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irakobra [83]
2 years ago
8

Find the Value of X. Trig Problem

Mathematics
1 answer:
Likurg_2 [28]2 years ago
8 0

Answer:

  x ≈ 13.4

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle.

__

The figure shows a marked angle (33°), the side adjacent (x), and the hypotenuse (16). The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(33°) = x/16 . . . . . . substitute given values

  x = 16·cos(33°) . . . . . multiply by 16

  x ≈ 13.419 . . . . . . . . evaluate

The value of x is approximately 13.4.

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<h3 /><h3>Methods used to obtain the above response</h3>

Let <em>x</em><em> </em>represent the width of the cars parked compact, and let a·x represent the width of cars parked in full size spaces.

We have;

Initial space occupied = 10·x + 12·(a·x) = x·(10 + 12·a)

New space design = 16·x + 9×(a·x) = x·(16 + 9·a)

When the dimensions of the initial and new arrangement are equal, we have;

10 + 12·a = 16 + 9·a

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Whereby the factor <em>a</em> < 2, such that the width of the full size space is less than twice the width of the compact spaces, by testing, we have;

10 + 12·a < 16 + 9·a

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x·(10 + 12·a) < x·(16 + 9·a)

Therefore;

The initial total car park space is less than the space required for 16

compact spaces and 9 full size spaces, therefore; the store owners are

incorrect.

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