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
goldfiish [28.3K]
2 years ago
7

A gymnasium is 40 m long. Starting at one end lines are taped every 5 yd across the floor.

Mathematics
1 answer:
Cloud [144]2 years ago
5 0

Answer:

8 lines

Step-by-step explanation:

5 yards = 4.572 meters

40 m /4.572 = 8.7489063867

8 lines

You might be interested in
What value of r makes the equation true? r 0.12 = 0.20
USPshnik [31]
I think the answer is 0.20 - 0.12 = 0.08
6 0
3 years ago
BRAINLIST BRAINLIST BRAINLIST
musickatia [10]

Answer:

0.5 onces

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
I need help with this page
Molodets [167]
For 1 the answer is Junior High B which is letter C
3 0
3 years ago
Which is the next step in following construction of a regular hexagon
irinina [24]

Answer:

The square is the next step

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%5Cint%5Climits%5Ea_b%20%7B%281-x%5E%7B2%7D%20%29%5E%7B3%2F2%7D%20%7D%20%5C%2C%20dx" id="TexFo
Ludmilka [50]

Answer:\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}General Formulas and Concepts:

<u>Pre-Calculus</u>

  • Trigonometric Identities

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Integration

  • Integrals
  • Definite/Indefinite Integrals
  • Integration Constant C

Integration Rule [Reverse Power Rule]:                                                               \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Rule [Fundamental Theorem of Calculus 1]:                                    \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

U-Substitution

  • Trigonometric Substitution

Reduction Formula:                                                                                               \displaystyle \int {cos^n(x)} \, dx = \frac{n - 1}{n}\int {cos^{n - 2}(x)} \, dx + \frac{cos^{n - 1}(x)sin(x)}{n}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution (trigonometric substitution).</em>

  1. Set <em>u</em>:                                                                                                             \displaystyle x = sin(u)
  2. [<em>u</em>] Differentiate [Trigonometric Differentiation]:                                         \displaystyle dx = cos(u) \ du
  3. Rewrite <em>u</em>:                                                                                                       \displaystyle u = arcsin(x)

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Trigonometric Substitution:                                                           \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[1 - sin^2(u)]^\Big{\frac{3}{2}} \, du
  2. [Integrand] Rewrite:                                                                                       \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[cos^2(u)]^\Big{\frac{3}{2}} \, du
  3. [Integrand] Simplify:                                                                                       \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos^4(u)} \, du
  4. [Integral] Reduction Formula:                                                                       \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{4 - 1}{4}\int \limits^a_b {cos^{4 - 2}(x)} \, dx + \frac{cos^{4 - 1}(u)sin(u)}{4} \bigg| \limits^a_b
  5. [Integral] Simplify:                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4}\int\limits^a_b {cos^2(u)} \, du
  6. [Integral] Reduction Formula:                                                                          \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg|\limits^a_b + \frac{3}{4} \bigg[ \frac{2 - 1}{2}\int\limits^a_b {cos^{2 - 2}(u)} \, du + \frac{cos^{2 - 1}(u)sin(u)}{2} \bigg| \limits^a_b \bigg]
  7. [Integral] Simplify:                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}\int\limits^a_b {} \, du + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]
  8. [Integral] Reverse Power Rule:                                                                     \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}(u) \bigg| \limits^a_b + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]
  9. Simplify:                                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3cos(u)sin(u)}{8} \bigg| \limits^a_b + \frac{3}{8}(u) \bigg| \limits^a_b
  10. Back-Substitute:                                                                                               \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(arcsin(x))sin(arcsin(x))}{4} \bigg| \limits^a_b + \frac{3cos(arcsin(x))sin(arcsin(x))}{8} \bigg| \limits^a_b + \frac{3}{8}(arcsin(x)) \bigg| \limits^a_b
  11. Simplify:                                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(x)}{8} \bigg| \limits^a_b + \frac{x(1 - x^2)^\Big{\frac{3}{2}}}{4} \bigg| \limits^a_b + \frac{3x\sqrt{1 - x^2}}{8} \bigg| \limits^a_b
  12. Rewrite:                                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(x) + 2x(1 - x^2)^\Big{\frac{3}{2}} + 3x\sqrt{1 - x^2}}{8} \bigg| \limits^a_b
  13. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:              \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

8 0
2 years ago
Read 2 more answers
Other questions:
  • Tom bought several clients is it a new car. He paid for a sales tax of 7.5% on the appliances and a tax of 6.5% on the car. Befo
    10·1 answer
  • Edgar purchased a home for $182,100 to home appreciates about 3.5% each year what is the value of the home after 12 years
    5·1 answer
  • Write 29/5 as a mixed number
    9·1 answer
  • How does writing 3.441 in expanded form show why the same digit can have different values?
    7·1 answer
  • Which ordered pair is a solution of this
    13·1 answer
  • Are these equations of lines parallel: Y=3X+4 and Y+3 = -3(-X+2)<br> NO<br> YES
    6·2 answers
  • Amy is 11 ⅚ years old. Camden is 1 ⅓ years younger than amy and Jane is 1 ¼ years younger than Camden How old is Jane​
    13·1 answer
  • What’s the points of the center of a circle?
    8·1 answer
  • What is the height of the cone below?
    5·1 answer
  • Question 23 of 40
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!