follows below:

Q: 2. Find the area of the shaded region shown below: (Hint: the entire curve is traversed once from 0…

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Q: QUESTION 4 In the diagram below, PQRS is a cyclic quadrilateral. PS and QR are produced to meet at…

A: Given that:  PQRS is a cyclic quadrilateral. RE is a tangent to the circle at R. RE∥QS.   We have…

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Q: Question 2 Find the length of the curve r(t) = (3 cos t)i + (3 sin t)j + 2ek, Osts3.

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Q: 9. Find the length of the curve: r = 1+ cos(28),0 < 0 < 2m

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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.