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Nataliya [291]
3 years ago
12

The director of a marching band asks the band members to line up in rows of four, but one is left over. Then she tries to line t

hem up in rows of six, but three are left over. Finally, she tries to line them up in rows of seven, but four are left over. The band has fewer than $100$ members. How many members are there?
Mathematics
1 answer:
lions [1.4K]3 years ago
6 0
I got 81 members. 4 x 20 = 80 81-80=1
6 x 13= 78 81-78= 3
7 x 11= 77 81-77= 4
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The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.
puteri [66]

Answer:

\displaystyle \frac{dA}{dt} = 102 \ m^2/day

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
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<u>Calculus</u>

Derivatives

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Derivative Rule [Product Rule]:                                                                              \displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle l = 10 \ meters<u />

<u />\displaystyle \frac{dl}{dt} = 4 \ m/day<u />

<u />\displaystyle w = 23 \ meters<u />

<u />\displaystyle \frac{dw}{dt} = 1 \ m/day<u />

<u />

<u>Step 2: Differentiate</u>

  1. [Area of Rectangle] Product Rule:                                                                 \displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}

<u>Step 3: Solve</u>

  1. [Rate] Substitute in variables [Derivative]:                                                    \displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)
  2. [Rate] Multiply:                                                                                                \displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day
  3. [Rate] Add:                                                                                                      \displaystyle \frac{dA}{dt} = 102 \ m^2/day

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

Unit: Implicit Differentiation

Book: College Calculus 10e

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3 years ago
The question is in the image! Please help if u can its due really soon
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Answer:

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Step-by-step explanation:

3x+38=10x

-3x         -3x

38=7x

x=5.4

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