Answers
Answer:
Amplitude: 4
Period: π
midline: y = 1
Step-by-step explanation:
r(x) = -4 sin(2x) + 1
r(x) = a sin(bx + c) + d where |a| is the amplitude and |b| for the period
a = -4 |a| = 4 : Amplitude = 4
b = 2 |b| = 2 period of sin(x) = 2π
period of sin(bx + c) = 2π/|b| = 2π/2 = π
range of sin(2x) ... -1 ≤ sin(2x) ≤ 1
range of -4 sin(2x) + 1: -4+1 ≤ -4 sin(2x) + 1 ≤ 4+1
-3 ≤ -4 sin(2x) + 1 ≤ 5
midline: y = (-3 + 5) / 2 = 1 y = 1
Answer:
Part A: The amplitude [tex]\displaystyle r[/tex]is [tex]\displaystyle 4.[/tex]
Part B: The period of [tex]\displaystyle r[/tex]is [tex]\displaystyle \pi.[/tex]
Part C: The equation of the midline of [tex]\displaystyle r[/tex]is [tex]\displaystyle y = 1.[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{r(x) = -4cos\:(2x - \frac{\pi}{2}) + 1} \\ \\ r(x) = 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 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle r(x) = 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 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
Keep in mind that although this IS a sine function, 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 centre photograph displays the trigonometric graph of [tex]\displaystyle r(x) = -4cos\:2x + 1,[/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 [centre photograph] is shifted [tex]\displaystyle \frac{\pi}{4}\: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 \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle r(x) = -4cos\:(2x - \frac{\pi}{2}) + 1.[/tex]So, with all that being said, to find the period, again, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]Now, the amplitude is obvious to figure out because it is the A-term. Moreover, 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 = 1,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Related Questions
In this diagram, CD is the perpendicular bisected of AB. The two-column proof shows that AC is congruent to BC.
A. AAS
B. SAS
C. SSS
D. ASA
Answers
What numbers do I put in the blank space
Answers
Answer:
5 1/3
Step-by-step explanation:
2 times 8 is 16 and 16 over 3 is 5 with a remainder of one. So it's 5 1/3
Answer:
[tex] \boxed{ 5} \frac{ \boxed{1}}{ \boxed{3}}\: miles [/tex]
Step-by-step explanation:
Total distance ran
[tex] = \frac{2}{3} \times 8 \\ \\ = \frac{16}{3} \\ \\ = \boxed{ 5} \frac{ \boxed{1}}{ \boxed{3}}\: miles [/tex]
Autos de F 1. En un circuito de Australia, Hamilton hizo el récord de vuelta. Si lo normal a 240km/h para completar el circuito de 6000 metros son 2 minutos ¿Qué tiempo debió hacer para recorrer el record de vuelta Y a qué velocidad promedio lo hizo?
Answers
Answer:
Tenía que hacerlo en menos de 2 minutos a más de 240 km/h
Step-by-step explanation:
La velocidad normal dada para completar el circuito de 6.000 metros = 240 km/h
El tiempo normal que se tarda en completar el circuito de 6000 metros = 2 minutos
Dado que Hamilton estableció el récord de vuelta, el tiempo que tuvo que hacer para recorrer el récord de vuelta es de 6000 metros en menos de 2 minutos
La velocidad media con la que lo hizo es de más de 240 km/h.
Two glasses of milk and 3 snack bars have a total of 62 carbohydrates, and 3 glasses of milk and 2 snack bars have a total of 58 carbs. Determine how many carbs are in one glass of milk in one snack bar.
Answers
Step-by-step explanation:
2+3=5
58+62=120
120÷5=24
so 24 carbohydrates are in one glass of milk
143 inches = ________ a) 14 feet 3 inches b) 13 feet 9 inches c) 12 feet 2 inches d) 11 feet 11 inches
Answers
Answer:
D. 11 feet 11 inches
1 foot= 12 inches
143/ 12 = 11 11/12
Answer:
D) 11 feet and 11 inches
Step-by-step explanation:
First we know that there is 12 inches in a foot. So let's start with a.
14 inches x 12 inches (one foot) is 168 inches (so it's not this one:)
13 inches x 12 inches is 156 inches (It's not this one either)
12 inches x 12 inches is 144 inches (not this one)
11 inches x 12 inches is 132 inches (so it could be this one, let's add the remaining inches).
132 + 11 inches = 143 inches.
(Notice I didn't add the remaining inches on A, B, or C because the number of inches was already too much. I did on D because the number of inches was below the given number of 143.
Hope this helps!!
Have a wonderful day!!
find the radius of the circle whose circumference is 22 cm
Answers
Answer:
3.5
Step-by-step explanation:
hope it helps
What Is the slope of the line on the graph? will mark brainliest
Answers
Answer:
The slope is 1/2
Step-by-step explanation:
The equation is y= 1/2x +2
So the slope would be 1/2
If the diameter of the tennis ball is 2.6 inches, what is its circumference, in inches?
Answers
Answer:
8.164
Step-by-step explanation:
The circumference of the ball is 8.164 inches.
Calculation of the circumference:
Since the diameter of the tennis ball is 2.6 inches
So here the radius should be half i.e. 1.3 inches
Now we know that
Circumference = [tex]2\pi r\\\\[/tex]
= 2(3.14)(1.3)
= 8.164 inches
Therefore, we can conclude that The circumference of the ball is 8.164 inches.
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Solve the system of equations
3x – 2y = 11
x + 2y = 9
Answers
Answer:
x=5, y=2. (5, 2).
Step-by-step explanation:
3x-2y=11
x+2y=9
--------------
4x=20
x=20/4
x=5
5+2y=9
2y=9-5
2y=4
y=4/2
y=2
Answer:
y ≤ 1
Step-by-step explanation:
Evaluate the following expression if x=3: x^1
Answers
Answer:
3
Step-by-step explanation:
Evaluate 5(r+12) when r=3.
Answers
Answer:
The answer is 75
Step-by-step explanation:
5(3+12)
15+60
75
Answer:
Step-by-step explanation:
5(3+12) = 5×15 = 75
Grace drew a triangle. Its sides were 6\text{ mm}6 mm6, start text, space, m, m, end text, 7\text{ mm}7 mm7, start text, space, m, m, end text, and 11\text{ mm}11 mm11, start text, space, m, m, end text.
It has one obtuse and two acute angles.
Complete the sentence to describe the triangle Grace drew.
Grace’s triangle is
and
.
Answers
Answer:
Grace's triangle is an obtuse triangle and a scalene triangle.
Step-by-step explanation:
Hope I helped!
Answer:
obtuse triangle and a scalene triangle
Step-by-step explanation:
:)
I NEED HHELLLPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
10.6
Step-by-step explanation:
Answer:
x = 122°
Step-by-step explanation:
since it is a right triangle, the sum of the other 2 interior angles = 90°
the angle opposite x = 90° - 32° = 58°
58° and angle x are supplementary angles. Their sum is 180°.
180° - 58° = 122°
Please help im doing my girl friend work and i dont know not a thing
The admission fee at a John Hay basketball game is $1.50 for students and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected.
How many of each type of ticket did they sell?
Student:
and
Adult
Answers
Answer:
See below, please!
Step-by-step explanation:
We can set up a system of equations to model this problem. Let's consider the student's ticket as x, and y for the adult ticket.
So since the student ticket is $1.50, and adult is $4, we can set up the following equation: [tex]1.5x+4y=5050[/tex], since they collected $5050 total.
We can set up another equation modeling the number of people who came to the game. This would be x+y=2200.
Solve this, and we get x= 1500 and y=700. So, they sold 1500 student tickets and 700 adult tickets.
Hope this helped!
plss helpppp !!!!! it’s urgent
Answers
Answer:
55° is x
Step-by-step explanation:
Angle sum property of triangle = 180°
180 - 70 = 110
As it is an isosceles triangle, two sides and of course angles will be same.
So, 110 ÷ 2 = 55.
So, the two remaining angles will be 55°
Hope it helps!!!
State which Of these decimals is heater then 2/5 and less than 1/2
0.042
0.43
0.51
0.4
Answers
For square ABCD, if m∠ACB = (8x – 27)°, find the value of x.
Answers
Answer:
x=9
Step-by-step explanation:
Since ABCD is a square, we know that AC bisects ∠BCD(=90), and therefore ∠ACB=45.
8x-27=45
8x=72
x=9
Answer:
x = 9°
Step-by-step explanation:
∠ACB = 45° because line AC bisects ∠BCD which is 90° (because square).
8x - 27° = 45°
add 27° to each side:
8x = 72°
divide both sides by 8:
x = 9°
If cylinder A has a diameter of 7 with a height of 12, and cylinder B has a diameter of 12 with a height of 7, which one has the greatest volume? What are A and B's volume?
Answers
Answer:
B ?
Step-by-step explanation:
how to get 15% off of 1.50?
Answers
answer: 1.275
could someone give me the equation? no need to solve
Answers
Answer:
I think the equation would be 345 = 121 + p
Solve for x and identify the type of solution
9x=8+5x
Answers
Answer:
2
Step-by-step explanation:
9x=8+5x
9x-5x=8
4x=8
x=8/4
x=2
4x=8
x=8/4
x=2
x has a unique solution
giving 10 points need urgently
Answers
Answer:
{-2, - 1, 0, 1}
Step-by-step explanation:
The integer solutions will be {-2, - 1, 0, 1}
Answer:
<3<3<3<3<3<3<3
{-2, - 1, 0, 1}
<3<3<3<3<3<3<3
Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.
Answers
Answer:
[tex]x = 9.9[/tex]
[tex]y= 7[/tex]
Step-by-step explanation:
Given
See attachment for triangle
Required
Find x and y
Considering [tex]\theta = 45[/tex]
From the attached triangle, length x is the hypotenuse and length y is the adjacent
Solving for x
[tex]Sin\theta = \frac{Opp}{Hyp}[/tex]
[tex]Sin\theta = \frac{7}{x}[/tex]
So, we have:
[tex]Sin45 = \frac{7}{x}[/tex]
[tex]x= \frac{7}{Sin45 }[/tex]
[tex]x = \frac{7}{0.7071}[/tex]
[tex]x = 9.9[/tex]
Solving for y
Considering [tex]\theta = 45[/tex]
[tex]Tin\theta = \frac{Opp}{Adj}[/tex]
So, we have:
[tex]Tin45= \frac{7}{y}[/tex]
[tex]y= \frac{7}{Tan45}[/tex]
[tex]y= \frac{7}{1}[/tex]
[tex]y= 7[/tex]
The value of x and y is 9.9 and 7.
Calculation of the value:Since theta is 45 degrees
So, we know that
Sin theta = opp/hyp
Sin theta = 7 /x
x = 7 / 0.7071
= 9.9
Now the value of Y should be
Tin theta = opp/hyp
y = 7 \tan 45
= 7 /1
= 7
Therefore, we can conclude that The value of x and y is 9.9 and 7.
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Click on the picture above ! Please help!
Answers
Answer:
A
Step-by-step explanation:
Answer:
the awnser to your question is letter c
Find the missing values in the ratio table. Then write equivalent ratios.
5:3 ?:12 10/3:? ?:5
Answers
Answer:
5 15 10/3 7
3 12 12/3 5
Step-by-step explanation:
The missing values in the ratio table will be;
Pies 5 20 10/3 25/3
Cakes 3 12 2 5
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
The ratio table is;
Pies 5 x 10/3 z
Cakes 3 12 y 5
Now,
Since, The ratios are equivalent to each other.
Thus, We can solve to find the value of x, y and z as;
⇒ 5 : 3 = x : 12
⇒ 5/3 = x/12
Multiply by 12;
⇒ 5 × 12 / 3 = x
⇒ 20 = x
And, 5 : 3 = 10/3 : y
⇒ 5/3 = 10/ (3× y)
⇒ 5/3 = 10/3y
Multiply by 3;
⇒ 5 = 10/y
⇒ y = 10/5
⇒ y = 2
And, 5 : 3 = z : 5
⇒ 5/3 = z/5
Multiply by 5;
⇒ 25/3 = z
⇒ z = 25/3
Therefore, The missing values in the ratio table will be;
Pies 5 20 10/3 25/3
Cakes 3 12 2 5
Learn more about the ratio visit:
https://brainly.com/question/277887
#SPJ5
You bought 3.5 pounds of turkey that costs $5.50 per pound. How much did you spend ?
Answers
Answer:
5.50 per pond
3.5 pound
3.5 × 5.50
$19.25
We need to multiply 5.50 and 3.5
5.50•3.5 = 19.25
Hope this helps!! :)
Using the binomial theorem , obtain the expansion of :
[tex](1+3x)^6+(1-3x)^6[/tex]
2. Using the binomial theorem , expand
[tex](1+2x)^5[/tex] , simplifying all the terms.
Answers
Answer:
see explanation
Step-by-step explanation:
Expand both factors and collect like term
Using Pascal' triangle with n = 6 to obtain the coefficients
1 6 15 20 15 6 1
Decreasing powers of 1 from [tex]1^{6}[/tex] to [tex]1^{0}[/tex]
Increasing powers of 3x from [tex](3x)^{0}[/tex] to [tex](3x)^{6}[/tex]
[tex]1+3x)^{6}[/tex]
= 1.[tex]1^{6}[/tex][tex](3x)^{0}[/tex] + 6.[tex]1^{5}[/tex][tex](3x)^{1}[/tex] + 15.[tex]1^{4}[/tex][tex](3x)^{2}[/tex] + 20.[tex]1^{3}[/tex][tex](3x)^{3}[/tex] + 15.1²[tex](3x)^{4}[/tex] + 6.[tex]1^{1}[/tex][tex](3x)^{5}[/tex] + 1.[tex]1^{0}[/tex][tex](3x)^{6}[/tex]
= 1 + 18x + 135x² + 540x³ + 1215[tex]x^{4}[/tex] + 1458[tex]x^{5}[/tex] + 729[tex]x^{6}[/tex]
--------------------------------------------------------------------------------------
[tex](1-3x)^{6}[/tex]
= 1.[tex]1^{6}[/tex][tex](-3x)^{0}[/tex] + 6.[tex]1^{5}[/tex][tex](-3x)^{1}[/tex] + 15.[tex]1^{4}[/tex][tex](-3x)^{2}[/tex] + 20.[tex]1^{3}[/tex][tex](-3x)^{3}[/tex] + 15.1²[tex](-3x)^{4}[/tex] + 6.[tex]1^{1}[/tex][tex](-3x)^{5}[/tex] + 1.[tex]1^{0}[/tex][tex](-3x)^{6}[/tex]
= 1 - 18x + 135x² - 540x³ + 1215[tex]x^{4}[/tex] - 1458[tex]x^{5}[/tex] + 729[tex]x^{6}[/tex]
----------------------------------------------------------------------------------
Collecting like terms from both expressions
[tex](1+3x)^{6}[/tex] + [tex](1-3x)^{6}[/tex]
= 2 + 270x² + 2430[tex]x^{4}[/tex] + 1458[tex]x^{6}[/tex]
----------------------------------------------------
(2)
Using Pascal's triangle with n = 5
1 5 10 10 5 1
Decreasing powers of 1 from [tex]1^{5}[/tex] to [tex]1^{0}[/tex]
Increasing powers of 2x from [tex](2x)^{0}[/tex] to [tex](2x)^{5}[/tex]
[tex](1+2x)^{5}[/tex]
= 1.[tex]1^{5}[/tex][tex](2x)^{0}[/tex] + 5.[tex]1^{4}[/tex][tex](2x)^{1}[/tex] + 10.[tex]1^{3}[/tex][tex](2x)^{2}[/tex] + 10.[tex]1^{2}[/tex][tex](2x)^{3}[/tex] + 5.[tex]1^{1}[/tex][tex](2x)^{4}[/tex]+ 1.[tex]1^{0}[/tex][tex](2x)^{5}[/tex]
= 1 + 10x + 40x² + 80x³ + 80[tex]x^{4}[/tex] + 32[tex]x^{5}[/tex]
NEEEEEEED HEEEEEEEELP !!!!!!!!!!!!!!!!! 13 POINTSSSSSS
Answers
the answer will be thirty three cm.
Find the area please. Round to the nearest tenth if necessary.
Answers
Answer:
235.6
Step-by-step explanation:
A=πr2
=π·52
=78.53982x3=235.61946
235.6
Can someone tell me a proportion to convert 5 pounds to ounces asap. pls someone reply quick
Answers
Answer:
5 pounds = 80 ounces
Hope it helps!!!
