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kvasek [131]
3 years ago
6

Sebastian wanted to order pizzas for $7 each. The delivery charge is $3.50. He has $20.

Mathematics
2 answers:
docker41 [41]3 years ago
8 0

Answer:

he can buy 2

Step-by-step explanation:

pashok25 [27]3 years ago
5 0

He can buy 2 pizzas.

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If the pattern continues, I believe it would be 2x.
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Determine the area of the given region under the curve <br> (1/x^4) [1,2]
Nikolay [14]

Answer:

\displaystyle \frac{7}{24}

General Formulas and Concepts:

<u>Algebra I</u>

  • Exponential Rule [Rewrite]: \displaystyle b^{-m} = \frac{1}{b^m}

<u>Calculus</u>

[Area] Limits of Riemann's Sums - Integrals

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)

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle f(x) = \frac{1}{x^4} \\ \ [1, 2]<u />

<u />

<u>Step 2: Find Area</u>

  1. [Integral] Set up area:                                                                                    \displaystyle \int\limits^2_1 {\frac{1}{x^4}} \, dx
  2. [Integral] Rewrite:                                                                                            \displaystyle \int\limits^2_1 {x^{-4}} \, dx
  3. [Integral] Reverse Power Rule:                                                                      \displaystyle \frac{-1}{3x^3} \bigg| \limits^2_1
  4. [Area] Fundamental Theorem of Calculus:                                                   \displaystyle \frac{7}{24}

Topic: Calculus

Unit: Basic Integration/Riemann Sums

Book: College Calculus 10e

6 0
3 years ago
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a ra
Dovator [93]
Circumference of a circle is C = 2πr.

part 1)

so the radius of the smaller gear is 3 inches, so after a full rotation, namely a revolution, the smaller gear has covered an arc of 2π(3), or 6π.

what angle has the larger gear of 7 inches in radius, has it covered with an arc of 6π?

\bf \textit{arc's length}\\\\&#10;s=r\theta ~~&#10;\begin{cases}&#10;r=radius\\&#10;\theta =angle~in\\&#10;\qquad radians\\&#10;------\\&#10;s=6\pi \\&#10;r=7&#10;\end{cases}\implies 6\pi =7\theta \implies \cfrac{6\pi }{7}=\theta



part 2)

since the larger gear has a radius of 7, in a revolution it will have an arc of 2π(7), or 14π.

now, we know the smaller gear does a 6π arc in a revolution, how many revolutions will it do in an arc of 14π?

\bf \begin{array}{ccll}&#10;arc&revolution\\&#10;\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\&#10;6\pi &1\\&#10;14\pi &x&#10;\end{array}\implies \cfrac{6\pi }{14\pi }=\cfrac{1}{x}\implies \cfrac{3}{7}=\cfrac{1}{x}\implies x=\cfrac{7}{3}
6 0
3 years ago
1728829+5363792002×82873992892/12=?​
son4ous [18]

Answer:

Simplify the expression.

Exact Form:

111129715061983798933/3

Decimal Form:

3.70432383⋅10^19

Step-by-step explanation:

7 0
3 years ago
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