1. Questions

Calculus

Polar Equation Question

The figure above shows the graph of the polar curve r=1−2cosθ for 0≤θ≤π and the unit circle r=1.
(a) Find the area of the shaded region in the figure.

Question 2
(b) Find the slope of the line tangent to the polar curve r=1−2cosθ at the point where x=−2. Show the computations that lead to your answer.

Question 3
(c) A particle moves along the polar curve r=1−2cosθ so that dθdt=2. Find the value of drdt at θ=2π3, and interpret your answer in terms of the motion of the particle.

Can’t post diagram because it is a url

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Gracie

  1. If you can't post the diagram, we can't post answers.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    PsyDAG

  2. (a) recall that A = ∫ 1/2 r^2 dθ

    (b) dy/dx = (dy/dθ) / (dx/dθ)
    = (r' sinθ + r cosθ)/(r'cosθ - r sinθ)
    so find r and θ when x=2, and plug and chug.

    (c) dr/dt = 2sinθ dθ/dt = 2(√3/2)(2)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    oobleck

  4. the diagram is 1-2costheta graphed from 0 to pi and a circle with a radius of 1. The shaded area is almost 3/4ths the unit circle except for the slivers that 1-2costheta cuts thru the first and third quadrants

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Gracie

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    Hi. Is PO4(3-) polar or non-polar? Why or why not? Thanks! Look up the electronegativity of P and O. I think I remember that O is about 3.5 and P is about 2.1; therefore, each P-O bond is somewhat polar. Thus, the ion will be

  2. chemistry

    What two conditions necessary for molecules to be polar? Her's my answer pls check. First, at least one covalent bond in the molecule has to be a polar covalent bond. For a bond to be polar, there must be a difference in the

  3. CHEM

    Which statement best describes the polarity of SF_4Cl_2?? (or: SF4Cl2, if that helps more) 1. Always polar. 2. Always nonpolar. 3. Depending on the arrangement of outer atoms, this molecule could be polar or nonpolar. & how can

  4. chem

    choose the compound below that contains at least one polar covalent bond, but is nonpolar a. ICl3 b SeBr4 c. CF4 d. HCN Im stuck between C and D C is a tetrahedral which has no net dipole so is non polar, and D is linear which

  1. precaculus

    Convert the rectangular coordinate (2,-2) to polar form and find two additional representations of this point. Can you check my work and explain how to finish the question? r=√(2)2+(-2)2 r=2√2 tan theta = (-2)/2 theta = -1

  2. Calculus

    Find the slope of the tangent line to the graph of the polar equation at the point specified by the value of 𝜃. r = 1/𝜃 𝜃 = 𝜋

  3. Chemistry

    Which is more soluble in water? Briefly explain why. Acetic Acid: CH3CO(OH) OR Ethanol : CH3CH2OH I think its acetic acid because when observing its structure it is more polar than ethanol. And when using the like dissolves like

  4. ap chem

    consider the molecules PF3 and PF5. b]is the PF3 molecule polar or is it nonpolar. explain C] on the basis of bonding principles, predict whether each of the following compounds exists. In each case explain your prediction. (i)

  1. Physics

    An 80 kg hunter gets a rope around a 400 kg polar bear. They are stationary and on frictionless level ice, initially 60 m apart. When the hunter pulls the polar bear to him, the polar bear will move: 1. 10 m 2. 30 m

  2. Chemistry

    Which of the following statements is (or are) true? I. All polar molecules have dipole moments. II. All polar molecules have oppositely charged regions. III. A polar molecule is attracted to other molecules because of

  3. Calculus 2

    Consider the polar curve: r=3cos(3ϴ) a) Find the area of the first leaf of the graph. -Thank you.

  4. Pre-calculus; urgent ! Please help !

    1.Graph the polar equation r=3-2sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write

View more similar questions or ask a new question.