1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aliun [14]
3 years ago
6

What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)

Mathematics
1 answer:
zzz [600]3 years ago
4 0

Answer:

B) 4√2

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

  • Integrals
  • Definite Integrals
  • Integration Constant C

Arc Length Formula [Parametric]:                                                                         \displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.

Interval [0, π]

<u>Step 2: Find Arc Length</u>

  1. [Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]:         \displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.
  2. Substitute in variables [Arc Length Formula - Parametric]:                       \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx
  3. [Integrand] Simplify:                                                                                       \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx
  4. [Integral] Evaluate:                                                                                         \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametric Integration

Book: College Calculus 10e

You might be interested in
Find the value of x<br> −8(x−6)=32
RUDIKE [14]

Answer:

x = 2

Step-by-step explanation:

-8(x-6) = 32 (distribute)

-8x+48 = 32 (subtract 48 from both sides)

-8x = -16 (divide)

x = 2

4 0
3 years ago
Read 2 more answers
Nine times nineteen<br> Equals to
Leokris [45]

Answer:

171

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
4. In a women's professional tennis tournament, the money a player wins depends on her finishing place in the
Stels [109]

Using geometric sequence concepts, it is found that:

a) The rule is: P_n = 750000(0.5)^{n-1}.

b) An exponential relationship exists between the two variables.

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term.

A geometric sequence represents an exponential relationship between the variables.

In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:

a_1 = 750000, q = 0.5.

Hence the nth term of the sequence is given by:

P_n = 750000(0.5)^{n-1}

More can be learned about geometric sequence concepts at brainly.com/question/11847927

#SPJ1

4 0
1 year ago
Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x − 4y − 6z = 22
madam [21]

The equation x^{2} +y^{2} +z^{2} +2x-4y-6z=22  in standard form looks like (x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}.

Given equation of sphere be x^{2} +y^{2} +z^{2} +2x-4y-6z=22.

We are required to express the given equation in the standard form of the equation of sphere.

Equation is basically relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation,quadratic equation, cubic equation or many more depending on the powers of variables. The standard form of the equation of sphere looks like  x^{2} +y^{2} +z^{2} =r^{2}.

The given equation is x^{2} +y^{2} +z^{2} +2x-4y-6z=22.

We have to break 22 which is in right side into various parts according to the left side of the equation.

x^{2} +y^{2} +z^{2} +2x-4y-6z=-1-4-9+36

x^{2} +y^{2} +z^{2} +2x-4y-6z+1+4+9=36

x^{2} +1+2x+y^{2}+4-4y+z^{2} +9-6z=36

x^{2} +(1)^{2} +2*1*x+y^{2} +(2)^{2} -2*2y+z^{2} +(3)^{2} -2*3z=36

(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}

Hence the equation x^{2} +y^{2} +z^{2} +2x-4y-6z=22  in standard form looks like (x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}.

Learn more about equations at brainly.com/question/2972832

#SPJ4

7 0
1 year ago
Can someone helpppp
Dmitry [639]
Yes, I can help what would you like me to do
5 0
3 years ago
Other questions:
  • Pls help me with this  11-3 and 11-4 u press the link below 
    8·1 answer
  • The marked price of a cellphone is $140 after a markup of 25%. Calculate i.) the cost price for this phone. [2]
    12·1 answer
  • HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • Darius Washington makes 72% of his free throws.
    8·1 answer
  • URGENT, PLEASE HELP!!!!
    6·1 answer
  • Select all the expressions that have a value of 40 when x = 10.8.
    7·1 answer
  • Helpppppppppp plsssssss
    10·1 answer
  • Beula has a collection of video games. There are 12 games in the collection, and 2/4 of them are console games. Beula decides to
    9·1 answer
  • 3(3u-2)=2(3u+3)<br> What is the steps
    11·1 answer
  • If you have a line with a Slope of -4 and a y-intercept of -2, what would be the equation of that line?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!