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The cosine function is the trigonometric function, so it is known as the periodic function.

The period of the given function is π/5. The option 4 is the correct option.

What is the period of the cosine function?

The cosine function is the trigonometric function, hence it is known as the periodic function.

The period of a function is the total interval in which the function repeats itself over and over again the of the function for a complete cycle. If,

[tex]f(x)=A\cos(Bx+C)+D[/tex]

Then the period of the cosine function can be given as,

[tex]I=\dfrac{2\pi}{|B|}[/tex]

Given information-

The given function in the problem is,

[tex]f(x)=\cos(10x)[/tex]

The above function is the cosine function. Let a cosine function of in with values of [tex]x[/tex] 0 to 2π.

Now the period of the periodic function is the interval of [tex]x[/tex] values in which the the cycle of graph repeats itself in both directions.

Compare the given function with above equation we get,

[tex]B=10[/tex]

Thus the period of the [tex]\cos (10x)[/tex] is,

[tex]I=\dfrac{2\pi}{|10|}\\I=\dfrac{\pi}{|5|}\\I=\dfrac{\pi}{5}\\[/tex]

Hence the period of the given function is π/5. Thus the option 4 is the correct option.

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Answer:

○ [tex]\displaystyle \frac{\pi}{5}[/tex]

Explanation:

[tex]\displaystyle \boxed{f(x) = sin\:(10x + \frac{\pi}{2})} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{20}} \hookrightarrow \frac{-\frac{\pi}{2}}{10} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{5}} \hookrightarrow \frac{2}{10}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{5}} \hookrightarrow \frac{2}{10}\pi \\ Amplitude \hookrightarrow 1[/tex]

From the information above, you have your answer.

I am delighted to assist you at any time.

Answer:

10.61 cm

Step-by-step explanation:

From the question,

The volume of the rectangular piece of metal = Volume of the 45 cylindrical plates.

Volume of a cuboid = 45×volume of a cylinder

lwh = 45×πr²h..................... Equation 1

Where l = length of the rectangular piece of metal, w = width of the rectangular piece of metal, h = height of the rectangular piece of metal, r = radius of the cylindrical plates, h = thickness of the cylindrical plates.

make h the subject of the equation

h = lwh/(45πr²).................... Equation 2

Given: l = 12 cm, w = 18 cm, h = 10 cm. r = 1.2 cm

Constant: π = 3.142.

Substitute these values into equation 2

h = (12×18×10)/(45×3.142×1.2²)

h = 2160/203.60

h = 10.61 cm.

Answer:

Step-by-step explanation:

Circumference is= to diameter * Pi

[tex]6\pi = 6*3.14=18.84\\15\pi=15*3.14=47.1[/tex]

For the ones that are radius, double it, then pi

[tex]21*2\pi = 42\pi =42*3.14=131.88\\6.7*2\pi=13.4\pi =13.4*3.14=47.076[/tex]

Answer:

The average yearly drop in enrollment is 12.

Step-by-step explanation:

The average refers to the central value in a group of numbers and with the information provided, you can find the average by dividing the number of students that dropped out of the school by the number of years over which that ocurred:

number of students= 60

number of years= 5

60/5=12

According to this, the answer is that the average yearly drop in enrollment is 12.

Answer:

B

Step-by-step explanation:

Please make  me branlist

Factoring ac + ad + bc + bd by grouping gives (a + b)(c + d)

An equation is an expression that shows the relationship between two or more numbers and variables.

Factorization by grouping means grouping the terms with common factors before factoring.

Given the equation:

ac + ad + bc + bd

Factorizing by grouping:

= a(c + d) + b(c + d)

= (a + b)(c + d)

Factoring ac + ad + bc + bd by grouping gives (a + b)(c + d)

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Answer: the answer will be a

Step-by-step explanation:

Answer: yes

Step-by-step explanation:

Answer:

1/ 125

Step-by-step explanation:

Answer:

Step-by-step explanation:

(53)−3. First, distribute the -3 in the exponent to the numerator and the denominator. (5−33−3) Because both of the exponents are negative=(35)3=27125

Answer:

The answer is 48.12, I didn't used calculator

Answer:

283

Step-by-step explanation:

Answer: 6b+7n+5y+11

Good luck!

Answer:

The first one is mean absolute deviation and the second one is did not improve

Step-by-step explanation:

I took the test

The MAD is greater for this year’s 100-meter dash, which suggests that all 30 students did not improve equally.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The given table is:

                  Mean     MAD

Last Year    16.2 s     1.2

This Year    14.7 s      1.9

Looking at this table we can see that this year, the meantime is smaller than the one from last year, so the runners are faster on average.

The mean absolute deviation is bigger, but the change in the mean is bigger.

difference of the mean   16.2 - 14.7 = 1.5

difference of the MAD  1.9 - 1.2 = 0.7

This means that the average speed of the runners increased since last year,

and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike as last year.

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Answer:C

Step-by-step explanation:

I am not that sure.. but I think the answer is C.

Answer:

w 2 x 6

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

4 to the power of 2 is 16

6 to the power of 2 is 36

Add them up and it's 52

10 the power of 2 is 100

100 does not equal 52 so therefore it is not a right triangle

Answer:

A=P×(1+r÷100)t

A=3000×108÷100×108÷100

A=17496÷2

A=3499.2

Step-by-step explanation:

Answer: um..

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

120/360 = 12/36 = 2/6 = 1/3

Answer:

56 degrees

Step-by-step explanation:

Hello there!

Remember the sum of the angles in a triangle is equal to 180

so to find the missing angle we subtract the given angles from 180

180 - 34 - 90 = 56

so we can conclude that the measure of the missing angle is 56 degrees

Note: the little square at the bottom left of the triangle indicates that the angle is a right angle. The measure of a right angle is 90 degrees so thats where the 90 came from

Answer:

hope it help you

Answer:

hahaha

Step-by-step explanation:

you said that you will give brainliest to the first person to answer not the first person to get it right

Answer:

9x/4 + 30 + 5x/4

Step-by-step explanation:

[tex]9x/4 +30 +5x/5[/tex]

The simplification of the expression (9/4x + 6) - (- 5/4x - 24) will be 3.5x + 30.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ (9/4x + 6) - (- 5/4x - 24)

Simplify the expression, then we have

⇒ (9/4x + 6) - (- 5/4x - 24)

⇒ (9/4)x + 6 + (5/4)x + 24

⇒ (14/4)x + 30

⇒ 3.5x + 30

The simplification of the expression (9/4x + 6) - (- 5/4x - 24) will be 3.5x + 30.

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Answer:

just do the exam

Step-by-step explanation:

Answer:

173,949 lb

Step-by-step explanation:

Volume of a sphere:

[tex] V_{sphere} = \dfrac{4}{3}\pi r^3 [/tex]

A hemisphere is half of a sphere, so its volume is half of the volume of a sphere with the same diameter. Also, radius = diameter/2.

[tex] V_{hemisphere} = \dfrac{2}{3}\pi (\dfrac{d}{2})^3 [/tex]

[tex] V_{hemisphere} = \dfrac{2}{3} \times 3.14159 \times (\dfrac{22~ft}{2})^3 [/tex]

[tex] V_{hemisphere} = 2787.639~ft^3 [/tex]

Now we use the density of water to find the weight of the water contained in the tank.

weight = volume * density

weight = 2787.639 ft^3 * 62.4 lb/ft^3

weight = 173,949 lb

Answer:

8

Step-by-step explanation:

Answer to this question is 3001pi

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

Answer:

175 miles

Step-by-step explanation:

3.5 has 2 miles in it so it has 100 then it has another 1 to make It 3 and half of 2 is ahh it's hard to explain but there's the anwser

Answer:

arc LM = 119°

Step-by-step explanation:

KL = LM

arc KL = arc LM

2(arc LM) = 360° - 122° = 238°

arc LM = 119°

Answer: [tex]432\ in.^3[/tex]

Step-by-step explanation:

Given

The dimension of a rectangular prism is [tex]12\times 6\times 10\ in.^3[/tex]

Water is filled [tex]4\ in.[/tex] from the top i.e. [tex]10-4=6\ in.[/tex] high

base area for the water is the same i.e.  [tex]12\ in.\times 6\ in.[/tex]

The volume of rectangular prism is [tex]l\times b\times h[/tex]

The volume of water in the vase is given by

[tex]\Rightarrow V=12\times 6\times 6=432\ in.^3[/tex]