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belka [17]
3 years ago
8

Ben and Carson went to the movies with friends. Ben purchased 3 popcorn and 2 boxes of candy for $41. Carson purchased 1 popcorn

and 2 boxes of candy for $29. How much did the popcorn cost?
Mathematics
1 answer:
vagabundo [1.1K]3 years ago
4 0

Answer:

$6

Step-by-step explanation:

B- 3P+2C=$41

C-1P+2C=$29

since they both bought at least 1 popcorn and 2 candy you can just subtract 29 from 41. you get 12 which equals the other 2 popcorns that ben bought

12/2=6

since you need to find the price of 1 popcorn you have to divide 12 by 2

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y=7x

Step-by-step explanation:

The job pays $7 per 1 hour so to find out how much money you get for x hours, you would multiply the hourly rate ($7) by the amount of hours (x)

3 0
2 years ago
Write the slope intercept form of a line going through
anyanavicka [17]
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Slope 2 turns into -1/2
Y = -1/2x + b
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5 0
3 years ago
Help me with this ASAP
N76 [4]

Add each term and divide it by 2.


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12/2 = 6

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The midpoint is 6 + 2i

3 0
3 years ago
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)
zzz [600]

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

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