1.02 quiz sinusoidal graphs

1.02 Quiz Sinusoidal Graphs

Answers

Answer 1

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

graph of the function.

Correct Response;The minimum of the sinusoidal function is 1

Method used to arrive at the above response;

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

y = a·sin(b·(x - h)) + k

a = The amplitude

b = Angular frequency

h = The horizontal shift

k = The vertical shift

Required:

The minimum value of the sinusoidal function.

Solution;

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;

The minimum value of the function is; 3 - 2 = 1

Learn more about sinusoidal functions here:

https://brainly.com/question/6666829

Answer 2

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.

1.02 Quiz Sinusoidal Graphs
1.02 Quiz Sinusoidal Graphs

Related Questions

Pls help me i don’t know what to do

Answers

Answer and Step-by-step explanation:

The answer that we have agreed upon is answer choice 2, C, A, B.

This is because the first distance is found, and could possibly be the hypotenuse, noted as C, then the other two sides are created, becoming the legs of a triangle, noted as A and B respectively.

I hope this helps and is correct!

#teamtrees #PAW (Plant And Water)

33333333333333333333333333333

Answers

Answer: All three methods would be easy and effective

Step-by-step explanation:  

Two trains, train a and train , weigh a total of 466 tons. Train A is heavier than train b. The difference of there weights is 326 tons. What is the weight of each train

Answers

Answer: A = 396 tons

B = 70 tons

Step-by-step explanation:

From the question,

Weight of A + Weight of B = 466

Weight of A - Weight of B = 326

A + B = 466 ......... i

A - B = 326 ..........ii

Subtract equation ii from I

2B = 140

B = 140/2

B = 70 tons

A = 466 - 70

A = 396 tons

In a bag, Bag C, the ratio of red counters to yellow counters is 3 : 4.
If 3 of the red counters are removed from Bag C, the ratio of red counters
to yellow counters is 3 : 5.

How many yellow counters are in Bag C?

Answers

Answer:

20

Step-by-step explanation:

The ratio of red : yellow is 3 : 4 = 3x : 4x ( x is a multiplier )

If 3 red counters are removed then

red : yellow = 3x - 3 : 4x = 3 : 5

Expressing in fractional form

[tex]\frac{3x-3}{4x}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )

5(3x - 3) = 12x

15x - 15 = 12x ( subtract 12x from both sides )

3x - 15 = 0 ( add 15 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

number of yellow counters = 4x = 4 × 5 = 20

what is the volume of the cube if one side is equal to 6 cm

Answers

Answer:

The volume is 216 cm³

Step-by-step explanation:

Hope this helped Mark BRAINLEST!!!

Someone help me PLZZ

Answers

Answer:

5/3

Step-by-step explanation:

The slope is the coefficient next to the x. Therefore, the slope is 5/3.

Answer:

m= 5/3

Step-by-step explanation:

Math wizzz

Worked it out

And online calculator verified!

What is the slope of the line in this graph?

Answers

Answer:

90% sure it's 5/7

Step-by-step explanation:

please help me complete this
https://easel.teacherspayteachers.com/activities/student/18109307

Answers

Answer:

can't see the question love

need the questions queen sorry

What is 7/10 of 650?

Answers

Answer:

455

Step-by-step explanation:

I answered first, but forgot to answer here.

Can anybody help me with these, they're awfully confusing.

Answers

Answer:

20) a) 6.8 b) 7

21) a) 26.2 b) 26

22) a) -7.8 b) -8

23) a) -10.2 b) -10

24) a) 2.6 b) 3

25) a) -12.9 b) -13

9) Real number

10) Real number

11) Real number

12) Real number

13) Real number

14) Real number

15) Not a real number

16) Real number

Explanation

In order to find the estimated integer of a square root, you simply find the perfect squares closest to the specified square root. For example, the closest perfect squares to [tex]\sqrt{46}[/tex] are [tex]\sqrt{36}[/tex] and [tex]\sqrt{49}[/tex]. Now, we need to find which perfect square is the closest between those two. 46 and 36 have a difference of 10, while 46 and 49 have a difference of 3. So, we know that 49 is the closest perfect square. Now, we simplify

what is your first step when solving x/15 = 3/5? Explain
I need this by tonight

Answers

Answer:

Let's solve your equation step-by-step.

x

15

=

3

5

Answer:

x=9

Step-by-step explanation:

Explain why the relation represented by each equation is or is not linear.
a. y=2+3x
b. y=2x(x - 5) - 2x2
C. y=4x2
d. y= 500

Please help T-T

Answers

Answer:

A, b, c, y are linear becouse every value of domain has one value in range

Step-by-step explanation:

If you need any explanation in it or anything on math you can communicate with me on Whats on this number +201557831028 or in email or face or anything

ABC is reflected over the y-axis what are the vertices of A'B'C'

Please help this is for my final

Answers

Answer: It is D

Step-by-step explanation: its is the placement Pretty basic.

Answer: D

Step-by-step explanation:

ap3x verified!!!

A test of a new car results in 370 miles on 10 gallons of gas. How far could you drive on 65 gallons of gas?
Show your work

Answers

Answer:

2405 miles

Step-by-step explanation:

370÷10 = 37

37×65 = 2405

-24 = x - ( - 2

need help please​

Answers

Answer:

okay here is the answer but no work shown

x= -16

i got -26 but i’m not sure if it’s correct

Using Pascal triangle, write down the binomial expansion of
[tex] {(1+y)}^{8} [/tex]
simplifying all the terms.​

Answers

Answer:

1 + 8y + 28y² + 56y³ + 70[tex]y^{4}[/tex] + 56[tex]y^{5}[/tex] + 28[tex]y^{6}[/tex] + 8[tex]y^{7}[/tex] + [tex]y^{8}[/tex]

Step-by-step explanation:

For the expansion of [tex](1+y)^{8}[/tex]

Using the row of Pascal's triangle for n = 8 , that is the coefficients are

1  8  28  56  70  56  28  8  1

Decreasing powers of 1 from [tex]1^{8}[/tex] to [tex]1^{0}[/tex]

Increasing powers of y from [tex]y^{0}[/tex] to [tex]y^{8}[/tex]

Then

[tex](1+y)^{8}[/tex]

= 1 . [tex]1^{8}[/tex].[tex]y^{0}[/tex] + 8. [tex]1^{7}[/tex].[tex]y^{1}[/tex] + 28. [tex]1^{6}[/tex].y² + 56. [tex]1^{5}[/tex].y³ + 70. [tex]1^{4}[/tex].[tex]y^{4}[/tex] + 56. 1³.[tex]y^{5}[/tex] + 28. 1².[tex]y^{6}[/tex] + 8. [tex]1^{1}[/tex].[tex]y^{7}[/tex] + 1. [tex]1^{0}[/tex].[tex]y^{8}[/tex]

= 1 + 8y + 28y² + 56y³ + 70[tex]y^{4}[/tex] + 56[tex]y^{5}[/tex] + 28[tex]y^{6}[/tex] + 8[tex]y^{7}[/tex] + [tex]y^{8}[/tex]

Answer:

y⁸ + 8y⁷ + 28y⁶ + 56y⁵ + 70y⁴ + 56y³ + 28y² + 8y + 1

Step-by-step explanation:

Given binomial

(1 + y)⁸

Expanding using Pascal triangle (attached)

Replace a and b with y and 1 in the bottom row of the triangle

(1 + y)⁸ = (y + 1)⁸ = y⁸ + 8y⁷ + 28y⁶ + 56y⁵ + 70y⁴ + 56y³ + 28y² + 8y + 1

Please help I need to get this done and I have no idea what I'm doing!

Answers

Answer:

5

Step-by-step explanation:

(125) ^ (1/3)

We can rewrite 125 as 5^3

( 5^3) ^ 1/3

We know that a^b^c =a ^ (b*c)

5 ^(3*1/3)

5^ 1

5

Answer:

5

Step-by-step explanation:

when something is to the power of 1/2, that means you square root it

when it is to the power of a third, that means you cube root it.

for example, if it is 25 to the power of a half, that means [tex]\sqrt{25} = 5[/tex] because

5 x 5 = 25

this is the same concept

we need to find a number that multiplies itself 3 times and equals to 125

5x5x5 = 125, meaning that

125 to the power of a third, is 5.

Find the X & Y value

Answers

Answer:

Step-by-step explanation:

x = 72°

y = 61°

does anyone know this i will give brainliest

Answers

Answer: -324.4

Step-by-step explanation:

Hi I need help please ASAP

Answers

Get photomath or Symbolab!!!

HELPPPPP PLSSSSSSSSSWSSSS

Answers

Answer:

D.

Hope that helps!

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Hope this helps

Please solve this and give answer

Answers

Answer:

Step-by-step explanation:

What is 3/4 divided by 2

Answers

Answer:

[tex] \frac{3}{8} [/tex]

Step-by-step explanation:

[tex] \frac{3}{4} \div 2 \\ \\ = \frac{3}{4} \times \frac{1}{2} \\ \\ = \frac{3 \times 1}{4 \times 2} \\ \\ = \frac{3}{8} [/tex]

Yesterday movie theaters sold 261 bags of popcorn a large bag of popcorn cost three dollars a small bag of popcorn cost one dollar in all the movie theater made $443 from popcorn sales right and solve a system of equations to find how many bags of each size of popcorn were sold

Answers

kannaoakaksmsamammamsmma 66

Lee wants to buy four tee shirts,
which were originally priced $12.94
each. He purchases four shirts at the
"Buy One Get One 50%" sale and pays
6.2% tax on the total cost of the
shirts. Including the tax, what will be
the cost of each shirt?

Answers

Answer:

$27.48

Step-by-step explanation:

He buys 1 shirt at 12.94 and gets one at 6.47

He does this 2 times and the total is 25.88

That times 1.062 to factor in the 6.2 percent tax rate is 27.48

So first you do:

.5 x 12.94=6.47

Next:

6.47 x 2=12.94

Then:

12.94 x 3=38.82

Now you have to do the tax:

38.82 x .062=2.41

After you get the answer for tax you have to add that to the price with out tax:

So, 38.82+2.41

=41.23

So you answer is 41.23 including the discount and tax

-4w - 3( -9 + 5w) Combine Like Terms Using the Distributive Property

Answers

Answer: =−19w+27

Step-by-step explanation:Hope this help :D

how many oz are in 1 gallon and a cup​

Answers

72038302229877777389Step-by-step explanation:


Order the ANGLES in each triangle from SMALLEST to largest.

Answers

Answer:

S,R,Q

Step-by-step explanation:

PLEASE HELP ASAP!! DUE TODAY

Answers

Answer:

Step-by-step explanation:

when  1/2 inch equals 4 feet the room is  2.25 inches, then

2 1/4 = 8/4 + 1/4  = 9/4

9/4 inches is the scale distance of the room

each 1/2 inch is 4 feet so divide  9/4 by 1/2 then multiply that by 4 to find the distance of the room

9/4 ÷ 1/2  = 9/4

9/4 * 2/1 = 18/4

18/4 = 9/2

9/2 * 4 feet = 9/2 * 4/1

9/2 * 4/1 = 36/2

36/2=18

the room is 18 feet across

then if the scale is 2/3 of an inch is  4 feet , then

2/3 * 9/4 = 18/12

18/12 = 3 inches  is the scale size of Quinto's room

i need help asap please

Answers

8x^2y is correct
Hope this helps
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