1. Determine the centroid of the first full enclosed region in the first quadrant between sin r and cos r. It does not start at the y-axis

Q: 4. Find the centroid of each of the given plane region bounded by the following curves: у? %3 2х, у…

A: Based on the integration concept we will answer the question.

Q: D

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Q: 24. Evaluate | x/x² + y² dA, where D is the shaded region enclosed by the lemniscate curve r² = sin…

A: Consider the given:

Q: Determine the distance y measured from the x axis to the centroid of the area of the triangle shown…

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Q: 6. Compute the area of the surface for 0 <u 1, 0 < v < using the first fundamental form..

A: Given xu,v=u2-cosv,u+sint,cosv

Q: Find the y coordinate of the centroid of the region shaded in the following diagram. 9 in. -27 in.

A: Here the figure has drawn for our convenience.  To find the centroid, the rectangle indicated in x…

Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: 28. Show that the circulation of F(x, y, z) = (x², y², z(x² + y²)) around any curve C on the surface…

A: Given figure Stoke's Theorem Here take single integral over closed path C and double integral over…

Q: What is the y=x^2 - 4 and O 1/4 O 1/2 01 03/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: 18. Show that the centroid of the sector in Figure 13 has y-coordinate 2R sin o (0, y) R FIGURE 13

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Q: 10. Use Green's Theorem to evaluate the line integral (e" - y) dx + x cos(y²) dy, where C is the…

A: 1/2 + ( (1/2 )sin 1)

Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: y=x², y = 1, y =9 y=9, first quadrant

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Q: Evaluate cos z dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

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Q: Calculate the volue of the de integral 23 - 1 2 F soro fallowing c a) Cil2+1|= 1 Curves. 6)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

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Q: Find the coordinates of the centroid of the curve x = cos t, y = t + sin t, 0&lt;=t &lt;= pai.

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Q: The region in the first quadrant is bounded by the curve y = 2 - x^2 and y = x^2. How far is the…

A: Given- The region in the first quadrant is bounded by the curve y = 2 - x2 and y = x2.  To find- How…

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: 1. Find the region in the xy-plane in which the following equation is hyperbolic: [(x-y) -1]u +2uy…

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Q: (z+ y – 1) cos D

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Q: 4. Locate the centroid (x, y)of the following composite areas: -3 ft 3 ft I 1.5 ft 1 ft

A: Consider the given composite area and divide then into four areas as shown in diagram below,

Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: ch is the centroid of the section reckoned lower left hand corner. 100 100 600 100 -500- Dim

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Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

Q: 2. Obtain the eccentricity e and centroid a, and y. of the following image. f(x.y)=1 (object: dark)…

A: From the figure, we have to write down all the dark box function, for which f(x,y)=1 x,y=3,2, 4,2,…

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant…

A: Consider the following equation of curves: y=tan-1xx=3y=0 Consider the following graph: Red curve…

Q: Question 34 Find the abscissa of the centroid of the region between the parabola y = 6 - x2 and the…

A: As we know that; The expression for the abscissa of the centroid; x=1A∬xdydx Where, A=Area=∬dydx or…

Q: 1. Find the centroid of each of the given plane region bounded by the following curves: y = 10x –…

A: We know that; The expression for the centroid is: x=1A∬xdydx &amp; y=1A∬ydydxWhere;Area=A=∬dydx…

Q: 5/10 Determine the coordinates of the centroid of the shaded area. y * = ky? a b.

A: Given:

Q: Sketch the regions enclosed by the given curves. y = 4 cos(7x), y = 4 sin(14x), x = 0, x = T/14 y y…

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Q: Calculate (1+ cos(y²))dA,where D is the triangular region with vertices(0, 0). (–2 - Vĩ,2· VT) e (0,…

A: Given problem:- The given integral is ∫∫D1+cosy2dA, where D is the triangular region with vertices…

Q: Compute the integral „2020 (5y + x*0 ") dx + (19x – e -e-4yCos(y) sin y) dy over the portion of the…

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Q: Question 3. Compute the integral - dz 8+z where y is the rectangle with vertices +3+ i with the…

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Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: Sketch the region enclosed by the given curves. y = 3D 4 cos(5x), у %3D4 —4 cos(5х), 0 < x < T/5

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Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

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Q: Evaluate |(2y+cos x)dx + (5x+ sin y)dy along the positively oriented curve C. C is the boundary of…

A: We have to evaluate the integral ∫2y+cosxdx+5x+sinydy along the positively oriented curve C. Where C…

Q: Find the centroid of the third quadrant area bounded by the following curves y2+ 2y + 8x = −1 and y…

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Q: Let R be the region in the first quadrant bounded by x = = 1, (x − 2)² + y² = 1, and x² + y² = 4.…

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Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: 6. Find the centroid of each of the given plane region bounded by the following curves: y? = x³, y =…

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Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.