All categories

3 years ago

General solution of equation sin x + sin 5x = sin 2x + sin 4x is

Mathematics

1 answer:

zaharov [31]3 years ago

7 0

Answer:

x=nπ3, n∈I

Step-by-step explanation:

sin x + sin 5x = sin 2x + sin 4x

⇒⇒ 2 sin 3x cos 2x = 2 sin 3x cos x

⇒⇒ 2 sin 3x(cos 2x - cos x) = 0

⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I

or cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x

⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3 , n∈I, n∈I

But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I

You might be interested in

What is <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B8%7D%20%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20" id="TexFormula1" ti

marysya [2.9K]

Hello there, and thank you for posting your question here on brainly.

Something I noticed right away is that 4/8 can be simplified.

4/8 ===> 2/4

So now we have 2/4 - 1/4

Just subtract the numerators only.

2/4 - 1/4 = 1/4

1/4 cannot be simplified, so 1/4 is your final answer.

Hope this helped!! ☺♥

5 0

3 years ago

Describe what each transformation does to pre image to create its image

Kamila [148]

A rotation rotates the pre image an x amount of degrees
a translation shifts a pre image up and down or left and right
a reflection reflects an image across an x or
y axis
a dilation stretches or compresses(shrinks) a pre image

7 0

2 years ago

50 POINTS!!!

san4es73 [151]

Step-by-step explanation:

<u>Step 1: Determine an ordered pair</u>

A solution of an equation just means that the point lies on the line. We can find any y-value when we plug in a specific x-value. For example, if we want to know what ordered pair lies at x=1, we just plug in y = -1/2(1) and solve for y which gives us -1/2. This gives us an ordered pair of (1, -1/2). We can continue to do this for any x value.

We can also reverse the order and plug in the y-value and get the x-value in order to accomplish the same goal but it's a bit harder.

Hope this helps!

6 0

1 year ago

Read 2 more answers

Write the equation of the graph

olchik [2.2K]

Answer:

$y = 2.cos(x) - 2$

Step-by-step explanation:

1. Shifting $cos(x)$ right or left, top or down, as the graph in the question has the same illustration of $cos(x)$ . Consider

$y = a.cos(x) + b$

2. find a and b by using two sample points from the graph: $(0, 0)$ and $(\pi, -4)$

$0 = a.cos(0) + b => a + b = 0\\ -4 = a.cos(\pi) + b => b-a=-4\\\left \{ {{2b=-4} \atop {2a=4}} \right.\\a = 2, b=-2\\$

5 0

3 years ago

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 75.6 Mbp

olga55 [171]

Answer:

a) 59.98

b) 2.99

c) 2.99

d) Significantly High

Step-by-step explanation:

Part a)

Highest speed measured = x = 75.6 Mbps

Average/Mean speed = $\overline{x}$ = 15.62 Mbps

Standard Deviation = s = 20.03 Mbps

We need to find the difference between carrier's highest data speed and the mean of all 50 data speeds i.e. x - $\overline{x}$

x - $\overline{x}$ = 75.6 - 15.62 = 59.98 Mbps

Thus, the difference between carrier's highest data speed and the mean of all 50 data speeds is 59.98 Mbps

Part b)

In order to find how many standard deviations away is the difference found in previous part, we divide the difference by the value of standard deviation i.e.

$\frac{59.98}{20.03}=2.99$

This means, the difference is 2.99 standard deviations or in other words we can say, the Carrier's highest data speed is 2.99 standard deviations above the mean data speed.

Part c)

A z score tells us that how many standard deviations away is a value from the mean. We calculated the same in the previous part. Performing the same calculation in one step:

The formula for the z score is:

$z=\frac{x-\overline{x}}{s}$

Using the given values, we get:

$z=\frac{75.6-15.62}{20.03}=2.99$

Thus, the Carriers highest data is equivalent to a z score of 2.99

Part d)

The range of z scores which are neither significantly low nor significantly high is -2 to + 2. The z scores outside this range will be significant.

Since, the z score for carrier's highest data speed is 2.99 which is well outside the given range, i.e. greater than 2, we can conclude that the carrier's highest data speed is significantly higher.

3 0

3 years ago