Choose the correct answer 1- The circle x+y 1, this mean :- a- C= 0,0, R=2 b- C= 0,0. R=1 c- C=1.1, R-0 2- We use the disk method when the region is . . on rotation axis. a- Border b- not border c- parallel 3- If a curved rotation about an adjacent axis results in:- a- hollow region b-area surface region c-se 4- Which of the following equations is closest to the y-axis? -solid region a- y= 3 5- the equation QF QR mean that the conic section is a- Ellipse b-parabola e-circle Find the volume of solid generated by revolving the region in the first quadrant bounded by (y=x) and (y 4x) about line (y 8) b- y= 5 e- y= 2*

Q: 4- The centroid of the shaded area is required to lie on the y-axis. Determine the distance b that…

A: Answer is mentioned below

Q: Calculate 8- Z dz, c z(4 – z) where C is the circle of radius 7, centre 0, negatively oriented.

A: Given that:∫C8-zz(4-z)dz, C is a circle of radius 7, centre 0, negtively oriented.

Q: Determine a∈R such that ∫CF⋅dr = −2−(3π/4), where F (x, y) = (ay, (x^2 − y)/2) and C is the part…

A:

Q: The circle x² + (? − 1) 2 = 1 is rotated around the line y = x-3. A torus is formed as a result of…

A:

Q: After rebuilding the resort complex, Wingbolt industries has decided to install a circular lazy…

A: Plug this in the given equation. Answer(a) F(r1) represents the area of the lazy river.

Q: Find the surface area of the torus obtained by rotating the circlex 2 + (y - b )2 = r 2 about the…

A: Given the equation of the circle  x2+(y-b)2=r2. We need to find the surface area of the torus…

Q: Here is some information about Circle J. • VR is tangent to the circle. MZXJT = 130° MZRST = 46° m…

A:

Q: 2. Find the contour integral f,zdz for (a) y is the triangle ABC oriented counterclockwise, where A…

A:

Q: 10. Let C denote the positively oriented circle z| = 1. Show that - Ti 2sin(z) dz cos(z) dz 4 z(z²…

A: See the attachment.

Q: Use the center and radius to answer the next two questions. 16 1 point Center: (4, 1) Write the…

A: Ans : given the centre and radius of the circle = (4,1) and 2 So we want to choose the equation of…

Q: Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Choose the correct answer 1- The circle x + y 1, this mean :- c- C=1,1. R= 0 2- We use the disk…

A:

Q: usino Calculs tor para metre Carbes Show that he perimeter of a Circle of radius. R J Sven by L=ZHR.

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

Q: Let F(x, y) = 4yi + (2æ + ev* ); Calculate ,F · dr, where C is the circle of radius 2 centered at…

A: Given that F(x,y)=4yi+2x+ey2j The objective is to calculate ∫CF.dr where C is the circle of radius 2…

Q: e surface generated by y=x^3 on [0,1], about the x-axis. Final Answer is A(s)=3.563 sq. units, Show…

A: Solution:- y=x3       0,1 y'=3x2 y'2=3x22y'2=9x4 Now find surface area S= ∫012πy1+y'2dx…

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: A circle has an equation of 22 +y? = 48. Compute the common area between the circle 2? + y? = 48 and…

A:

Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = x2 - 1 -…

A:

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A:

Q: Match the part of the circle with the term that best describes it. 1. GH A. Center G 2. М B. Chord K…

A: GH¯ B. Chord M E. Point of tangency JM¯ D. Radius J A. Center MH¯ C. Diameter

Q: The shaded band shown here is cut from a sphere of radius R byparallel planes h units apart. Show…

A:

Q: where y is the circle {|z – 2| = 1} with counter clockwise orientation. (b) cos(2) -dz, 22 + 2iz – 1…

A:

Q: Given a sphere with center (7,3, – 4) and radius 5. Find an equation of the intersection of this…

A:

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

Q: Q2 Calculate 8-る dz, where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Trapezoid KLMN has sides KL= 20 unuits , LN= 60 units MN= 22units , KN= 66units, with KL parallel to…

A: Given that  Trapezoid KLMN has sides KL= 20 unuits , LN= 60 units MN= 22units , KN= 66units, with KL…

Q: If the infinite curve  y = e−8x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A: Given: y=e-8x , x≥0

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes h units apart.…

A:

Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

A:

Q: The arc of the parabola y = x? from (1, 1) to (2, 4) is rotated about the y-axis. Draw the surface…

A: Given: Equation of parabola : y= x2  Arc of parabola passes through (1,1) and (2,4).

Q: Find the surface area of the torus generated by revolving the circle given by r = 5a about the line…

A:

Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

A:

Q: Match the part of the circle with the term that best describes it. - 1. GH A. Center 2. М B. Chord…

A:

Q: Jse Green's theorem to evaluate $ (2°e* + 4y) dz + (-5x+ y* sin(y)) dy, where C is the…

A: The given path C is circle x2+y2=16. Therefore: D= (x, y) : x2+y2≤16

Q: When the shaded region is rotated around the y-axis, a horizontal strip of vertical span Ay creates…

A: We have to find the volume V of the solid obtained by rotating the region bounded by the given…

Q: If the infinite curve y = eSX, x > 0, is rotated about the x-axis, find the area of the resulting…

A:

Q: Find the area of the region inside both the circle r=6 and the cardioid r=4+4cos(theta) (in other…

A: Given a circle and a cardiod in the polar form. We need to find the area inside the circle and…

Q: Evaluate ds where C is the upper half of the circle centered at the origin with radius 1 with the…

A: Draw the curve C:  Here, we divide C in two parts:  C1 represented by the curved part C2…

Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

A:

Q: Calculate 8-z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented. (2ー2

A:

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

A: Given: The given curve is, y=x3=x1/3,  2≤x≤4   To determine: The area of the resulting surface.…

Q: The accompanying figure shows a spherical cap of height h cut from a sphere of radius r. Show that…

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Q: Find the surface area of the torus obtained by rotating the circle x2 + (y – b)? =r² about the…

A:

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A:

Q: Calculate 8-2 dz, z(4 – z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: What is the approximate sector area of a sector defined by minor arc (i.e. the shaded region)?…

A: We see that the circumscribed angle ∠ADB=50°So the central angle ∠ACB=2(50°)=100°

Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

A:

Q: A circle has an equation of ² + y? = 48. Compute the common area between the circle 2 + v? = 48 and…

A: Given:   x2 + y2 = 48    x2 + 8y = 0

Q: Consider the curve C given by the arc of the circle x² + y = 9, from (3,0)to (0, 3). Parameterize C…

A:

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.