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]
2 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]2 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
The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for
lions [1.4K]

In the question it is given that,

The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for each flower

And the October price was a 20% increase of the September price.

Let the price of the flower in October be $x

So we have

x+  \frac{20}{100}x = 1.50 \\ \frac{120x}{100} = 1.50 \\ x = \frac{1.50*100}{120} = 1.25

So the price of the flower in Septembet is $1.25 .

7 0
3 years ago
An architect in Brussels measures something to be 2.5 feet (using the Brussels measurement). How many feet is this in Aalst (usi
borishaifa [10]

Answer:

2.487F

Step-by-step explanation:

From the question we are told that

Architect Measures 2.5 feet (using the Brussels measurement)

Generally in Brussels  1F=275.75mm

Therefore

    2.5F=689.375mm

Generally in Aalst 1F=277.2mm

Therefore Mathematically converting  to feet in Aalst measurement we get

    689.375mm*\frac{1}{277.2} =2.487F

   

6 0
2 years ago
Segment AB has point A located at (4, 2). If the distance from A to B is 3 units, which of the following is the coordinate for p
olganol [36]
The distance between two points is given by:
d² = (x₂-x₁)² + (y₂ - y₁)²
9 = (x₂ - 4)² + (y₂ - 2)²
Now, we can check different ordered pairs in this equation to see which satisfies it:
The one that satisfies this equation is (4 , -1).
3 0
2 years ago
Read 2 more answers
Find the surface area of the composite figure. 6cm 5 cm 20cm 4cm 12cm 6cm​
Crazy boy [7]

Answer:

644 cm²

Step-by-step explanation:

Surface area of the composite figure = surface area of the large rectangular prism + surface area of the small rectangular prism - 2(area of the surface of the small rectangular prism that joins the larger prism)

✔️Surface area of the large rectangular prism = 2(LW + LH + WH)

L = 6 cm

W = 5 cm

H = 20 cm

Surface area = 2(6*5 + 6*20 + 5*20)

= 500 cm²

✔️Surface area of the small rectangular prism = 2(LW + LH + WH)

L = 6 cm

W = 4 cm

H = 12 cm

Surface area = 2(6*4 + 6*12 + 4*12)

= 288 cm²

✔️area of the surface of the small rectangular prism that joins the larger prism = L*W

L = 12 cm

W = 6 cm

Area = 12*6

= 72 cm²

✅Surface area of the composite figure = 500 + 288 - 2(72)

= 644 cm²

7 0
2 years ago
Solve 1-12 or any of them please.
ladessa [460]
1. y = 4x - 3
2. y = -x + 4
3. y = 1/3x +1
4. y = ----
5. y = 1/7x + 2
6. y = -4x + 2.75
7. y = 3x + 5
8.
9.
10.
11.
12.

3 0
3 years ago
Read 2 more answers
Other questions:
  • Ryan made 65 ounces of apple jelly. He put the same amount of jelly into 6 jars. How much jell is in each jar.
    7·2 answers
  • I need the answer with the work
    9·1 answer
  • Find the decimal equivalent to 4/15
    11·1 answer
  • HELP ME WITH MATH PLZ !!!!
    7·1 answer
  • What are the solutions of the following system
    10·2 answers
  • PLEASE HELP QUESTION 31
    6·1 answer
  • Hi there ummm let me cut to the chase...
    14·1 answer
  • Company X has $128,000 in a saving account that pays 6% interest per year. How much interest will earn at the end of 1/2 year?​
    13·2 answers
  • Please help ME I NEED THIS also theres a photo
    15·2 answers
  • =<br> 100 points for all 6
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!