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Tatiana [17]
2 years ago
13

You can do one-half of a job in you can do one half of a job in a an hour. Your friend can do one-third of the same job in an ho

ut How long will take to do the job if you work together?
te your answer as a decimal

Mathematics
1 answer:
AlladinOne [14]2 years ago
5 0

Answer:

  • 1.2 hours

Step-by-step explanation:

Let the amount of the job is x.

You can do 1/2x in an hour.

Your friend can do 1/3x in an hour.

<u>Together you can do:</u>

  • 1/2x + 1/3x = 5/6x of a job in an hour

<u>You need time to finish the job:</u>

  • x ÷ 5/6x = 6/5 = 1.2 hours
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Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 + 2x + 3 y2 = 2x + 12F
Svet_ta [14]

Answer:

A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36

Step-by-step explanation:

The equations are:

y = x^{2} + 2x + 3

y = 2x + 12

The two graphs intersect when:

x^{2} + 2x + 3 = 2x + 12

x^{2} = 0

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To find the area under the curve for the first equation:

A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx

To find the area under the curve for the second equation:

A_{2} = \int\limits^3__-3}{2x + 12} \, dx

To find the total area:

A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx

Simplifying the equation:

A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx

Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).  

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2 years ago
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