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3 years ago

Find the area of the regular polygon

Mathematics

1 answer:

kodGreya [7K]3 years ago

7 0

Answer:

Step-by-step explanation:

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What is the final net price of a designer swimsuit, originally priced at $85, when the Fall discounts are 25/60 (hint: Find the

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Answer:

The final net price of a designer swimsuit is $\$49.58$

Step-by-step explanation:

Let

x-----> the final net price of a designer swimsuit

we know that

$x=\$85[1-\frac{25}{60}]$

$x=\$85[\frac{35}{60}]$

$x=\$49.58$

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4 years ago

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3 years ago

Cos^2 x+4sin^2 x/2=1

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$Let\ \dfrac{x}{2}=a,\ therefore\ x=2a.\\\\\cos^2x+4\sin^2\dfrac{x}{2}=\cos^22a+4\sin^2a\\\\\text{use}\ \cos2x=\sin^2x-\cos^2x\\\\=(\sin^2a-\cos^2a)^2+4\sin^2a\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(\sin^2a)^2-2(\sin^2a)(\cos^2a)+(\cos^2a)^2+4\sin^2a\\\\=\sin^4a-2\sin^2a\cos^2a+\cos^4a+4\sin^2a\\\\=\underbrace{\sin^4a+2\sin^2a\cos^2a+\cos^4a}_{(*)}-4\sin^2a\cos^2a+4\sin^2a\\\\\text{use}\ (*)\qquad(a+b)^2=a^2+2ab+b^2$

$=\underbrace{(\sin^2a)^2+2\sin^2a\cos^2a+(\cos^2a)^2}_{(*)}-4\sin^2a(\cos^2a-1)\\\\=(\sin^2a+\cos^2a)^2-4\sin^2a(\cos^2a-1)\\\\\text{use}\ \sin^2a+\cos^2a=1\to\sin^2a=\cos^2a-1\\\\=1^2-4\sin^2a(\sin^2a)=1-4\sin^4a=1-(2\sin^2a)^2$

$\cos^22a+4\sin^2a=1\\\\1-(2\sin^2a)^2=1\qquad\text{subtract 1 from both sides}\\\\-(2\sin^2a)^2=0\to2\sin^2a=0\qquad\text{divide both sides by 2}\\\\\sin^2a=0\to\sin a=0\\\\a=k\pi\ for\ k\in\mathbb{Z}\\\\\dfrac{x}{2}=k\pi\qquad\text{multiply both sides by 2}\\\\\boxed{x=2k\pi\ for\ k\in\mathbb{Z}}$

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3 years ago

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den301095 [7]

Answer:

C. 1.5w^2 + 7.5w + 9

Step-by-step explanation:

Without frame:

The width is w. The height is 1.5w.

With frame:

The width is w + 1.5 + 1.5 = w + 3

The height is 1.5w + 1.5 + 1.5 = 1.5w + 3

The area of the framed portrait is height * width

area = (1.5w + 3)(w + 3)

area = 1.5w^2 + 4.5w + 3w + 9

area = 1.5w^2 + 7.5w + 9

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4 years ago

Which best describes the resulting three-dimensional

Harman [31]

Answer: C

Step-by-step explanation:

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3 years ago

Read 2 more answers

Find the area of the regular polygon​

Find the area of the regular polygon