37. Eliminate the parameter t in the following: x= - cos2t y = -cos t 38. Eliminate the parameter t from the following and then sketch the graph: x= 3sin : y = Scos r = 1 25 104 -10 -10 -6 -8 -8 -10 -10 = 9 104 -10 -6 -10 -6 10 -10 -10을 10- -10 -2

Q: Eliminate the parameter t from the following. x = sin t − 5, y = cos t − 4

A: Eliminate the parameter and simplify it.

Q: (7) Find the lengths of the curve r =2/(1 - cos 0), a/2<0<n.

A:

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

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

Q: The second derivation of y = cos(2x)

A: Given  y = cos(2x)   ........ (1) We know that  d (cosx)dx= -sinx        ........ (a) and  d sinxdx…

Q: 2.3 Evaluate the integral sinh 2 dz, 7 3i (z – 2i)4 2i 2+ 4 where C is the circle |z – 2i| = 4…

A:

Q: 4. Sketch a graph of y = -2 cos 2 for-2x SxS2n. v List 3 points below.

A: The given function is: The general form of the cosine function is: where, |a| represents the…

Q: 6/155) cos 0, 1+ cos 29

A:

Q: points

A:

Q: 1. Prove that the composite trapezoidal rule with h = 2-i, i E N, is exact for ſ cos? (Tx) dr

A: We know that in composite trapezoidal rule, we approximate the integral as follows: ∫abf(x) dx ≈  h…

Q: A particle moves in the xy-plane in such a way that its path is defined by x = et cos t and y = et…

A: Given that, x=etcost, y=etsin2t. Differentiate x with respect to t, dxdt=etcost-etsint=etcost-sint…

Q: 3. Draw the graphs of: y = 2 sin (2x) y = 3 cos (.5x) a.) b.) c.) y = tan(2x)

A: (a) Sketch the graph as shown below.

Q: Use your results from problem 6 and the fact that Vz = Vr (cos (*2kz) + i sin(*2kz)) for k =…

A: Finding roots of imaginary numbers.

Q: 3 9) Use y'(3) to determine if the graph of y = 4 cos x +- is increasing or decreasing when x = 3.…

A:

Q: 8. Sketch the following graphs for 0 < 0 <2n a) y= 3 sin x - 1 b) 4 sin 3x - 2

A: Topic = Graph

Q: 5. If the functions y = sin x and y = cos x are both subjected to a horizontal compression by , and…

A: y=sinx is subjected to compression by 13 y1=sin3x Then taking reflection in x-axis y2=-sin3x

Q: Use Superposition approach to find the genral solution of the following equation: y" – 2y' + 3y = -6…

A:

Q: 4) It turns out the three-dimensio ball than a football. A footba a trig function like y = a cos(E…

A: Volume

Q: 35. Eliminate the parameter t in the followin x = 9+4tant y = 4+4sect 36. Eliminate the parameter t…

A:

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: 7) Suppose cos(x – y) = xy. Find at the following points 7.1) (0, 5) 7.2) (0,– 5)

A:

Q: Find the total length of an astroid x2/3 + y2/3 = 22/3, which can be parameterised as x = 2 cos³ 0,…

A:

Q: 7)Use Taylor theorem to estimate cos(0.23) with Jerror|< 10-2

A: Here we are to estimate cosx at x=0.23=23100 with error≤10-2,using Taylor theorem i.e, using Taylor…

Q: Find the exact lanth of the 4=1n (sec(x)), Odyct3

A:

Q: Chapter 12, Section 12.1, Question 003 Find the domain of r(t) and the value of r(to). r(t) = cos…

A: r(t) = cos(πt)i-ln(t)j+√(t-8)k

Q: Eliminate the parameter t from the following. x = sin t − 3, y = cos t − 2

A: Eliminate t by squarring

Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

A:

Q: Show that r = cos20 is symmetric about the y-axis.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Use an appropriate local linear approximation to estimate the value of cos(29°). cos(29°) -

A:

Q: Let r(t) (sin(4t), cos(41), sin(4f) cos(81)). Find the point where r(t) intersects the xy-plane on…

A:

Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: Show that r = cos(2theta) is symmetric about the y-axis.

A:

Q: 5-Find the avea between the curve y= tann the n-anis and from n=-1/4

A: This question is related to area under curves , we will use integeration to solve this problem

Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: @) skelch a graph of the Punehion y=sinx-sinsx at Le,zn] 4) Given Secanda -10 and sr casd x =3,…

A:

Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

A:

Q: 2x Cos 23 find diy %3D

A:

Q: Eliminate the parameter t in the following. x = 4 + 3 tan t, y = 6 + 3 sec t

A:

Q: Use an appropriate local linear approximation to estimate the value of cos(59°). cos(59°) ~

A:

Q: 7. Suppose that x2 + y? = r² and x = r cos 0, as in polar coordi- nates. Find дr ax дr and дх

A:

Q: 4. Write u = -2 cos Tt – 3 sin at in the form u = Rcos(wot – 8).

A:

Q: If A =x 2sinyi+z?cosyj -xy2k then -=x?cosyi - z?cosyj-2xyk 1O ду =x?cosyi-z2sinyj-y?k ду .II O…

A: We use partial derivatives to answer the given question.

Q: 1o₂ = 2 · (² x (+) · cos (nwot) at O 11 2 1 = 2 25+ (1-1) cos (2nrrt) dt = 21- - [² (1-t) d 2 Los (n…

A: Using the integration by parts can be stated that: ∫udv=uv-∫vdu.

Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

A:

Q: A T 3n 4n Sn 6 7n 8A 9n 10n11n 12n Match the graph to the equation. 4 cos -1 O y = 3 sin - n) - 1…

A:

Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

A:

Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

A:

Q: 3.1 Find and classify singularities of ina - sin(32) 3.2 Find and classify zeros of z(e* – 1).

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.