1. Graphs of two trigonometric functions are shown below
(note: not certain if my answers are accurate)
Answers
Answer:
Part VI: [tex]\displaystyle y = sec\:x[/tex]
Part V: [tex]\displaystyle y = 3csc\:(2x + \frac{\pi}{2}) \\ y = 3sec\:2x[/tex]
Part III: In addition, although this is a secant graph, it can also be a cosecant graph when you apply the C-value of [tex]\displaystyle -\frac{\pi}{2}[/tex]to the equation.
Part II: [tex]\displaystyle \frac{\pi}{2}[/tex]
Part I: [tex]\displaystyle \pi[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = 3csc\:(2x + \frac{\pi}{2})} \\ y = Acsc\:(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]
OR
[tex]\displaystyle \boxed{y = 3sec\:2x} \\ \\ y = Asec\:(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]
Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS the secant graph, if you plan on writing your equation as a function of cosecant, 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 = 3csc\:2x,[/tex]in which you need to replase "secant" with "cosecant", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosecant 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 cosecant graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the secant graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2},[/tex]and with that, the cosecant graph of the secant graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3csc\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, we can move forward. To find the period, in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are at [tex]\displaystyle \frac{5}{6}\pi = x, \frac{\pi}{3} = x, -\frac{\pi}{6} = x, and\:-\frac{2}{3}\pi = x.[/tex]From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{\frac{\pi}{2}} = -\frac{\pi}{6} + \frac{2}{3}\pi.[/tex]So, the period of this function is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of the graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = 0.[/tex]
*So, double-check your first two answers because they are incorrect.
I am delighted to assist you at any time.
Related Questions
Answer this question to get marked as brainliest!!!!
Answers
Answer:
Diameter is the second option
Radius is the first option
Circumference is the third option
Area is the sixth option.
Step-by-step explanation:
Diameter is the distance between two circles from one end to another.
Radius is from the center to any part of the circle
To find cirumfrnce it’s diameter*π
To find area is πr^2 or in this case π*radius*radius
Determine the area of the following trapezoids.
(Hint): A = 1/2(b1 + b2)(h)
Answers
pls help
Sasha had to run 1/3 of a mile. She decided to walk, jog, and run the 1/3 mile, in equal parts. What fraction of the mile will she run?
9
3/3
3/9
1/9
Answers
Answer:
Fraction Sasha run = 1/9
Step-by-step explanation:
Given:
Sasha had run = 1/3 mile
Total part [Walk , jog , run] = 3 parts
Find:
Fraction Sasha run
Computation:
Fraction Sasha run = Total mile Sasha run x [1/3]
Fraction Sasha run = [1/3] x [1/3]
Fraction Sasha run = 1/9
which expression is equal to 24x^2-22x+5
Answers
Answer: (12x−5)(2x−1)
Step-by-step explanation: Hope this help :D
Answer:
24(x^2)-22x+5
=24(x^2)-(12+10)x+5
=24(x^2)-12x-10x+5
=12x(2x-1)-5(2x-1)
=(2x-1)(12x-5)
Fill in the missing number on the table, based on the graph?
Answers
Answer:
0.5
Step-by-step explanation:
sana panget kayong lahat
Find the product of (x+6)(x−4).
Answers
Step-by-step explanation:
(x+6)(x−4)
x²- 4x+6x - 24
x² + 2x - 24
Answer:
x²+2x-24
Step-by-step explanation:
see attachment below
2.Use the digits given below to make the largest possible number
without repetition off digits. .Then round off nearest ten, hundred and
thousand
a) 2, 5,4 , 3, 6, 7
b) 0 ,9, 8, 7 ,6, 4
Answers
Answer:
1)765432
Nearest ten: 765430
Nearest hundred: 765400
Nearest thousand: 765000
2) 987640
Nearest ten: 987640
Nearest hundred: 987600
Nearest thousand: 988000
Not sure if this is what you want.
square root of 110 - n
Answers
Answer:
√(110 - n)
Step-by-step explanation:
This can't be simplified. All we can do here is re-write "square root of 110 - n" symbolically, which comes out to √(110 - n). The parentheses are essential for clarity.
if y varies inversely as x, and y =35 when x =14, find x when y =15.
Answers
Answer:
[tex]x = 32 \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]y = \frac{k}{x} ,where \: k \: is \: a \: constant.[/tex]
Let's find the value of k first.
When y= 35, x= 14,
[tex]35 = \frac{k}{14} [/tex]
k= 14(35)
k= 490
Substitute the value of k into the equation:
[tex]y = \frac{490}{x} [/tex]
When y= 15,
[tex]15 = \frac{490}{x} [/tex]
15x= 490
x= 490 ÷15
[tex]x = 32 \frac{2}{3} [/tex]
LM is a common tangent. PL=10, QM=2, and LM=20. Find the measure of LN.
Answers
Answer:
25cm
Step-by-step explanation:
using similar triangles.
10/2 = (20+y)/y
where y is length of MN
10y = 40+2y
40= 8y
y= 5.
LN = LM + MN
= 20+5
25cm
Please help.
Is algebra.
Answers
The answer for question 4 is C and the answer for question 5 is D.
Resuelve usando el método de sustitución o el de eliminación. Para un juego de baloncesto se vendieron 1,850 boletos. Se recaudo un total de $ 8,800. Si los boletos de niños cuestan $ 4 y los de adultos cuestan $ 6. ¿Cuántos boletos de cada clase se vendieron?
Answers
Answer:
Se vendieron 700 boletos para adultos y 1,150 boletos para niños.
Step-by-step explanation:
Primero tenemos que definir dos variables:
x = número de boletos de niños vendidos
y = número de boletos de adultos vendidos.
Entonces podemos escribir la recaudación total como:
x*$4 + y*$6
Y sabemos que la recaudación total fue $8,800, entonces:
x*$4 + y*$6 = $8,800
También sabemos que se vendieron 1,850 boletos, entonces:
x + y = 1,850
Entonces tenemos el sistema de ecuaciones:
x*$4 + y*$6 = $8,800
x + y = 1,850
En este caso podemos utilizar el método de sustitución, para ello primero debemos aislar una de las variables en una de las ecuaciones.
Si aislamos x en la segunda ecuación tenemos:
x = 1,850 - y
Ahora podemos sustituir esto en la otra ecuación para obtener:
(1,850 - y)*$4 + y*$6 = $8,800
Ahora podemos resolver esto para y.
$7,400 - y*$4 + y*$6 = $8,800
y*$2 = $8,800 - $7,400 = $1,400
y = $1,400/$2 = 700
Entonces se vendieron 700 boletos para adultos.
Ahora podemos usar la ecuación x = 1,850 - y para obtener el valor de x.
x = 1,850 - y
x = 1,850 - 700 = 1,150
Se vendieron 1,150 boletos para niños.
Nancy, Bryan and Jamie combined their money to purchase a laptop. Together, they paid a total of 490 dollars for the laptop, including tax.
Nancy paid 50 dollars more than Bryan paid.
Bryan paid twice as much as Jamie paid. How much did Nancy paid
Answers
Answer:
226 dollars
Step-by-step explanation:
Bryan = 176
Jamie = 88
Nancy = 226
Since Nancy paid 50 dollars more than Bryan paid that is 226.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Nancy, Bryan and Jamie combined their money to purchase a laptop. Together, they paid a total of 490 dollars for the laptop, including tax.
The total = 490 dollars
Given that Nancy paid 50 dollars more than Bryan paid and Bryan paid twice as much as Jamie paid.
Bryan = 2 x Jamie
Nancy = 50 + Bryan
Let Jamie = J
J + 2J + 50 + 2J = 490
5J + 50 = 490
5J = 440
J = 88
Therefore, Bryan = 176
Jamie = 88
Nancy = 226
Hence, Since Nancy paid 50 dollars more than Bryan paid that is 226.
Learn more about the unitary method;
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PLEASE HELP!!! I WILL RATE YOU BRAINLIEST
The first laptop ever was sold was the Osborne 1. It came onto the market in 1981, and it had a mass of 11 kg. Suppose that since 1981 the mass of laptops has decreased at an average rate of 4.7% per year. What was the approximate weight of a laptop in 2019?
a. 6.43 kg
b. 8.10 kg
c. 4.62 kg
d. 1.76 kg
Answers
Answer: (d)- 1.76 kg
Step-by-step explanation:
Given
The first laptop mass was 11 kg
The rate of mass decreases by 4.7% per year
In 1982, it was
[tex]\Rightarrow 11-11\times 4.7\%=11-11\times 0.047\\\Rightarrow 11(1-0.047)\ kg[/tex]
In 1983, it was
[tex]\Rightarrow 11(1-0.047)-11(1-0.047)\times 0.047=11(1-0.047)^2[/tex]
In 2019 i.e. after 38 years, it is
[tex]\Rightarrow 11(1-0.047)^38=11\times 0.953^{38}=1.76\ kg[/tex]
Jenny bought scrapbooking supplies for $70.75. She paid $5.66 in sales tax. What was the sales tax rate on the supplies? If necessary, round your answer to the nearest tenth.
Answers
Answer:
8%
Step-by-step explanation:
solve the equation b - 7 - 6 = 15 + 5b
Answers
Answer:
b = -7
Step-by-step explanation:
b - 7 - 6 = 15 + 5b
b - 13 = 15 + 5b
4b = -28
b = -7
Urgent please help..
Answers
Answer:
30cm
Step-by-step explanation:
The perimeter of the triangle is the sum of all of its sides
Since the triangle is an isosceles triangle, then AC = BC
Since AC = 3cm + 9cm = 12cm, then;
AC = BC = 12cm
For AB;
AB = 3cm + 3cm
AB = 6cm
Perimeter of the polygon = AC+BC + AB
Perimeter of the polygon = 12cm + 12cm + 6cm
Perimeter of the polygon =30cm
Find the perimeter and area of the shape.
Answers
Answer:
The perimeter is 41
Step-by-step explanation:
The perimeter of a shape is just the sum of all its sides added up. In this case, that would mean the perimeter is:
12 + 9 + 9 + 4.6 + 6.4 = P30 + 11 = P41 = PHope this helps!
I really need help Please and thank you
Answers
la B s la correcta por que es el que esta mas serca :)
The sides of a right triangle are used to construct three squares, as shown below. The number of square units, representing area, is shown in two of the squares. A represents the area of the largest square.
Answers
1. We know that the distance formula will be be d=√((x_2-x_1)²+(y_2-y_1)²), then we can do x2-x1=3. Y2-Y1=5. 3x3+5x5=34, the square root of 34 is around 5.83. The answer is F.
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The solution is Option D.
The area of the square with the side having the hypotenuse of the triangle as the side is 34 units²
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the area of the square A be = S
Let the triangle be represented as ΔABC
The base of the triangle BC = 5 units
The height of the triangle AB = 3 units
So , the hypotenuse of the triangle AC = Side of the square A
And , from the Pythagoras theorem
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
AC² = 5² + 3²
AC² = 25 + 9
AC² = 34 units²
AC² = Area of the square A with side AC
Therefore , the value of S is 34 units²
Hence , The area of the square with the side having the hypotenuse of the triangle as the side is 34 units²
To learn more about triangles click :
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hi! please help with question b! thank you
Answers
Answer: here is the anwser
Step-by-step explanation:
BRAINLIEST plz
hello please help i’ll give brainliest
Answers
Answer:
-8/6 is equivalent to the -8.(1/6).
Step-by-step explanation:
third an forth options are correct
[tex] - \frac{1}{6} \times 8[/tex]
[tex] - \frac{8}{6} [/tex]
Which best describes the relationship between the line that passes through (4,4) and (7,6) and the line that passes through (-3,-6) and (0,-4)
Answers
Answer: I think it's cause there both the same length from each one and there both diagonal
Step-by-step explanation:
HELP PLEASE ILL GIVE BRAINLIEST
Answers
Answer:
y=3x+3
Step-by-step explanation:
First find put the intersect point at the end then find slope.
easy
2) Zaria rolls a dice and flips a coin. What is the
probability that she will get a number greater
than 3 and heads?
Answers
Step-by-step explanation:
probability of dice
3/6 or 1/2
probability of coin
1/2
What is the best way to pay attention in school ???? Also what is the opposite of the opposite of 18
Answers
Answer:
No idea what the opposite of 18 is but the best way to pay attention in school is to not get distracted easily by anything like literally get everything that will distract you put aside get it far away from you otherwise you're not going to pay attention and I'm going to get distracted
What is a linear function in the form y=mx+b for the line passing through (2, -4) with y-intercept 2?
Answers
Answer:
A linear function in the form y = m·x + b for the line passing through the point (2, -4) with y-intercept 2 is;
y = -3·x + 2
Step-by-step explanation:
From the question, it is required to find the a linear equation passing through the point (2, - 4) with a y-intercept 2 in the form y = m·x + c
Given that the y-intercept is the point at which the line cuts the y-axis, we have, x = 0
Therefore, we have the point on the line representing the y-intercept is (0, 2)
Therefore, the slope of the graph is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore, we have;
[tex]Slope, \, m =\dfrac{2-(-4)}{0-2} = \dfrac{6}{-2} = -3[/tex]
The equation of the graph in point and slope is given as follows;
y - 2 = -3 × (x - 0) = -3 × x
Therefore, the equation of the line in the form y = m·x + c is given as follows;
y - 2 + 2 = -3 × x + 2
∴ y = -3·x + 2
The equation of the line in the form y = m·x + c is y = -3·x + 2.
pls help me with this math
Answers
Answer: C
Step-by-step explanation:
1. the area of a circle is 132.7 square inches. find the radius. round to the nearest tenth
2. in terms of pi, find the area of a 120 degree sector in a circle with a 6m radius
Answers
Answer:
no ):(
Step-by-step explanation:
Answer:
1. r ≈ 6.5in
2. 132
Step-by-step explanation:
1. A=πr2
Solving for r
r=A
π=132.7
π≈6.49921 in
2. = 120°/ 360° x 22/7 x 6²
= 1/3 x 22/7 x 6 x 6
= 22 x 6 x 6 / 7 x 3
= 22 x 6
= 462
take the difference of 7x² + 9 and 2x² -2x from the sum of 5x² + 4x + 7 and 2 - x.
Answers
Answer:
bro i am not smart enough for this