Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.
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Q: Q2 Q1 Find the points of intersection of the polar curves r-cos () = 0 and 2-cos A-r=0
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Q: 12/2 Use polar coordinates to evaluate dydx.
A: The region is bounded by x=1,x=2,y=0 and y=x
Q: Match the graph with its polar equation. r = 2 sin(0) 1/2 A/2 4 -2 -2 A/2 3- A/2 -1 1 2 4 -2 -1 1 2…
A: Topic :- Geometry Corect Answer= 3 r=2sinθr θ0 01 π62 π20 π
Q: 1. For the polar coordinate (r,0) = (-2,7x/6), give one coordinate rUand -2nsOs 2n.
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Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²
A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…
Q: Solve the problem. Te 1) Plot the point 2, and find other polar coordinates (r, 0) of the point for…
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Q: Convert the given Cartesian equation into a polar equation. x² + y? = 2x + 3y Select the correct…
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Q: Q2: Sketch the polar function r = 6 cos 30 ,-n <0 < T
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Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs
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Q: 9. Transform the equation 2x?+2y?3 into a equa tion. Polar
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Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…
A: Given artesian equation,x2+y2-2x=0Put…
Q: Show that the polar equation for x2/a2 + y2/b2 = 1 is r2 =…
A: Plug x=rcosθ and y=rsinθ
Q: Replace the polar equation with an equivalent Cartesian equation. r² = 44r cos 0 (x-22)² + y²-0…
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Q: 2 Convert the equation x+y¯-4=0 to polar form. Then solve the resulting equation for r.
A: x2+y2-4=0
Q: 1. Change to polar form, then evaluate: -x-1 х — у dydx V1-x² /x² + y² -1
A: Solution is given below..
Q: Match the graph with its polar equation. r = 2 sin(0) A/2 л/2 4 2 2 4 A/2 3- A/2 2 -1 2 - 2 -1 1 2
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Q: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…
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Q: 1. Change ſ, Lz xy dydx to polar form. 4-x2
A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…
Q: 3 Convert the equation y = -x to polar form. 3 Then solve the resulting equation for 0. e = 0
A: Explanation of the solution is given below....
Q: 11. Give the polar equation of this graph. 司) (6,0) O2 4 8 10 0=0
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Q: r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis
A: rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…
Q: Convert x2 -4x+y2=0 into a polar equation.
A: Convert x2 -4x+y2=0 into a polar equation
Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…
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Q: 2. Transform the polar equation into a Cartesian equation. 4 r = 4 + sin 0
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Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…
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Q: 8 Convert the polar equation r 2 = -2 sin 2θ to a Cartesian equation. x2 + y2 = 2 xy ( x2 + y2) 2…
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Q: .2 Convert the equation X +y“- 36= 0 to polar form. 2 Then solve the resulting equation for r. JT
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Q: Q1// Converting r= 12 cos 0 r = 12 cos 0 from polar to the equation of a circle?
A: Given problem:- Converting r = 12cos(θ) from polar to the equation of a circle?
Q: 1. Sketch the graph of r = 2 sin(20) in polar coordinate system T/4 31/4 5T/4 7T/4 in the polar…
A: Consider the provided polar equation, Sketch the graph of the polar equation. Now make the graph of…
Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.
A: To evaluate the integral using polar coordinates
Q: 2 Q3: Discuss the symmetry and plot the locus of polar equation r 1-cose
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Q: 6. Consider the polar equation r = 2 – 2 cos(0) a) Complete the table of values for r = 2 -2 cos(0).…
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Q: 1. Change Lxy dydx to polar form. V4-x2 Xy dydx to polar form.
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Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e
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Q: Find the length L of the polar curve r = 6 sin for 0 < 0 <- 2 2 OL= 12 OL= 6 OL = 6/2 OL = 12 – 6/2
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Q: 9. 1.7e1.2-/2.5 into polar form Ans.
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: 2. Convert from a rectangular equation to a polar equation. x = 2y2
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Q: A particle moves along the polar curve r =1– 2 cos 0 so that = 2. Find the value of d at e = , and…
A: We are given that, Now, When , Then
Q: cos (0.48-j0.38) express in polar form
A: we have to express cos 0.48-j0.38 in polar form: we know that cosx-jy=cosxcoshy+jsinxsinhy Now, here…
Q: Convert the given Cartesian equation into a polar equation. a² +y? - 2x + 3y %3D Select the correct…
A: Put x=rcos thetha and y=rain they ha to get polar equations
Q: 4. a) Express the given rectangular equation in polar form. Solve for r or r2 if possible. x? = y? +…
A: Use x= rcostheta Y= r sin theta X2+y2=r2
Q: 7. Convert the rectangular equation 3x – 4y = 5 into a polar equation.
A: The equation in rectangular coordinates is given by 3x-4y = 5 To evaluate : The equation in polar…
Q: 3.3. Show that in a polar coordinate system, the distance d between the points (r1,01) and (r2, 02)…
A: The distance between r1,θ1 and r2,θ2 is d=r12+r22-2r1r2cos θ1-θ2
Q: The Cartesian equation of the polar curve r = 6 sin 0 is (x – 6)² + y? = 36 - (x – 3)² + y² = 9 O a?…
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Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…
A: see below the answer
Q: Find the polar coordinates of the point with r> 0 and 0 < 0 < 2n. (r, 0) = 2 2 3 4
A: From the Figure it is clear that the value of r is 4 because it lies on the fourth circle.
Q: Q2:- find the polar coordinates for the fol 1:-(-2,2) 2:- (-1, /3) 3:- (2/3,2)
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Q: Match the graph with its polar equation. r = 2 sin(0) A/2 A/2 4 2 -2 2 4 - 2 2 - 4 A/2 3| л/2 2 1 1…
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- 4. Find the exact length of the polar curve r = e2θ, 0 ≤ θ ≤ 2π.Find the slope of the polar curve r = 2( 1 – cosx ) when x = pi/4 . a. 1.707 b. 2.414 c. 1.866 d. 2.545 Find the slope of the curve x = 3t2 – 2 , y = t3 + 4 at t = 2 a. 2 b. 1 c. - 1 d. - 211. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t and Y=2t
- Find an equation (in polar coordinates) of the line tangent to the cycloid x = t - sin t, y = 1 - cos t at the points corresponding to t = pi/6 and t = 2pi/3.A lizard moves through the plane with its position at t seconds given by the parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1. The lizard begins moving at t=0 seconds. a. How long does it take for the lizard to return to its starting position for the first time? b. how far does it go in 4 seconds?Consider a particle traveling clockwise on the elliptical path x2/ 100 + y2/25 = 1. The particle leaves the orbit at the point (−8, 3) and travels in a straight line tangent to the ellipse. At what point will the particle cross the y-axis?
- Find the 1st and 2nd Derivate of y with respect to x from parametric equations. x=(t-2)5/2 y=t3-512. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. x=e^t, y=e^(-2t)What does the graph of the parametric equations x(t)=2−t and y(t)=(t+3)2, where t is on the interval [−4,0], look like? Drag and drop answers into the boxes to correctly complete the statements.
- Find the First and Second Derivate of y with respect to x from parametric equations. x=1/(t-5)3 y=3t2-5Find the First and Second Derivate of y with respect to x from parametric equations. Clear Solution. x=3-t5;y=7t-5Suppose a ball is hit with a horizontal velocity of 80 ft/sec and an initial upward velocity of 90 ft/sec. The parametric equations (without regard for air resistance) for position (x,y) at time t seconds are: x(t)=80t y(t)=90t−16t^2 d. A 25-foot high fence is at x=400 ft. According to this parametric function, will the ball go over the fence, hit the fence, or hit the ground before reaching the fence? e. At what time does the ball reach its maximum height ? What is the horizontal distance at this time?