1.02 sinusoidal graphs
WHAT IS THE MAXIMUM OF THE SINUSOIDAL FUNCTION?
Enter your answer in the box.
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Answers
Answer:
[tex]\displaystyle -2[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = 2cos\:(\frac{4}{13}\pi{x} - \frac{\pi}{2}) - 4} \\ \\ 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 -4 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{1\frac{5}{8}} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{4}{13}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\frac{1}{2}} \hookrightarrow \frac{2}{\frac{4}{13}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle \boxed{y = 2sin\:\frac{4}{13}\pi{x} - 4} \\ \\ 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 -4 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\frac{1}{2}} \hookrightarrow \frac{2}{\frac{4}{13}\pi}\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{4}{13}\pi{x} - 4,[/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 approximately shifted [tex]\displaystyle 1\frac{5}{8}\:unit[/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 1\frac{5}{8}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{1\frac{5}{8}} = \frac{\frac{\pi}{2}}{\frac{4}{13}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(\frac{4}{13}\pi{x} - \frac{\pi}{2}) - 4.[/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 [-6\frac{1}{2}, -4],[/tex]from there to the y-intercept of [tex]\displaystyle [0, -4],[/tex]they are obviously approximately [tex]\displaystyle 6\frac{1}{2}\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 6\frac{1}{2}.[/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 = -4,[/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 maximum value is the highest possible value the graph touches, and in this case, the graph's highest peaks cycle around [tex]\displaystyle y = -2,[/tex]therefore the maximum of this sinusoidal function is [tex]\displaystyle -2.[/tex]
I am delighted to assist you at any time.
Related Questions
Will the product of two positive numbers be positive or negative? Why?
PLEASE HELP1!1!1!1!!1
Answers
Answer:
Positive
Step-by-step explanation:
Two positive integers multiplied will always be positive.
Answer:
Positive
Step-by-step explanation:
two positive will always be a positive because of the rule of multiplication
7
4
8
1
Write down the largest even number
you can using all four cards
Answers
Answer:
8
7
4
1
Step-by-step explanation:
8 is the answer
PLS HELP WITH BOTH SCREEN SHOTS I WILL MARK BRAINLIEST
Answers
Answer:
Answer 1. 3in
Answer 2. 0.875in
Answer 3. 26 miles
Answer 4. 7.67in
Step-by-step explanation:
Answer 1. We know that 2 feet in real life is going to equal 1 inch, so since the person is 6 feet, we divide that by 2 to get 3. So the action figure is going to be 3in.
Answer 2. In this case, we see that 1 foot is equal to four inches. That must mean that 1 inch is equal to a quarter foot. So we just multiply
0.25 x 3.5 = 0.875
The length is 0.875 feet
Answer 3.
We know that 1 inch = 6.5 miles, and there are 4 inches on the map, so we have to multiply 6.5 x 4 to find out how many miles there is.
Answer 4.
To find this one out, we have to divide 9 into 69. That gives us 7.67. So 69 nautical miles would be equal to 7.67 inches on the map
Hope this helps you out :)
Answer:
ty
Step-by-step explanation:
I need help on this pls
Answers
Answer:
Area= 56 cm²
Step-by-step explanation:
Figure given is a rhombus
Area= 1/2*d1*d2
Please help me with this question!
Answers
Answer:
Your Answer Is 10
Step-by-step explanation:
1st Factor the Numerator and Denominator then cancel the common factor.
Hope It Help You If Yes then Please make me the Brainiest.
Thank You
Parshv
−2x=x2−6 Rewrite the equation by completing the square.
Answers
Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
Martin likes to make flower bouquets that have 333 daffodils and 444 tulips per vase. A daffodil has a mass of ddd grams, a tulip has a mass of ttt grams, and the vase has a mass of vvv grams.
The expression 5(3d+4t+v)5(3d+4t+v)5, left parenthesis, 3, d, plus, 4, t, plus, v, right parenthesis describes the mass of 555 bouquets.
Match each amount in the situation with the expression that represents it.
Situation
Expression
Answers
Answer:
Answer:
Mass of a bouquet = v + 3d + 4t
Step-by-step explanation:
Mass of daffodil = d gm
Mass of Tulip = t gm
Mass of vase = v gm
Mass of a bouquet = mass of vase + Mass of 3 daffodils + Mass of 4 tulips
=> Mass of a bouquet = v + 3d + 4t
Flower bouquet weight = v + 3d + 4t
Answer:
Step-by-step explanation:
Situation Expression
Number of bouquets 555
Mass of one bouquet 3d+4t+v
Mass of the tulips in one bouquet 4t
Mass of the daffodils in one bouquet 3d
If EBCD is a parallelogram, EB = 16, ED = 25, BF = 11, EC = 34, mZBED = 55°, mZCDB = 67°,
and mZBCE = 24º, find each missing measure.
B
с
BC =
mZEDC =
BD =
mZEBD =
F
FC =
E
D
mZBEC =
mZDBC =
CD =
Answers
Answer:
1. BC = 25
2. m∠EDC = 125°
3) BD = 22
4) m∠EBD = 67°
5) FC = 17
6) m∠BEC = 24°
7) CD = 16
8) m∠DBC = 58°
Step-by-step explanation:
The dimensions of parallelogram EBCD are;
EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°
1. BC = ED = 25 Opposite sides of a parallelogram are equal
2. m∠BCD = m∠BED = 55 opposite angles of a parallelogram are equal
m∠BCD + mEDC = 180° adjacent sides of a parallelogram are supplementary
m∠EDC = 180° - m∠BCD
∴ m∠EDC = 180° - 55° = 125°
m∠EDC = 125°
3) BD = BF × 2 Diagonals of a parallelogram bisect each other
∴ BD = 11 × 2 = 22
BD = 22
4) m∠EBD = m∠CDB = 67° from alternate angles between parallel lines
5) FC = EC/2 from diagonals of a parallelogram bisect each other
∴ FC = EC/2 = 34/2 = 17
FC = 17
6) m∠BEC = m∠BCE = 24° Alternate angles between parallel lines
m∠BEC = 24°
7) CD = EB = 16 Opposite sides of a parallelogram are equal
8) m∠EBC = m∠EDC = 125° from opposite angles of a parallelogram are equal
m∠DBC + m∠EBD = m∠EBC from angle addition postulate
∴ m∠DBC = m∠EBC - m∠EBD
m∠DBC = 125° - 67° = 58°
m∠DBC = 58°
What is a congruence statement? PLEASE ANSWER HURRY
Answers
Answer:
A congruence statement says that two polygons are congruent.
Step-by-step explanation:
To write a congruence statement, list the corresponding vertices in the same order.
Write 33 % as a fraction in simplest form.
3
Answers
Answer:
33/100
Step-by-step explanation:
33/100 bc percentage goes up to 100
How many groups of 1/2 day are in 1 week? Use a multiplication or division equation to explain your answer
Answers
Answer:
14
Step-by-step explanation:
you need to do 1 week divided by 1/2 so 1 week is 7 days.7 divided by 1/2 is basically 7*2 =14
may someone please help?
Answers
Answer:
B' = (-7,3)
Step-by-step explanation:
B = (7,3)
mirrored would be:
B' x position would be -7
B' y position would not change
B' = (-7,3)
Find the value of i^9
Answers
Answer:
The answer is i (i^9)
Step-by-step explanation:
polygon ABCD is dilated using a scale factor of 6/5 to produce polygon A'B'C'D with the origin as the center of dilation.
Answers
Answer:
the answer is A
Step-by-step explanation:
1) calcula a.b , si 120 =1+2+3+... +ab
Answers
Answer:
ab=195
Step-by-step explanation:
Anybody know? Need help
Answers
Answer:
option c is the correct answer
Answer:
C consecutive angle
Step-by-step explanation:
pls help meeeee....zzzz
Answers
Answer:
I think its a or b? But I think mostly a, sorry if I'm wrong
The answer is D:3,4,5
ANSWER THIS NOW please. An amusement park constructed a new ride called the "Haunted Hotel." There are x2 –
3 floors in this hotel. Each floor is 2x2 + 5 feet high. Which expression shows the total
height of this hotel?
Answers
Answer:
2x⁴ - x² - 15
Step-by-step explanation:
(X² - 3)(2x² + 5)
[x²(2x² + 5)] - [3(2x² + 5)]
= 2x⁴ - x² - 15
Read the problem below. Type in your answer on the box.
The length of a rectangle is (3x - 1) and its width is ( 2x + 5). What is the area of the rectangle?
Answers
Answer:
3x^2 + 13x - 5
Step-by-step explanation:
To find the area, you multiply the length by width. So its is (3x - 1) * (2x + 5)
Then distribute. (3x * 2x) + (3x *5) + (-1 *2x) + (-1 * 5)
So 3x^2 + 15x -2x -5
Final Answer: 3x^2 + 13x - 5
Answer:
30 INCHES
Step-by-step explanation:
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
+.5
Step-by-step explanation:
im using all my points for this pls help
A. The area of a square is 196 cm.?. What is the length of each side?
B. The area of a rectangle is 94.5 in.. The length is 9 inches. What is the
width?
What is the answer to a and b
Answers
Answer:
A. 14 cm
B. W== 0.5in
Step-by-step explanation:
Hope this helps
Determine the y intercept
Answers
Answer:
The Y intercept adds on +6 every time.
Step-by-step explanation:
Hope this helps! :3
Answer:
(0, 19)
Step-by-step explanation:
Find the equation.
Find the slope:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
22-16/1-(-1) = 6/2 = 3
Here's our equation so far:
y = 3x + b
Find b by plugging in one pair of (x,y) coordinates.
22 = 3(1) + b
22 = 3 + b
b = 19
Now we now the equation:
y = 3x + 19
So, the y-intercept is 19.
if
[tex]a = \frac{2x + \sqrt{x} }{x} [/tex]
and
[tex]b = \frac{1 - 2 \sqrt{x} }{ \sqrt{x} } [/tex]
without sing a calculator, show that
[tex](a + b) {}^{2} = \frac{4}{x} [/tex]
Answers
Answer:
Step-by-step explanation:
Rationalize the denominator of b. So, multiply the numerator and denominator by [tex]\sqrt{x}[/tex]
[tex]b = \frac{(1-2\sqrt{x}) *\sqrt{x}}{\sqrt{x}*\sqrt{x} }=\frac{1*\sqrt{x} -2\sqrt{x} *\sqrt{x} }{\sqrt{x} *\sqrt{x} }\\\\=\frac{\sqrt{x} -2x}{x}\\[/tex]
Now, find a +b
[tex]a +b = \frac{2x+\sqrt{x} }{x}+\frac{\sqrt{x} -2x}{x}\\\\=\frac{2x+\sqrt{x} +\sqrt{x} -2x}{x}[/tex]
Combine like terms
[tex]= \frac{2x-2x+\sqrt{x} +\sqrt{x} }{x}\\\\=\frac{2\sqrt{x} }{x}[/tex]
Now find (a + b)²
(a +b)² = [tex](\frac{2\sqrt{x} }{x})^{2}[/tex]
[tex]= \frac{2^{2}*(\sqrt{x} )^{2}}{x^{2}}\\\\= \frac{4* x}{x^{2}}\\\\= \frac{4}{x}[/tex]
Hint: [tex]\sqrt{x} *\sqrt{x} =\sqrt{x*x}=x[/tex]
50 = -2.5%
Can someone help me with this????
Answers
Answer:
what is the question? like... what is -2.5% of 50?
Step-by-step explanation:
If the question is what is -2.5% of 50?
The Answer is -1.25
can y’all please help. I will send points if you want me to.
Answers
Answer:
the third one has a 2 acute angles 2 abuse angles and the x value is 110
Step-by-step explanation
the x value has to be bigger then 90 degree angles because it is a abuts angle and the 57 angle is a acute angle
Scientific notation of 48200
Answers
Answer:
4.82 × 10^4
Step-by-step explanation:
An angle measures 27.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answers
Answer:
Step-by-step explanation:
Supplementary angles have a sum of 180 degrees.
a+a-27.2=180
2a-27.2=180
2a=207.2
a=103.6, and since b=a-27.2
b=76.4
So one angle is 103.6 degrees and the other is 76.4 degrees.
The volume of a box is 400 in.^3in. 3 . The height is 5 in. What is the area of the base of the box?
Answers
Answer:
The area of the base is 80 in². 80 square inches.
Step-by-step explanation: V = b×h
Divide the volume by the height to find the area of the base.
400 ÷ 5 = 80
Matthew has $0.72. He wants to buy stickers that cost $0.08 each. How many stickers can he buy?
Answers
he can buy 9
Answer:
Matthew can buy 9 stickers.
Step-by-step explanation:
0.72 / 0.08 =
72 / 8 = 9
so he can buy 9 stickers
Plz mark as brainliest if correct! Have a nice day!!!
-Lil G
help if u mayy:)))))))
Answers
Answer:
R= 16
M= -12
N= -4
Step-by-step explanation:
what you need to do next time is when you figer out one of the numbers see what it is multiplying by so you know what the numbers would be
Have a nice week. Please mark as brainllest
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