please help asap!!!!

The characteristics of the sinusoidal function can be found from the given

graph of the function.

The sinusoidal function is the sine function that has the following general equation;

a = The amplitude

b = Angular frequency

h = The horizontal shift

k = The vertical shift

The minimum value of the sinusoidal function.

From the given graph, we have;

The amplitude, a = 2

The period, T = 10 = 2·π/b

b = π/5

The vertical shift, k = 3

The horizontal shift = 0

The minimum value of the function = k - a

Therefore;

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Answer:

[tex]\displaystyle 1[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 2cos\:(\frac{\pi}{5}x - \frac{\pi}{2}) + 3} \\ \\ 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 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{2\frac{1}{2}} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{\pi}{5}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{10} \hookrightarrow \frac{2}{\frac{\pi}{5}}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle \boxed{y = 2sin\:\frac{\pi}{5}x + 3} \\ \\ 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 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{10} \hookrightarrow \frac{2}{\frac{\pi}{5}}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:\frac{\pi}{5}x + 3,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle 2\frac{1}{2}\:units[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle 2\frac{1}{2}\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{2\frac{1}{2}} = \frac{\frac{\pi}{2}}{\frac{\pi}{5}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(\frac{\pi}{5}x - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph approximately hits [tex]\displaystyle [-10, 3],[/tex]from there to the y-intercept of [tex]\displaystyle [0, 3],[/tex]they are obviously approximately [tex]\displaystyle 10\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 10.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

**Now, the minimum value is the lowest possible value the graph touches, and in this case, the graph's lowest peaks cycle around [tex]\displaystyle y = 1,[/tex]therefore the minimum of his sinusoidal function is [tex]\displaystyle 1.[/tex]

I am delighted to assist you at any time.

Answer:

243,000

Step-by-step explanation:

(2.7×10^-3) ÷ (9×10^7) | Given (thanks for proper formatting :')

(2.7 × 0.001) ÷ (9 × 10,000,000) | Start with exponents

0.0027 ÷ 90,000,000 | Multiply what's in the parenthesis

243,000 | Divide these numbers

Answer:

20c= 30(c-9)

Step-by-step explanation:

The first step in solving a word problem is always to organize the information you have, and put it into equations to solve.

Let c be the cost per student originally.

The cost of the bus has not changed, so the cost/student * the number of students has not changed:

The equation of line is solved and Health Club B costs $ 7 less in monthly membership fees that Health Club A

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 3 , 106 )

Let the second point be Q ( 6 , 187 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 187 - 106 ) / 3

Slope m = 27

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 106 = 27 ( x - 3 )

y - 106 = 27x - 81

Adding 106 on both sides , we get

y = 27x + 25   be equation (1)

Now , let the equation of line be represented as B

And , the value of B is

Let the first point be R ( 3 , 105 )

Let the second point be S ( 6 , 165 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 165 - 105 ) / 3

Slope m = 20

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 105 = 20 ( x - 3 )

y - 105 = 20x - 60

Adding 105 on both sides , we get

y = 20x + 45   be equation (2)

Now , when x = 1

Substitute the value of x = 1 in equation (1) and equation (2) , we get

y₁ = 27 + 25 = $ 52

y₂ = 20 + 45 = $ 65

So , health club B costs $ 7 less than health club A every month

Hence , the equation of lines is solved

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Answer:

its D

Step-by-step explanation:

Answer:

c=36 degrees

d=54 degrees

Answer:

PQ = 35 km

Step-by-step explanation:

Here, we want to get the length of PQ

Let PQ = x

PR is 10 km longer than PQ

PR = 10 + x

QR = 2 * PR

QR = 2(10 + x)

Adding all gives 170;

x + 10 + x + 2(10 + x) = 170

2x + 10 + 20 + 2x = 170

4x + 30 = 170

4x = 170-30

4x = 140

x = 140/4

x = 35 km

PQ = 35 km

The length of the road PQ of the town where, towns P, Q and R are connected by roads PQ ,PR and QR is 35 km.

Length of line segment (say YX) is the distance of both the ends of it (y to x).

Towns P, Q and R are connected by roads PQ ,PR and QR.

The line segment PR is 10 km longer than PQ. Therefore,

[tex]PR=PQ+10\\PQ=PR-10[/tex]            ......1

The line segment QR is twice as long as the line segment PR. Therefore,

[tex]QR=2PR[/tex]                 .....2

The total length of three roads is 170 km. Therefore,

[tex]PQ+PR+QR=170[/tex]

Put the value of PR and QR from equation 1 and 2 in the above equation as,

[tex](PR-10)+PR+(2PR)=170\\PR-10+PR+2PR=170\\4PR=170+10\\PR=\dfrac{180}{4}\\PR=45\rm km[/tex]

As the line segment PR is 10 km longer than PQ and length of PR is 45 km. Therefore,

[tex]PR=45-10\\PR=35\rm km[/tex]

Hence, the length of the road PQ of the town where, towns P, Q and R are connected by roads PQ ,PR and QR is 35 km.

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Answer:

Step-by-step explanation:

Quadrilaterals

Square

Rectangle

Rhombus

Trapezoid

Parallelogram

Answer:

2

Step-by-step explanation:

Total number of cards = 65

she makes the same number of cards everyday for 7 days

Number of days = 7

Cards per day = 65 / 7 = The result is 9 with a remainder of 2.

This means, she makes 9 cards per day for 7 days. Then on the last day she is left with 2 cards to make.

Answer:

D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

x=6

Hopefully it is correct and I tried my best good luck

Answer:                         t=33

Step-by-step explanation:

Answer:

t = 33

Step-by-step explanation:

t/3 = 11

t = 11 × 3

t = 33

Answer:

4x+2y

Step-by-step explanation:

6x is the answer to this question

Answer:

(0, -6)

Step-by-step explanation:

At the y-intercept, the x-coordinate equals zero.

3x - 4y = 24

3(0) - 4y = 24

-4y = 24

y = -6

Answer: (0, -6)

Answer:

1 = 2.25

Step-by-step explanation:

4.5/2 = 2.25

Meaning 1 is 2.25

Hope this helped!

Answer:

2.25

Step-by-step explanation:

Answer:

2nd

Step-by-step explanation:

the highest exponent value is the degree.

if I had [tex]x^{6} x^{2} x^{-7}[/tex] , the degree would be 6.

Answer:

1/4

Step-by-step explanation:

Answer:

hi :)

910

use a percantage calculator, i looked it up and 182 percent of 500 would be 910

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

just took the quiz

Answer:

C

Step-by-step explanation:

Edge2021

Answer:

519

Step-by-step explanation:

or 519.125

The maximum amount of profit the company can make, to the nearest dollar should be considered as the $519.

Since the amount of profit made expressed as [tex]y=-2x^2+105x-859[/tex]

Now

At maximum profit, dy/dx = 0

So,

dy/dx = -4x + 105

0 = -4x + 105

4x = 105

x = 105/4

x = 26.25

Now

[tex]y=-2x^2+105x-859\\\\y=-2(26.25)^2+105(26.25)-859[/tex]

y = - 1,378.125+2,756.25-859

y = 519.125

Hence the maximum amount of profit the company can make is $519.

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This problem is just try and error.

First we try number 2.5 since its the average of all the answers.

2.5^2=6.25

This is smaller than 7 so the answer is either 2.6 or 2.8

Now let's try 2.7

2.7^2=7.29

Which is bigger than 7 and that means the correct answer is 2.6 :)

Answer:

152cm^2

Step-by-step explanation:

Find area of whole rectangle = 12 * 18 = 216cm^2

Find area of smaller square = 8 * 8 = 64cm^2

Take away the larger area from the smaller area = 216 - 64 = 152cm^2

(^2 indicates cm squared)

Hope this helps :)

Answer:

Area of the given figure is 152 sq.cm

Step-by-step explanation:

area of given figure (A)

= area of rectangle - area of minor square

=》A = (12 × 18) - (8 × 8)

=》A = 216 - 64

=》A = 152 sq.cm

Answer:

45.5

Step-by-step explanation:

....................

Answer:

150

Step-by-step explanation:

1/2 multiply base times hieght

Answer:

150

Step-by-step explanation:

given in the pic above

in the pic its 15×10

i have written mistakely 15×12

Around my room before you came.

Answer: around my room before you came

Step-by-step explanation:

Answer:

r(0) = -7

r(2) = -5

r(5) = -12

Step-by-step explanation:

The volume of the cylinder is 288π units²

volume of a cylinder = πr²h

where

Therefore,

r = 6 units

h = 8 units

volume of the cylinder = π × 6² × 8

volume of the cylinder = π × 36 × 8

volume of the cylinder =  288π units²

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Answer I don't know the answer but i can help you find it out, so basically your going to times 3.14 by the numbers in the circle

Step-by-step explanation:

Step-by-step explanation:

In order to find each one, you use the formula A=pi R², meaning you put the radius to the power of two(multiply it by itself) and then multiply that by pi. ex: 7.4×7.4= 54.76,

next 54.76×3.14=171.9, which is your answer. If it gives you the diameter of the circle, divide that by two to get the radius, and follow the steps from before. Ex: 2.24÷2=1.12, next 1.12×1.12=1.2544, next 1.2544×3.14=3.9, the answer.

answer)

Answer:

3 hours

Step-by-step explanation:

Answer:

3 hours

Step-by-step explanation:

120/40=3