Daniela is a stain glass artist; she created the window below for her living room. What is

Mathematics

1 answer:

OLga [1]3 years ago

3 0

The window has a shape of a semi-circle (half of a circle).

We know the diameter d = 12 ft.

The area of a (complete) circle is given by the formula:
A = π × r²

The radius can be found by halving the diameter:
r = d ÷ 2
= 12 ÷ 2
= 6 ft

Therefore the area of the circle will be:
<span>A = π × r²
= 3.14 × 6</span>²
= <span>3.14 × 36
= 113.04 ft²

And the area of the semi-circle:
A = </span><span>113.04 </span>÷ 2
= 56.52 ft²

Hence, the area of the window will be 56.52 ft².

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Sum n=3 ^ infty (2n+5)<br>find the series shown

Margarita [4]

<h3>Answer: Choice C) 11 + 13 + 15 + 17 + ...</h3>

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Explanation:

We're adding terms in the form (2n+5)

The first term is when n = 3, so

2n+5 = 2*3+5 = 6+5 = 11

The next term is when n = 4, so

2n+5 = 2*4+5 = 8+5 = 13

The next term is when n = 5, so

2n+5 = 2*5+5 = 10+5 = 15

And so on

This means,

$\displaystyle \sum_{n=3}^{\infty} (2n+5) = 11+13+15+17+\ldots$

which matches with choice C. The three dots indicates the pattern goes on forever.

-------------------

Choice B does not have these dots, so that's why choice B is not the answer. If we replaced the infinity symbol with 7, then choice B would be the answer.

I.e,

$\displaystyle \sum_{n=3}^{7} (2n+5) = 11+13+15+17+19$