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babymother [125]
3 years ago
13

Keenan is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool,

he will complete a 118-yard warmup and then swim laps in a lane that is 41 yards long. If Keenan swims at the indoor pool at his gym, he will complete a 154-yard warmup, plus a main set that consists of 32 yards per lap. If Keenan swims the correct number of laps, he can complete the same distance in either pool. How many laps will that take? How long will Keenan's workout be in total?
Mathematics
1 answer:
hoa [83]3 years ago
6 0

9514 1404 393

Answer:

  • 4 laps
  • 282 yards

Step-by-step explanation:

For n laps, the length Keenan swims in the rec center pool is ...

  118 + 41n

and the length he swims in the gym pool is ...

  154 +32n

These are equal length for equal numbers of laps, so we have ...

  118 + 41n = 154 + 32n

  9n = 36 . . . . . . . . . . . . . subtract 32n+118

  n = 4 . . . . . . . . divide by 9

Then the length of Keenan's workout is ...

  118 +41(4) = 282 . . . . yards

It will take 4 laps to make the workout total 282 yards in each pool.

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The diameter of a circle is 23 inches and the circle has two chords of length 14 inches what is the distance from each chord to
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Answer:

9.12 + 9.12 = 18.24 inches

Step-by-step explanation:

Diameter = 23 inches (given)

Radius = 11.5 inches

2 Chords of length = 14 inches ( You didn't specify if the 14 inches is for both chords or for a single cord. I'll assume it's for two cords 14 and 14inches apart.

To clearly solve this, we'll make some mild assumptions.

Let the perpendicular distance of the chords from the center of the circle to represented as " x and y"

Therefore:

x^2 + 7^2 = 11.5 ^ 2

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Since the cords have thesame length (Assumed from the way the question was structured, the distance would still be thesame)

y^2 + 7^2 = 11.5 ^ 2

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General term for -13, -11, -9, -7
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The general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

<h3>Arithmetic progression</h3>

-13, -11, -9, -7

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  • Second term = -11

Common difference, d = Second term - first term

= -11 - (-13)

= -11 + 13

= 2

Therefore,

Tn = a + (n - 1)d

Where,

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Tn = a + (n - 1)d

= -13 + (n - 1)2

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Tn = -15 - 2n

So therefore, the general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

Learn more about arithmetic progression:

brainly.com/question/6561461

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