Question 1: Show that x = h + r cos t and y = k +...

Question 1: Show that x = h + r cos t and y = k + r sin t represents the equation of a circle.

Question 4: Find the area above the polar x-axis and enclosed by r = 2−cos(θ).

Question 5: If r = f(θ) is a polar curve, ﬁnd the slope of the tangent line at a point (r₀,θ₀).

Expert Solution

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milcah answered 2 years ago

a. (5 Marks) 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) =...

a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y) +-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the numeric value for the AM index of modulation, m, fors(f) ?

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) =...

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) = ? Please complete this table. I am having trouble converting functions from polar to cartesian in the three dimensional plane. I understand that x=rcos(?) and y=rsin(?) and r2 = x2 + y2 , but I am having trouble understanding how to apply these functions.

PART A: Suppose X and Y are independent. Show that H(X|Y) = H(X) . (H represents...

PART A: Suppose X and Y are independent. Show that H(X|Y) = H(X) . (H represents entropy i think) PART B: Suppose X and Y are independent. Show that H(X,Y) = H(X) + H(Y) PART C: Prove that the mutual information is symmetric, i.e., I(X,Y) = I(Y,X) and xi∈X, yi∈Y

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos...

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos t). Find the length of the arc from t = 0 to t = pi. [ Hint: 1 + cosA = 2 cos2 A/2 ]. and the arc length of a parametric

using / for integral Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the...

using / for integral Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the trapezoidal region with vertices (1,0), (2,0), (0,2), and (0,1)

y''+y=2t+1+(cos(t))^-2

Convert x=cos(3t)+sin(3t) & y=cos(t)-sin(t) into an equation of x-y form (cartesian equation). Thank you

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π...

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π Part (a): Find the Cartesian equation of the curve by eliminating the parameter. Also, graph the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. Label any x and y intercepts. Part(b): Find the point (x,y) on the curve with tangent slope 1 and write the equation of the tangent line.

The function y(x, t) = (20.0 cm) cos(πx - 17πt), with x in meters and t...

The function y(x, t) = (20.0 cm) cos(πx - 17πt), with x in meters and t in seconds, describes a wave on a taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement y = +17.0 cm? Number Enter your answer in accordance to the question statement Units Choose the answer from the menu in accordance to the question statement This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2...

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is...

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is a cycloid. (a) Find the slope of the tangent line to the cycloid for 0 < t < 2π. dy dx (b) Find an equation of the tangent line to the cycloid at t = π 3 (c) Find the length of the cycloid from t = 0 to t = π 2

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