If C is a circle of radius 4 centered at the point ( 5, 5 ), then evaluate (3y- esin () ) da + (10a – sin(y + y))dy. value = T• %3D (Note: the factor of T is already there!) Check Answer

Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to…

A:

Q: (h + R cos(t), k +R sin(t)), o sts 2r. Thus, the given circle with center (9, 8) and radius 6 can be…

A: Solution : We have given rt = 9 + 6 cos(t), 8 + 6 sin(t) First we will find out the derivative of…

Q: Consider the following. X = sin y = os(플e), -π sθ<π (a) Eliminate the parameter to find a Cartesian…

A: As we know that the trigonometric identities:- cos2(θ)+sin2θ=1

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 0 < x < 12

A: Recall: when the function y= f(x) is rotated around y-axis . the interval a≤x≤b,then the surface…

Q: 2. For Parts (a) (b), find ſ F · dr for the given F and C. (a) F = 5xyi+ 2y² j; C is the parabola r…

A: This question is from area under the curves.

Q: Let P(cos t, sin t) be a point on the unit circle x2 + y2 = 1 in the first quadrant. Show that t is…

A:

Q: Ans: x+ yy' 0 1. All circles center at the origin.

A: From the answer I can deduce that you want the differential equation that represents the family of…

Q: Find the regions of the (x, y)-plane where the equation ey. + e*. dxðy + 2e2". +x³. + e*-Yu = 0 ду |…

A: The given PDE is        ey∂2u∂x2+ex∂2u∂x∂y+2e2x∂2u∂y2+x3∂u∂x-(x+y)2∂u∂y+ex-yu=0. A second order PDE…

Q: Find the area in the first quadrant inside the curve r = 4 + cos 2θ but outside the curve r = 3 cos…

A: Given  The outside the curve r = 4 + cos 2θ but inside the curve r = 3 cos 2θ . Formula for area…

Q: 1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the…

A:

Q: Eliminate the parameter t from the following. x = 3 + sin t, y = 5 + cos t Sketch the graph of the…

A:

Q: Find the length of the curve y In (cos x), 0sxs- 3 The length of the curve is (Type an exact…

A: The length of any curve for x1≤x≤x2 is given by,l(Length)  = ∫x1x21+dydx2  dx   Also use ∫secx dx =…

Q: Find the length of the curve r(t) (e" cos(2t), e" sin(2t), e"), -2 sts 2 %3D

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

Q: Find the lengths of the curves 1.The curve r = cos^3 (u/3), 0&lt;= u&lt;= pai/4 2. The curve r =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the area of the region that hosmside the Circle r = 3COS 6 and outside the cardioid r =1+ cos…

A:

Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 3. y=…

A:

Q: Done Find the area between a large loop and the enclosed small loop of the curve r = 4 + 8 cos(30).…

A:

Q: I Eliminate the ar bi fary constant )- y= Ax+ B sec x 2 2 %3D I. Find the difFCrntial equation +that…

A:

Q: A particle moves in the xy-plane in such a way that its position at time t is r(t) = (t – sin t) i +…

A: Given: The motion of a particle is, rt=  1-sin ti +  1-cos tj ........1

Q: Find the arc length of the graph of y = (x3/6) + (1/2)x on the interval [ 1/2 , 2], as shown

A:

Q: 3- The equations X= að -a sinð, Y= a- a cosº,(0<< 2n Represent one arch of a cycloid .show that the…

A:

Q: A uniform cable is suspended between two poles of equal height. Assume that the equation of the…

A: (a)

Q: Consider the following. x = sin(10), y = cos(0). (a) Eliminate the parameter to find a Cartesian…

A: Given problem:- x=sin(θ/2) , y=cos(θ/2) , -π≤θ≤ π  Eliminate parameter and find Cartesian equation…

Q: the regions enclosed by the given curves. y = 6 cos(5x), y = 6 sin(10x), x = 0, x = 1/10

A: Given: y = 6 cos(5x) y = 6 sin(10x) x = 0,  x = π10 To find: Area in between the two given curves.

Q: c) Find the curve length of the lemniscate of the area Inside the lemniscate r² = 6 cos 20 and…

A: Solution:-

Q: 2/3 2/3 2/3 2. Find the area of the four-cusped hypocycloid x + y = a 3. Find the area bounded by y…

A: Here we have to find the area enclosed by the given curves. We will use following formulas-…

Q: 2 and r = 3 + 2 cos 0. Show all work needed Consider the regions enclosed by the curves r = to set…

A:

Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

A:

Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3In(cos(t)) k, 0 stsn/4 Submit Answer

A:

Q: The infinite curve y = e¬*,where x > 0 ,is rotated around the x –axis. Find the area of the…

A: Find area of surface.

Q: ) Let C be the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of…

A:

Q: II. Draw a sketch of the given arc C and evaluate Sc [(x² − 2y)dx + (2x + y²)dy]. → 1. C is part of…

A:

Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

A:

Q: A particle travels along the path of a helix with the equation r(t) = cos(t)i+ sin(t)j+tk. See the…

A: Consider a vector r(t), which is differentiable. Then a unit tangent vector along the curve r(t) is…

Q: that the reparametrizatIon by arc-length traverses the curve with unit speed. That is, snow ||7…

A:

Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

A:

Q: Utilize Green's Theorem to find the exact area of the y 10 illustrated shape, which is traced out by…

A:

Q: 4:- Consider the image of the sphere r(0; Ø) = (a cos 0 sin Ø; a sin 0 sin Ø; a cos Ø) where 0 0…

A:

Q: Find the length of the curve y = In (cos x), 0sxs 4 The length of the curve is (Type an exact…

A:

Q: Find the area of the interior of r = 6 sin 0. Find the area between the loops of r 1+2 cos 0. Find…

A: Let's find.

Q: Find the lengths of the curves 1. The cardioid r = 1 + cos u 2. The curve r = a sin^2 (u/2), 0&lt;=…

A:

Q: Find the area of the specified region. Shared by the circles r=D 3 cos 0 and r= 3 sin 0

A: Consider the given circles r=3·cosθ and  r=3·sinθ To find the area of the region first find the…

Q: A uniform cable is suspended between two poles of equal height. Assume that the equation of the…

A:

Q: A curve in spherical coordinates x' for the line element ds? = (dx')² + (x')²(dx²)² +…

A: To Find the arc length to use the formula

Q: 16. Let C be the curve given by r(t) (t cos(t), t sin(t), t). Show that C lies on the cone x2 + y? =…

A:

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface.: y = x3/2,    5…

A:

Q: Find the length of the following two-dimensional curve. 兀 r(t) = (9 cos t + 9t sin t 9 sin t-9t cos…

A:

Q: Find the length of the following two-dimensional curve. r(t) = (6 cos t,6 sin t) , for 0<tsa The…

A:

Q: (a) Circle: x = h +r cos 0, y = k + r sin 0 (b) Ellipise: x = h + a cos 0, y = k + b sin 0 (c)…

A: We have to find out in rectangular form

Q: A particle moves in the xy-plane in such a way that its position at time t is r(t) = (t – sin t) i +…

A: A particle moves in the xy plane in such a way that it's position at time t is rt=t-sinti+1-costj…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.