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Kisachek [45]
3 years ago
13

A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diam

eter of the semicircle. What is the total area of the banner? Use 3.14 for pi (please show work)
Mathematics
1 answer:
Anna007 [38]3 years ago
7 0
Your answer is 891.33
26*26 = 626 (area of the square)
26 / 2 = 13 ( radius of the semecircle )
13*13 = 169
169 * 3.14 = 530.66
530.66 / 2 = 265.33 ( area of the semecircle)
265+626 = 891.33
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Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

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In this case:

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So

(f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when x = 0, f(g(x)) = 25. So

4a^2 - 8a - 20 = 25

4a^2 - 8a - 45 = 0

Solving a quadratic equation, by Bhaskara:

\Delta = (-8)^2 - 4(4)(-45) = 784

x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5

x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5

The possible values are a = -2.5 or a = 4.5.

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