2. The distance between the points (sin x, cos x) and (cos x, -sin x) is: А. 1 В. V2 C. 2 sin x cos x D. 4 sin x cos x

Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

A:

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A: Given:x=2cosθ and y=1+2 sinθWe need to express the circle in cartesian coordinates.

Q: Given line YZ tangent to OJ at point Y and mzWYZ = 119, what is the measure of arc WXY %3D Y W X.

A: Measurement of arc is the angle subtended by arc at the center of circle.

Q: If UV = 8, UX = 4, and XY is x + 3 find x. Assume that segments %3D that appear tangent are tangent.…

A:

Q: Find the area bounded by the trigonometric curves Ⓒ 3.450 square units O 2.828 square units O 1.414…

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Q: Use Green's Theorem to evaluate (sin r + y) dr + (cos y +a?) dy, where C is the square con- sisting…

A:

Q: Find the area of the region inside the circle r = 2 sin (θ + π/4)and above the line r = sec (θ −…

A: Given : Circle   r=2sinθ+π4 and Line  r=secθ-π4   We have to find the Area of the region inside the…

Q: 1) Find area inside the circle r= 4cuse and to the right of line r = sece %3D

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Q: In AXYZ with a right angle at Y, the cosine ratio can be used to find the length of XZ as O a) XY…

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Q: If z = cos (r + cos y), show that az Fz ar ərðy dy dr

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Q: 2. Construct tangent segments drawn from an external point to a circle are congruent. Given:…

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Q: The circles r = (3)^1/2 cos u and r = sin u intersect at the point (((3)^1/2)/2, pi/3) . Show that…

A: We have given circles equation r=3cosu and r=sinu For intersection point of these circles…

Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: If UV = 8, UX = 5, and XY is x + 3 find x. Assume that segments that appear tangent are tangent.…

A:

Q: If y = arctan x, then what restriction is placed on the value of y?

A: Consider the given function:  y=arctanxDomain of  arctanx:  −∞ &lt;x&lt;∞Range of arctanx:…

Q: If UV = 7, UX = 5, and XY is x + 3 find x. Assume that segments that appear tangent are tangent.…

A: Given : UV = 7UX = 5XY = x+3

Q: PR is tangent to circle Q at R and PS Is tangent to circle Q at S.Find mZP.

A: Given: PR is tangent to Q at R and PS is tangent to Q at S ∠P =  x° ∠Q =  4x° ∠R =  90° ∠S =   90°

Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: b) Calculate again an approximate value of the length L of the curve arc from the previous…

A: The distance (d) between two points (x1,y1) and (x2,y2) is given by the equation;…

Q: 2.) What is line QP called? * U R. V S T Secant Tangent O Slicer Chord

A: In circle, all the point are at the same distance from the center.

Q: Н.W 是, and , if ay Find ax Je az 11. f(x. y) = sin(y- x) 12. f(x. y) = tan %3D %3D por

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Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: Calculate the area of the circle r = 3 sin θ bounded by the rays θ = π/3 and θ = 2π/3.

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Q: Find the areas of the regions . 1. Shared by the circles r = 2 cos u and r = 2 sin u 2. Shared by…

A: 1. Area of the region shared by the circles r = 2 cos u and r = 2 sin u Replace the variable u by θ…

Q: 2- find Ow/ar if w = (x + y + z)?, z = sin(r + s) y = cos(r + s), at the point (r, s)=(1, -1) X = r…

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Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: Let (a, b) be an arbitrary point on the graph of y = 1/x, x &gt; 0. Prove that the area of the…

A: The given function for the curve is, y=1x The slope (m) of the tangent at the curve is,…

Q: s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the…

A: Since, we know that s=rθ, where θ is the central angle.s denotes the length of the arc of a circle…

Q: of the negioa cut from the first Find the area quadrant by the regisn r= I+ Sin@ ?

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Q: Et eNcise the fo is linemr OTDE which of eii> +* - 1ogx dy

A: Given some differential equation. We need to find which of the following is linear differential…

Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

A:

Q: Express the circle specified by x = 2 cos(0) y = 1+2 sin(0) in Cartesian coordinates and find the…

A: Given: x=2cos θ y=1+2sin θ Now, x2=cos θ and y-12=sin θ Squaring both: x22+y-122=cos2θ+sin2θ…

Q: What formula would be used to calculate the right rectangle approximation of " (sin x · cos x)dx…

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Q: What angle does the tangent to the curve y(x) = sin² (x/9) + 13sin(x/9) at x = 9n make with the…

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Q: 1) Find area inside the circle r 4cose and to the right of line r = sece %3D

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Express the circle specified by x 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A: Note: Equation of a circle with radius r and center at (h, k) is given by (x-h)^2 + (y-k)^2 = r^2

Q: 2. A CIRCLE IS TANGENT TO THE CINCLES x7 y? = 4 x*+ y? = 12Y+ 64 2 F IND THE LOcuS OF IT3 CENTEN AND…

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Q: Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the…

A:

Q: Express the circle specified by x = 2 cos(0) y = 1 +2 sin(0) in Cartesian coordinates and find the…

A: Given that,   x=2 cosθ and y=1+2 sinθ

Q: 8. PT is tangent to circle O at P If mNP = 90°, and mMXP : 186°, find %3D %3D X/ d. mZ4 e. mZ5 f.…

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Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: 1) Evaluate each line each line integral. a) (x*yds where C:x=sin 2t, y = cos 2t, with 0<ts C

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Q: Find the length of one arch of the cycloid x = 9(t – sin(t), y = 9(1 – cos(t)).

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Q: PRIS tangent to circle Q at point R and PS is tangent to circle Q at point S. Determine mZP and mZQ.…

A: Circle tangent property

Q: 1. Isosceles Triangle XYZ with XY = ZY %3D 2. Line XY perpendicular to segment AB, where B lies on…

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Q: A circle of area 1018 cm² is cut into two segments by a chord which is 5 cm from the center. 1.…

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Q: PRis tangent to circle Q at R, and PS is tangent to circle Q at point S. Determine mZQ. 42° P

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Q: Find the length of the entire perimeter of the region inside r = 6 sin 0 but outside r = 1.

A: Given that  r=6sintheta and r=1 To find the length of the entire perimeter of the region

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.