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algol [13]
3 years ago
8

ANSWER ALL THE QUESTIONS IN THIS WORKBOOK.

Mathematics
1 answer:
777dan777 [17]3 years ago
8 0

Answer:

i. 15, 18, 20, 20, 25

ii.

a) 19.6

b) 20

c) 20

d) 10

Step-by-step explanation:

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I just need to know how do I find the domain for this function Y=-4x+2
mihalych1998 [28]
Answer: Set of all real numbers

The domain is the set of all real numbers because we can plug in any x value we want to get some y value. There is no worry about dividing by zero. We don't have to worry about taking the square root of a negative number. There are no restrictions for x.
6 0
3 years ago
A light bulb is designed by revolving the graph of:
nadya68 [22]

Answer:

\displaystyle 0.251327 \ in. \ of \ glass

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Terms/Coefficients
  • Expand by FOIL (First Outside Inside Last)
  • Factoring

<u>Calculus</u>

Differentiation

Derivative Notation

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Integration

  • Integration Property: \displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx
  • Fundamental Theorem of Calculus: \displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)
  • Area between Two Curves
  • Volumes of Revolution
  • Arc Length Formula: \displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx
  • Surface Area Formula: \displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}]

<u>Step 2: Differentiate</u>

  1. Basic Power Rule:                    \displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}
  2. [Derivative] Simplify:                \displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}
  3. [Derivative] Simplify:                \displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}

<u>Step 3: Integrate Pt. 1</u>

  1. Substitute [Surface Area]:                                                                             \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx
  2. [Integral - √Radical] Expand/Add:                                                               \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx
  3. [Integral - √Radical] Factor:                                                                         \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx
  4. [Integral - Simplify]:                                                                                       \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx
  5. [Integral] Integration Property:                                                                     \displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx

<u>Step 4: Integrate Pt. 2</u>

  1. [Integral] Define:                                                                                             \displaystyle \int {|9x + 1|(3x - 1)} \, dx
  2. [Integral] Assumption of Positive/Correction Factors:                                 \displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx
  3. [Integral] Expand - FOIL:                                                                                 \displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx
  4. [Integral] Integrate - Basic Power Rule:                                                         \displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)
  5. [Expression] Multiply:                                                                                      \displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}

<u>Step 5: Integrate Pt. 3</u>

  1. [Integral] Substitute/Integral - FTC:                                                              \displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}
  2. [Integrate] Evaluate FTC:                                                                                \displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})
  3. [Expression] Multiply:                                                                                     \displaystyle SA = \frac{\pi}{27} \ ft^2

<em>It is in ft² because it is given that our axis are in ft.</em>

<u>Step 6: Find Amount of Glass</u>

<em>Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.</em>

  1. Convert ft² to in²:                    \displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2
  2. Multiply:                                   \displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass

And we have our final answer! Hope this helped on your Calc BC journey!

5 0
3 years ago
Question 1 (1 point)
Artemon [7]

Answer:

the answer is simply the one in the bottom right, B

3 0
3 years ago
Find f '(a).<br> f(x) = 4x2 − 4x + 3
Vinvika [58]
Use the power rule
  d(x^n)/dx = n·x^(n-1)
to form the derivative.
  f'(x) = 4·2x -4
  f'(x) = 8x - 4

Now, substitute "a" for "x" to find f'(a):
  f'(a) = 8a - 4
3 0
4 years ago
What is the length of side a? Round to the nearest tenth of an inch
slamgirl [31]

Answer:

ok this is easy all it is 16-7=9 so a=9 so all it is 7x9=72 then its 72 divided by 2 so your answer is 36

3 0
3 years ago
Read 2 more answers
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