8. In the diagram below, secants RP and RT have been drawn from exterior point R such that mQS = 40° and mPT = 84° . Which of the following represents the measure of ZR? (1) 104° R (2) 64° (3) 62° o. (4) 22°

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: Graph the limaçon. Oval limaçons r = 2 + cos u

A: Given- r=2+cosθ To sketch- The graph of the above limaçon.

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = %3D (플) = 프2

A: Given:

Q: 13-Find the terminal point  P(x, y) on the unit circle determined by the given value of t. t = −…

A: Coordinates  of the terminal point would be    x=cos -2π3, y=sin  -2π3

Q: Calculate the length of the side XY given the following data for 29°: Sin 29° = 0.485 Cos 29° =…

A: Solve for xy

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A:

Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…

A:

Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: 4. a) Find the entire are length of the curve r = 2a cos³ (0/3).

A: 4a Given curve is r=2acos3θ3. We have to the entire arc length of the given curve. The entire arc…

Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

A: Given : r(t)=3cos(t), t-4, 3sin(t) is the position function of a particle. To find : If the particle…

Q: 4 .Using n=8 approximate the value of cos(1+Vx )dx using 0. (a) the Midpoint Rule, (b) the Trapezoid…

A: Formula used: Midpoint rule- The interval [a,b] into n subintervals of equal width,…

Q: Find the angle(s) that satisfy the given values in the interval (0, 2r) 1. cos I = 2. secz = V2 3.…

A:

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: Q1 Find all the points of intersections of the curves r = 1+cos0 and r=1+sin r-1+(8) r=1+1)

A:

Q: With the hints of using the relationship sin (r) + cos²(r) = 1 and choosing u = sin(r) integrate /…

A: To evaluate: I=∫cos3(x)sin4(x) dx=∫cos2(x)sin4(x) cos (x) dx=∫(1-sin2(x))sin4(x) cos (x) dx

Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

A:

Q: Eliminate the parameter t from the following. Sa(t) = 2 sin t + 5 ly(t) = 5 cost – 6

A: Rewriting the given equations:

Q: Choose the only equation below that does NOT represent a circle. Ox =1+ 4cos(t) y = 3+4cos(t) O x2…

A:

Q: Graph the limaçons. Oval limaçons r = 2 + cos u

A: Consider the given:  Graph the limcons:r=2+cosθThere are four basic shapes:r=a±bcosθr=a±bsinθ

Q: Find the angle at which the cardioid r = a(1 – cos 0) crosses the ray 0 3D п/2.

A: To find the angel at which the below cardioid crosses the ray θ=π/2

Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: 3. What we want to do next is write (x + jy)as Reie where R= J(x? + y? ) and tan-(e) = (2)

A:

Q: Find the length of the curve. r(t) = , −4 ≤ t ≤ 4

A: The length of the curve is given by  r(t) = &lt;5t, 3 cos(t), 3 sin(t)&gt; r'(t) = &lt;5, -3…

Q: 2:03 AA A mathspace.co E C. 10 11 12 11. Which of following is a radius of the attached circle? JK…

A:

Q: Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular…

A:

Q: az az Use the chain rule to find and as at sin(8) = r = st, 0 = s + t4 az %3D ds az %3D at Submit…

A:

Q: The figures shown are three similar ARST AUVW ~ AXY Z 2. Find the Values of in Vand tan Y and drag…

A: Given,

Q: Find the lengths of the curves The cardioid r = 1 + cos θ

A: Given:r=1+cosθl=∫r2+drdθ2 dθ

Q: d the area of the surface generated by revolving the curve x =cos (2t), y = 7+ sin ( 2° - xis. .....…

A:

Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: -7. х 3D sin?t, у— cos t yA

A:

Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0 <T

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Consider the following. X = 7 cos(0), y = 8 sin(0), - T/2 < 0 S TT/2 (a) Eliminate the parameter to…

A:

Q: 21. ds: C is the quarter-circle r(t) = (2 cos t, 2 sin t), for 0SIST/2.

A:

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

A:

Q: 3IZ 21 C 2 3 3 y

A: With the given information, r(t),x(t),y(t),z(t).... Let us start the solving the problem step by…

Q: Ary sin(r'y) +r + [x? sin(x²y) + 2y]y = 0

A:

Q: Q8:- Find the intersection points between the given curves. r= cose 1- r= sin0 2- r= 3cos0, r=1+…

A:

Q: (b) Consider the cycloid C parametrized by x = t – sin t and y = 1 – cos t, for all real t. Find…

A: Solution x= t-sint, y =1-cost C(0) = (0,0) C(pi) = (pi-sin pi, 1-cos pi) = (pi, 2) C(2pi) = (2pi-0,…

Q: Consider the following. x = sin coso), -n s 0 sa co). (a) Eliminate the parameter to find a…

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

Q: 12.The temperature at each boint of a metel plate i given by the functien %3D :) In What disection…

A: The temperature function is given by Tx,y=excosy+eycosx the Temperature rise will be given by…

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: 1. Given y + 0=90°. Find the measurement of angle 0 in the triangle below using cofunction…

A: Given,

Q: If the area enclosed by the curve x = 5 cos³ t and y = 5 sin° t (where t E R) is A, then what is A?…

A:

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

A:

Q: By about how much will h(x, y, z) = cos (paixy) + xz2 change if the point P(x, y, z) moves from…

A: The given function is,

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.