7. Eliminate the paramet er to find a Cartesian equation of the curve, x = sin t, y = csc t, 0 < t < . Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: 1. Calculate the moment of inertia about x-axis of the first quadrant portion of the curve: y = 4-…

A:

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

A:

Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: Which of the following is the equation of tangent line of the curve that is given 2t by parametric…

A: As two Questions are given , I will solve the first one :We are given  the parametric Equations :…

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

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: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D

A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…

Q: Find the slope of the tangent line to polar curve r = 6 – 9 sin 0 at the point (6-

A:

Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

A:

Q: 4 Find the slope of the tangent line to polar curve r = 7 – 4 sin 0 at the point ( 7 - - 2' 6 Submit…

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: A curve passes through point leio) and the Sloge dt line of each point (^,y) is egual to xe-BY .In…

A: Curve passes through (e6, 0)f(e6)=0slope of Normal line=x e-8ySlope of normal line*slope of tangent…

Q: A curve is parametrized by the given equations. Find the equation of the tangent line to the curve…

A: Equation of the tangent line

Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

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

A:

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: 3 Consider cune detined by y cos (T2) =UY +y+2 2 ) Verify point (2,-2) belongs to this curve, fond…

A:

Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

A:

Q: Find the slope of the tangent line to polar curve r = 8 – 7 sin 0 at the point (8 %3D 2' 6

A: Given the equation of polar curver=8−7sinθ       .......(1)(8−72,π6)

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

A:

Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

A:

Q: Suppose an object moves in an elliptical orbit parametrized by x = 4 cos t and y = 5 sin t, where t…

A:

Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

A:

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Given the parametric equations x=3cost+2sint and y=e6t . We need to find the equation of the tangent…

Q: Please solve

A: Parametrization of tangent lines is given by

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

A:

Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

A:

Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

A:

Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: The parametric equations of a curve are given by 1 = In (Vi +1) and y= cosh(2t). dy when t = 1. dr…

A: According  to question given thatx=ln(t+1)y=cosh-1(2t)

Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: Find the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

A:

Q: Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the…

A: We have the given parametric curve t,t2, t∈0,1x=ty=t2 for t∈0,1the first order derivative the curve…

Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

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

Q: Find the slope of the tangent line to polar curve V3 T 3 2 r = 6 – 3 sin 0 at the point | 6 3…

A:

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Given:

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.