The parent cosine function is transformed [tex]y=3cos(10(x-\pi ))[/tex] by vertically stretching it by a factor of 3 (amplitude), horizontally compressing it by a factor of 10 (frequency), and shifting it to the right by [tex]\pi[/tex] units (horizontal shift or phase shift).
The question asks which transformations are required to alter the parent cosine function to [tex]y=3cos(10(x-\pi ))[/tex]. The transformations involved in this equation are:
Amplitude modification: The coefficient '3' indicates that the amplitude of the cosine function is scaled by a factor of 3.Frequency adjustment: The factor '10' inside the cosine function affects the function's frequency, indicating the function has 10 complete cycles within the interval of [tex]2\pi[/tex] radians. This is a horizontal scaling transformation.Horizontal shift (or phase shift): The subtraction of [tex]\pi[/tex] within the argument of the cosine function translates the function [tex]\pi[/tex] units to the right along the x-axis.No vertical shift is present because there is no addition or subtraction outside the cosine function.
To transform the parent cosine function [tex]\(y = \cos(x)\) to \(y = 3 \cos(10(x-\pi))\)[/tex], apply a vertical stretch by 3, horizontal compression by 1/10, and a right shift by [tex]\(\pi\)[/tex] units.
To transform the parent cosine function[tex]\(y = \cos(x)\)[/tex] to the function [tex]\(y = 3 \cos(10(x-\pi))\)[/tex], we need to apply the following transformations:
1. Amplitude change: Multiply the function by [tex]\(3\)[/tex], which increases the amplitude.
2. Horizontal compression: Multiply the input of the cosine function by [tex]\(10\),[/tex]which compresses the graph horizontally.
3. Phase shift: Shift the graph to the right by [tex]\(\pi\)[/tex]units, indicated by the term [tex]\(x - \pi\).[/tex]
So, the transformations needed are:
- Amplitude change: Vertical stretch by a factor of [tex]\(3\).[/tex]
- Horizontal compression: Compression by a factor of [tex]\(1/10\).[/tex]
- Phase shift: Right shift by [tex]\(\pi\)[/tex] units.
Which step should be used to prove that point a is equidistant from points c and b? (1 point)?
How long will it take for $2800 to grow to $24,900 at an interest rate of 5.6% if the interest is compounded continuously? round the number of years to the nearest hundredth?
Find the quotient and remainder using long division. x6 + 4x4 + 4x2 + 16 x2 + 4
If HE = 3p + 7, /, LP = 5p – 19, and /, find the values of p and q for which quadrilateral HELP is a parallelogram. A. p = 18, q = 13 B. p = 13, q = 8 C. p = 8, q = 18 D. p = 13, q = 1
Which quadrilateral HELP is a parallelogram? The corrsect answer is P=13, q=18
THE TOTAL COST OF A SUIT AND 4 TIES IS $292. THE SUIT COST $200. eACH TIE COST THE SAME AMOUNT. fIND THE COST OF ONE TIE
What are the names of the eight line section and the six line section that combine to form the 14 lines of a petrarchan sonnet?
The answer is an octave and a sestet. A sestet is the title specified to the second split of an Italian sonnet (as contrasting to an English or Spenserian sonnet), which must contain of an octave, of eight lines and must be followed by a sestet, of six lines. The first recognized user of this poetical type was the Italian poet named Petrarch.
Functions f(x) and g(x) are shown below:
f(x) = -4(x - 6)^2 + 3
g(x) = 2 • cos(2 • x - pi) + 4
Using COMPLETE SENTENCES, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
suppose the correlation coefficient between the number of the college students in a city and the number of city buses is 0.89. which statement must be true?
Answer:
Step-by-step explanation:
Given that the correlation coefficient between the number of college students in a city and the number of city buses is 0.89.
We find that correlation coefficient is a measure of linear association between two variables.
When the absolute value of correlation coefficient is near 1, there is strong correlation. If correlation has a positive sign, there is a posiitive association between the two variables.
Here the correlation coefficient is positive and also near 1. Thus there is a strong linear correlation between the two variables.
Or whenever there is an increase in one variable there will be an increase in other variable also.
Debra travels a distance of 2 miles in 1 minute. how much distance can she cover in 25 minutes? choose the correct equivalent rate.
Debra traveled 50 miles in 25 minutes at a rate of 2 miles per minute.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Debra travels a distance of 2 miles in 1 minute.
Which is already in unit measure, therefore to determine the distance traveled by Debra in 25 minutes we'll multiply the distance traveled in 1 minute and the total time Debra traveled.
= (2×25) miles.
= 50 miles.
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Helpppppppppppppppppp
Write the equation of the function whose graph is shown.
Answer:
[tex]y=1(x-5)^2 + 3[/tex]
Step-by-step explanation:
Given : from the graph vertex is (5,3)
Also graph passes through point (8,12)
We use vertex form of quadratic equation
General vertex form is
[tex]y=a(x-h)^2 + k[/tex]
vertex is (5,3)
h= 5 and k =3
So equation becomes [tex]y=a(x-5)^2 + 3[/tex]
Now we need to find out 'a'
We use (8,12) to find out 'a'
Plug in x=8 and y = 12
[tex]12=a(8-5)^2 + 3[/tex]
[tex]12=a(3)^2 + 3[/tex]
12= 9a + 3
subtract 3 on both sides
9 = 9a
divide both sides by 9
so a=1
Final equation is
[tex]y=1(x-5)^2 + 3[/tex]
An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]
Given the following data:
Points on the x and y-axis = (8, 12).Vertex (h, k)= (5, 3).How to write a function.The vertex form of a quadratic equation can be used to write an equation of the function of a graph.
Mathematically, the vertex form of a quadratic equation is given by this formula:
[tex]y=a(x-h)^2 + k[/tex]
Substituting the given parameters into the formula, we have;
[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]
a = 1.
For the equation:
[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]
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Joe walked of a mile in of an hour. what is his unit rate in miles per hour? (1 point) = mile per hour = miles per hour = miles per hour = mile per hour
Jasmine is 23 years old. jasmine is 3 years less than half of george's age. write and solve an equation to find george's age.
take 23 and multiply by 3 then divide by 2 and your answer should be x34
terrell wants to drive his car at a speed of 50 miles per hour for 2.75 hours. his car has a fuel efficiency of 25 miles per gallon. How many gallons of fuel does terrell need for his journey
I need this asap! Please help me!! Brainliest answer! The line plot below represents the frequency distribution of the number of book reports done by students in grades nine and ten. Each x represents 3 students. How many students did less than 4 or more than 17 reports?
Find the number of hours it would take to drive 510 miles at 55 mph. Round to the nearest tenth of an hour. i THINK ITS 9.3 BUT IM NOT SURE?
Answer: It would take 9.3 hours to take 510 miles.
Step-by-step explanation: We are given to find the number of hours it would take to drive 510 miles at 55 mph.
We will be using the UNITARY method to solve the given problem.
According to the given information, we have
Number of hours taken to drive 55 miles = 1 hour.
So, number of hours taken to drive 1 mile will be
[tex]\dfrac{1}{55}~\textup{hour}.[/tex]
Therefore, the number of hours it would take to drive 510 miles is given by
[tex]\dfrac{1}{55}\times510=\dfrac{102}{11}=9.27~\textup{hour}.[/tex]
Rounding to nearest tenth of an hour, we get
9.27 hour ≈ 9.3 hour.
Thus, it would take 9.3 hours to take 510 miles.
Explain the difference between exponential growth and exponential decay
Final answer:
Exponential growth occurs when a population increases at an increasing rate, whereas exponential decay involves a decrease at a rate proportional to the current size. Logistic growth, adding the concept of carrying capacity, more accurately reflects natural populations with initial exponential increase followed by a plateau as resources become limited.
Explanation:
The key difference between exponential growth and exponential decay lies in the direction and rate at which a quantity changes over time. Exponential growth occurs when a population grows at an increasing rate as time passes, often depicted as a J-shaped curve, whereas exponential decay describes a process of decrease at a rate proportional to the current value, leading to a rapid reduction in size or quantity over time.
In the context of biology and population growth, exponential growth describes how populations can grow dramatically when there are no limits to resources or space. This type of growth can be formalized as a mathematical model where the population after n time periods has increased by a factor of 2n when the base growth rate is 2. In natural populations, this is idealized and does not usually last long as resources become depleted and other limiting factors come into play. On the other hand, exponential decay in biology might refer to the rapid loss of a population due to harsh conditions, lack of resources, or other negative impacts.
Find y to the nearest tenth.
2.7
2.9
7.5
y = 8 x cos(20)
y = 7.517
y = 7.5
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer: smh
Step-by-step explanation:
How does the radius of a positive and negative ion compare to a neutral atom?
A neutral atom contains equal amount of proton and electron.
A negative ion contains extra electrons hence there is additional outer shell so it is expected that the radius is bigger than that of a neutral atom.
While a positive ion contains less electron so there is less outer shell so the radius is smaller than that of a neutral atom.
Arranging the radius in increasing order:
positive ion, neutral atom, negative ion
Can you help me solve #s 43 an 44 pleeeease
The initial balance of a mutual fund is $1800. The fund is expected to grow in value at an annual rate of 5%.
Let x represent the number of years since the fund was started. Let y represent the value of the fund x years later.
What equation models the value of the mutual fund x years after it was started?
This graph of a function is a translation of y = 2/x . What is an equation for the function?
A. y = 2/(x - 6) – 3
B. y = 2/(x – 6) + 3
C. y = 2/(x – 3) - 6
D: y = 2/(x – 3) + 6
Answer: The answer is C, the rest of the answers are
1:B
2:C
3:A its a graph
4:C y=2/x-3 -6
5:D19, as of 2019
Step-by-step explanation:
Answer:
The correct option is C) [tex]y=\frac{2}{x-3}-6[/tex]
Step-by-step explanation:
Consider the provided information.
Transformation:
The graph of parent function f(x) move up b unit for f(x)+b.
The graph of parent function f(x) move down b unit for f(x)-b.
The graph of parent function f(x) move left b unit for f(x+b).
The graph of parent function f(x) move right b unit for f(x-b).
Since, the graph of the parent function moves down, Therefore Option Option B and D are incorrect.
Here, we can observe that vertical asymptote shifted from x = 0 to x = 3.
Horizontal Shift: Right 3 Units
Vertical Shift: Down 6 Units
Therefore, the correct option is C) [tex]y=\frac{2}{x-3}-6[/tex]
South of the White House in Washington, D.C., is the President’s Park South, or the Ellipse, which hosts events such as the White House Garden Tours. The Ellipse is 880 ft from north to south and 1057 ft from east to west. Write an equation in standard form for the Ellipse, centered at the origin.
Note: If any values of a2 or b2 are greater than 1,000, include the comma.
Given the dimensions of the Ellipse, the major axis is the east-west distance (1057 ft) and the minor axis is the north-south distance (880 ft). Taking half these lengths as 'a' and 'b' respectively, the equation of the ellipse in standard form centered at the origin is (x^2/(528.5^2)) + (y^2/(440^2)) = 1.
Explanation:The given dimensions of the Ellipse represent the lengths of the major and minor axes. In an ellipse centered at the origin, the equation in standard form is given by:
(x^2/a^2) + (y^2/b^2) = 1
where 'a' is half the length of the major axis and 'b' is half the length of the minor axis. Here, since the measurement from east to west (1057 ft) is greater than the measurement from north to south (880 ft), 'a' will have a value of 1057/2 and 'b' will have a value of 880/2. Consequently, the ellipse equation would be:
(x^2/(528.5^2)) + (y^2/(440^2)) = 1
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in what quadrant does the angle 11 pi / 4 terminate?
Which list contains ONLY rational numbers?
Answer:
B. [tex]0.4166\overline{6}[/tex], [tex]\sqrt{81}[/tex], [tex]\frac{1}{8}[/tex].
Step-by-step explanation:
We are asked to find the list that contains only rational numbers.
We know that a number is known as rational, when it can be expressed as a fraction.
Upon looking at our given choices, we can see that option B is the correct choice.
In [tex]0.4166\overline{6}[/tex], the digit 6 has a bar on it, this means that it is repeating. We know that a repeating decimal is a rational number.
[tex]\sqrt{81}=9[/tex]. We can represent 9 as a fraction: [tex]\frac{9}{1}[/tex].
[tex]\frac{1}{8}[/tex] is already written as a fraction, therefore, it is a rational number.
In the diagram below XY is the perpendicular bisector of JK. Which of the following statements must be true?
Answer:
Step-by-step explanation:
A B D F
Use two or three unit fractions to convert. 1515 daysdaysequals=_______ secondsseconds
It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the unit fractions to convert 15 days into seconds.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 x 60 = 86400 seconds
There are 86400 seconds in one day.
Then 15 days = 15 x 86400 = 1,296,000
Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
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The width of a rectangle is 2m less than the length. the area is 48m squared. find the dimensions
The length of the rectangle is 8m and the width is 6m
This question involves the area of a rectangle and we can use the formula to solve this problem.
Data given;
A = 48m^2w = (L - 2)mAreaThe area of a rectangle is given as
[tex]A = L * W[/tex]
l = lengthw = widthsubstitute the values and solve
[tex]A = lw\\48 = L * ( L - 2)\\48 = l^2 -2l\\l^2 -2l - 48 = 0[/tex]
solve this quadratic equation to find the length
a = 1, b = -2, c = -48
[tex]l = \frac{-b+-\sqrt{b^2 - 4ac} }{2a} \\l = \frac{-(-2)+-\sqrt{(-2)^2-4*1*(-48)} }{2*1} \\l = 8[/tex]
Taking only the positive value of l, l = 8
but we also know that
[tex]w = l -2\\w = 8 -2\\w= 6[/tex]
from the above, the length of the rectangle is 8m and the width is 6m
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please help and explain to me!