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2 years ago

Suppose the two sinusoidal curves shown above are added together. which of the plots shown below best represents

Mathematics

1 answer:

Valentin [98]2 years ago

7 0

The sinusoidal curves are shown in the picture attached.

Note that the two waves have the same amplitude (same "height"), the same wavelength (same distance from one peak to the next one) and therefore the same frequency, but different phase (they start in different points).

When you sum two different sinusoidal curves with the same amplitude and frequency, but different phase you get a sinusoidal wave with the same frequency as the original curves, but a different amplitude and a different phase.

Therefore, the correct answer is graph B).

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Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

Question 1:

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

Question 2:

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

8 0

2 years ago

Each of four friends orders a sweatshirt from a catalog. There are 18 colors of sweatshirts, 6 of which are all cotton and 12 of

Digiron [165]

Answer:

1/204.

Step-by-step explanation:

That would be

6/18 * 5/17 * 4/16 * 3/15

= 1/3 * 1/4 * 1/5 * 5/17

= 5/1020

= 1/204.

5 0

1 year ago

Find the 3rd term in the expansion of (a+b)^8 in simplest form.

Art [367]

Answer:

The fifth term is the middle term of nine, with coefficient given by all the ways of choosing 4 items out of 8 , namely the ways of choosing 4 a 's out of 8 binomial factors.

Step-by-step explanation:

4 0

2 years ago

. The area of a rectangle is 45.5 square inches. The base of the rectangle is 7 inches.

Ugo [173]

What the question then

7 0

2 years ago

Read 2 more answers

Write [2(cos15*+isin15*)]^3 in standard form a+bi

Marysya12 [62]

Hello :
by moivre theorem :
[2(cos15*+isin15*)]^3 = 2^3(cos(3×45*)+isin(3×45*))
=8 (cos45*+isin45*)
= 8 ( √2/2 +i √2/2)
= 4√2 + 4√2 i ..... ( in standard form a+bi)
a = b = 4√2

8 0

3 years ago

Read 2 more answers