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bixtya [17]
1 year ago
11

Find all solutions of the equation in the interval [0, 2).

Mathematics
1 answer:
Margaret [11]1 year ago
6 0

Answer:

  x = 3π/2

Step-by-step explanation:

The given equation can be rewritten as a quadratic in sin(x), then solved by factoring.

<h3>Rewrite</h3>

Using the identity ...

  cos²x = 1 -sin²x

the equation can be rewritten as ...

  sin(x) = -(1 -sin²(x)) -1 . . . . . .substitute for cos²x

<h3>Solution</h3>

The new equation can be solved by considering it a quadratic in sin(x).

  0 = sin²(x) -sin(x) -2 . . . . . . subtract sin(x)

  (sin(x) -2)(sin(x) +1) = 0 . . . . factor quadratic

The solutions to this are ...

  sin(x) -2 = 0   ⇒   sin(x) = 2 . . . .  no solutions

  sin(x) +1 = 0   ⇒   sin(x) = -1   ⇒   x = 3π/2 (one solution)

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Answer:

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Step-by-step explanation:

Part A.

The surface area of each figure is the sum of the end area and the lateral area.

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  S = (2)(πr²) +2πrh = 2πr(r +h)

  S = 2π(5 cm)(5 cm +10 cm) =150π cm² ≈ 471.2 cm²

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  <u>triangular prism</u>

  S = (2)(1/2)bh + PL . . . . b=triangle base; h=triangle height; P=triangle perimeter; L=length of prism

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_____

Part B.

Surface area is useful in the real world wherever products are made from sheets of material or wherever coverings are applied.

Carpeting or other flooring, paint, wallpaper are all priced in terms of the area they cover, for example.

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2 years ago
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Answer:

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Step-by-step explanation:

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Answer:

76

Step-by-step explanation:

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(4x4) x (5x5) - (18x 18)

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Now we multiply: (PEMDAS)

= 400 - 324

then subtract: (PEMDAS)

=76

3 0
3 years ago
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