Consider the function y = -2cos + a) What is the amplitude? b) What is the period? c) Describe the phase shift. d) Describe the vertical translation. e) Graph the function. Compare the graph to the given parameters.
Answers
a) Amplitude: 2
b) Period: 2π
c) Phase Shift: 0
d) Vertical Translation: None
e) Graph: y = -2cos(x)
Function: y = -2cos(x)
a) Amplitude:
The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. In this case, the coefficient is -2. Therefore, the amplitude is 2.
b) Period:
The period of a cosine function is given by 2π divided by the coefficient of the x term. In this case, there is no coefficient of the x term, which implies that the period is the default period of a cosine function, which is 2π.
c) Phase Shift:
The phase shift determines the horizontal shift of the graph. In this case, there is no additional horizontal shift, so the phase shift is 0.
d) Vertical Translation:
The vertical translation determines the vertical shift of the graph. In this case, there is no additional vertical translation, so the function remains centered on the x-axis.
e) Graph:
The graph of the function y = -2cos(x) is a cosine function with an amplitude of 2, a period of 2π, no phase shift, and no vertical translation. It oscillates above and below the x-axis symmetrically.
The graph is given below.
The graph oscillates between the maximum value of 2 and the minimum value of -2, with each complete cycle covering a distance of 2π. It is symmetric with respect to the x-axis, showing the characteristics of a cosine function with the given parameters.
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Related Questions
State the image of the point (3,7) after a reflection in the y-axis:(Blank 1:Blank 2:
Answers
In order to reflect a point over the y-axis, we just need to change the signal of its x-coordinate.
So for the point (3, 7), the reflection over the y-axis would be (-3, 7).
Therefore we have:
Blank 1: -3
Blank 2: 7
Help me with this please
Answers
Answer:
a -30
b - 40
c - 40
d - 40
e - 110
f - 110
g - 30
h - 140
i - 70
j - 70
I believe all of these are right. Sorry if they are not. I hope this helps!
5. ( 30pts) Using the master theorem, find Θ-class of the following recurrence relatoins a) T(n)=2T(n/2)+n
3
b) T(n)=2T(n/2)+3n−2 c) T(n)=4T(n/2)+nlgn
Answers
Using the master theorem, the Θ-class are: a) T(n) = Θ(n)b) T(n) = Θ(n) and c) T(n) = Θ(√n log n).
a) T(n)=2T(n/2)+n³
To find the Θ class of T(n), we need to apply the Master Theorem. In the Master Theorem, if T(n) = aT(n/b) + f(n) where a >= 1, b > 1, and f(n) is an asymptotically positive function, then:
T(n) = Θ(nᵈ)
where d = logₐ(b).
Here a = 2, b = 2 and f(n) = n³.
So, d = log₂(2)
= 1T(n)
= Θ(nᵈ)
= Θ(n¹)
= Θ(n)
Therefore, the Θ class of T(n) is Θ(n).
b) T(n)=2T(n/2)+3n−2
Similarly to part (a), we can find the Θ class of T(n) by using the Master Theorem.
In this case, a = 2, b = 2 and f(n) = 3n - 2.
Here, d = log₂(2)
= 1T(n)
= Θ(nᵈ)
= Θ(n¹)
= Θ(n)
Therefore, the Θ class of T(n) is Θ(n).
c) T(n)=4T(n/2)+nlogn
For this recurrence relation, a = 4, b = 2 and f(n) = nlogn.
In this case, d = log₄(2) = 0.5.
So,
T(n) is
= Θ(nᵈ)
= Θ(n⁰.⁵)
= Θ(√n log n)
Therefore, the Θ class of T(n) is Θ(√n log n).
Hence, the correct options are:a) T(n) = Θ(n)b) T(n) = Θ(n)c) T(n) = Θ(√n log n).
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Huey can wash 6 cars or mow 3 lawns in one hour. Dewey can wash 3 cars or mow 3 lawns in one hour. Louie can wash 3 cars or mow 6 lawns in one hour. They each work 8 hours per day. If two of them wash cars and one mows lawns then at most they can wash cars and mow lawns. Enter whole numbers.
Answers
At most, they can wash 96 cars and mow 96 lawns.
To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.
Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.
Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.
Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.
Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.
The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.
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HELP (0,-3) and (5,-5) what is the slope
Answers
Answer:
-2/5
Step-by-step explanation:
To find the slope, we use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -5 - -3)/( 5 - 0)
= ( -5+3)/( 5-0)
= -2/5
Hi! I can help you with joy! :)
Use the slope formula:\(\displaystyle\frac{y2-y1}{x2-x1}\)Wherey2 is the y-coordinate of the second point (in this case, it's equal to -5)y1 is the y-coordinate of the first point (in this case, it's equal to -3)x2 is the x-coordinate of the 2nd point (in this case, x2=5)x1 is the x-coordinate of the 1st point (in this case, x1=0)Plug in the values:\(\displaystyle\frac{-5-(-3)}{5-0} \\\frac{-5+3}{5}\)\(\displaystyle\frac{-2}{5}\)\(\displaystyle-\frac{2}{5}\)Answer:
\(\huge\boxed{\bold{Slope=\displaystyle-\frac{2}{5} }}\)
Hope it helps!
~Nature~
Rewrite the equation by completing the square.
x^2 – 8x + 7 = 0
Answers
Answer: (x+ -4)^2=9
Step-by-step explanation: We compete the square by taking had of the coefficient of our x term is -8, half of it would be -4, and squaring it gives us 16 then simplify
The solution to the quadratic equation is x = 7 or x = 1 and the equation is given as ( x - 7 ) ( x - 1 ) = 0
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - 8x + 7 = 0 be equation (1)
On simplifying the equation , we get
x² - x - 7x + 7 = 0
Taking the common factors in the equation , we get
x ( x - 1 ) - 7 ( x - 1 ) = 0
Now , on factorizing the equation , we get
( x - 7 ) ( x - 1 ) = 0
So , when ( x - 7 ) = 0
Adding 7 on both sides of the equation , we get
x = 7
And , when ( x - 1 ) = 0
Adding 1 on both sides of the equation , we get
x = 1
So , the two solutions to the equation is x = 7 or x = 1
Hence , the equation is ( x - 7 ) ( x - 1 ) = 0
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What is the greatest common factor of 12 and 18? *
1. 6
2. 3
3. 2
4. 9
Answers
Guess a number from 1-10 for 100 points!
Answers
Ashley owns a food truck that sells tacos and burritos. She sells each taco for $3 and
each burrito for $5.25. Ashley must sell at least $340 worth of tacos and burritos each
h day. Write an inequality that could represent the possible values for the number of
tacos sold, t, and the number of burritos sold, b, that would satisfy the constraint.
Answers
Answer:
3t + 5.25b ≥ 340
Step-by-step explanation:
Find the value of the expression below when a = 9 , b = - 2 and c = - 7 . (c - a)/b - |b + c|
Answers
Answer:
-1
Step-by-step explanation:
Which of the following is equivalent to 3^4 ?1281764
Answers
Here we must calculate the power from 3 to 4.
Solving:
\(\begin{gathered} 3^4 \\ 3*3*3*3 \\ 9*9 \\ 81 \end{gathered}\)The answer would be 81
The following table shows the number of alligators in each body of water near Tom's house. Number of alligators 7,0,11,10 find the mean number of alligators.
Answers
Answer:
Mean number of alligators = 7
Step-by-step explanation:
Given that:
Number of alligators
7, 0, 11, 10
Sum of quantities = 7 + 0 + 11 + 10
Sum of quantities = 28
Number of quantities = 4
We can find the average by dividing the sum of quantities by number of quantities.
Mean = \(\frac{28}{4}\)
Mean = 7
Hence,
Mean number of alligators = 7
Answer:
7
Step-by-step explanation:
So there were four different places and four different amounts of alligators.
The numbers are 7, 0, 11, 10.
When you add 7, 0, 11, 10, you get the number, you get 28.
You then divide 28 by 4, because there are four different numebrs on the chart. 7(1), 0(2), 11(3), 10(4).
After you divide this, the mean would be 7 because 28/4 = 7. (28/4 means 28 divided by 7)
Can anyone help me? TwT TwT
Answers
Answer:
2:1
Step-by-step explanation:
An anyone,
4/6 : 1/3
We are asked to write this as a unit rate hence:
4/6 ÷ 1/3
4/6 × 3/1
= 2/1
= 2:1
Therefore, 4/6 : 1/3 as a unite rate is 2:1
An object is dropped from a small plane flying at 5819ft. Assume that a(t)=−22ft per second per second and v(0)= 0 , where a(t) and v(t) represent the acceleration and velocity of the object. Find s(t), which gives the distance from the starting point of the object. How long will it take the object to hit the ground?
Answers
The formula to find the distance covered by the object when it falls down is given by:S(t) = −16t^2
The formula for the velocity of an object is given by:v(t) = -32t
The formula for the acceleration of an object is given by:a(t) = -32
Given that,a(t) = -22ft/s^2 And, v(0) = 0
To find:
S(t) gives the distance from the starting point of the object. And how long it will take the object to hit the ground.Solution:The acceleration of the object is given by:
a(t) = -22ft/s^2
The initial velocity of the object is given by:v(0) = 0
The formula for the distance travelled by the object is given by:
S(t) = ut + 1/2 at^2
Putting the given values in the above formula, we get:
S(t) = 0t - 1/2 * 22t^2= -11t^2
When the object will hit the ground, the distance travelled by it will be equal to the height from where the object is dropped.
Given that the object is dropped from a small plane flying at 5819ft
Hence,5819 = -11t^2⇒ t^2 = 529⇒ t = 23 sec
Therefore, it will take the object 23 seconds to hit the ground.
Therefore, we can say that the distance travelled by the object when it falls down is S(t) = -11t^2. And the time taken by the object to hit the ground is 23 seconds.
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Determine whether the given sequence could be geometric, arithmetic, or neither. If possible, identify either the common ratio or the common difference.
9, 13, 17, 21,....
Answers
suppose that two boys named davis, three boys named jones, and four boys named smith are seated at random in a row containing nine seats. what is the probability that the davis boys will occupy the first two seats in the row, the jones boys will occupy the next three seats, and the smith boys will occupy the last four seats?
Answers
The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).
There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.
Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)
= \(\frac{2!3!4!}{9!}\)
= 0.0007937
= 7.937×\(10^{-4}\)
Hence, the probability is 7.937×\(10^{-4}\).
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as part of a statistics project, a teacher brings a bag of marbles containing 700 white marbles and 400 red marbles. she tells the students the bag contains 1100 total marbles, and asks her students to determine how many red marbles are in the bag without counting them.
Answers
By using the concept of probability, it can be determined that there are approximately 400 red marbles in the bag.
To determine the number of red marbles in the bag without counting them, we can utilize the concept of probability. The probability of drawing a red marble from the bag can be calculated by dividing the number of red marbles by the total number of marbles in the bag. In this case, there are 400 red marbles and 1100 total marbles, resulting in a probability of 400/1100.
Since the probability is a ratio, we can use it to estimate the number of red marbles in the bag. Multiplying the probability by the total number of marbles in the bag gives us an estimate of the number of red marbles. Therefore, by multiplying (400/1100) by 1100, we find that there are approximately 400 red marbles in the bag.
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3. The number of goals by Jaromir Jagar in each of his 19 NHL seasons is recorded below 27,32,34,32,32,62,47,35,44,42,52,31,36,31,54,30,25,19,16 a) Construct a steam-and-leaf plot to display the data.[2] b) Determine the percent of seasons where greater than 35 goals were scored.[2]
Answers
a) To construct a stem-and-leaf plot for the given data, we separate each number into its stem (tens digit) and leaf (units digit). The plot would look as follows:
Stems:
1 | 9
2 | 5 5 6 7
3 | 0 1 1 1 2 2 4 5 6
4 | 2 2 2 4
5 | 2 4
6 | 2
The plot shows the frequency distribution of goals scored by Jagr in each season.
b) To determine the percentage of seasons where greater than 35 goals were scored, we count the number of seasons where the goal count exceeds 35, which is 14 out of the total 19 seasons. Therefore, the percentage is (14/19) * 100 ≈ 73.68%.
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Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.
S:{−5}
S:{3}
S:{12}
S:{42}
Answers
The solution of the inequality 3(n - 6) > 2(n + 12) will be less than 42. Then the correct option is D.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
3(n - 6) < 2(n + 12)
Simplify the inequality, then we have
3(n - 6) < 2(n + 12)
3n - 18 < 2n + 24
3n - 2n < 24 + 18
n < 42
The solution of the inequality 3(n - 6) > 2(n + 12) will be less than 42. Then the correct option is D.
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Find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.
Perimeter:
Área:
Answers
The area and Perimeter of (ΔABC) are respectively; 17.5 square units and 24.16 units
What is the area and Perimeter of the Triangle?
The formula for the area of a triangle ABC with 3 coordinates is;
Area (ΔABC) = (¹/₂) |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
The coordinates are;
(x₁, y₁) = (-6, 6)
(x₂, y₂) = (2, 3)
(x₃, y₃) = (-3, -2)
Thus;
Area (ΔABC) = (¹/₂) |-6(3 − (-2)) + 2(-2 − 6) + -3(3 − 6)|
Area (ΔABC) = (¹/₂)|-30 - 16 + 9|
Area (ΔABC) = ¹/₂ * |-35|
We are taking absolute value and so;
Area (ΔABC) = ¹/₂ * 35
Area (ΔABC) = 17.5 square units
To get the perimeter, we will use distance formula between two coordinates and we have;
AB = 8.544
BC = 7.071
AC = 8.544
Thus;
Perimeter = 2(8.544) + 7.071
Perimeter = 24.16 units
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there are digits 1,2,3,4. if they can be repeated, how many different 3 digit numbers can they form?
Answers
From the counting principal, the possible formed distinct 3 digit numbers from the digits 1,2,3,4 with repititions is equals to the 64 ways.
W have a total number of digits = 4 = {1,2,3,4}
We have to form three digit number with repetition.
The unit’s place can be filled by any of the four digits. Since, the repetition of the digits is allowed, thus, the remaining two places that are ten’s and hundred’s places can also be filled by any of the four digits. So, the number of ways in which the three-digit numbers can be formed from these digits can be calculated by multiplication principle which states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the order is m×n. Since, each place have 4 ways to obtain any of digit.
The total number of ways to form three digit numbers with repetition is = 4³ = 64
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B) Arturo compró un automóvil usado y pago $2.500.000. Si este automóvil se devalúa (baja su precio) en un 20% anual. ¿Cuánto se devalúa el primer año el precio del automóvil?
Answers
Answer:
$500.000
Step-by-step explanation:
Lo que debemos hacer es calcular el porcentaje de devaluación del precio total del automóvil, es decir calcular el 20% de $2.500.000, y eso lo podemos hacer de la siguiente manera:
2500000*0.2 = 500000
Lo que quiere decir que el primer año el automóvil de devaluó en $500.000
a ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, find the total distance traveled by the ball.
Answers
A ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, the total distance traveled by the ball is approximately 11.926 feet.
How do we calculate the total distance?We have to calculate the distance traveled by the ball with the help of the given data, as shown below;The first height of the ball is 6 feet. Distance traveled by the ball at the first instance = 6 feet.The ball rebounds to one-third of its previous height, and the ball goes to a height of:6/3 = 2 feet.
Distance traveled by the ball after the first bounce = 6 + 2 + 2 = 10 feet.The ball rebounds again to one-third of its previous height, and the ball goes to a height of:2/3 = 0.6667 feet. Distance traveled by the ball after the second bounce = 10 + 0.6667 + 0.6667 = 11.3334 feet.
The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.6667/3 = 0.2222 feet. Distance traveled by the ball after the third bounce = 11.3334 + 0.2222 + 0.2222 = 11.7778 feet. The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.2222/3 = 0.0741 feet.
Distance traveled by the ball after the fourth bounce = 11.7778 + 0.0741 + 0.0741 = 11.926 feet. Therefore, the total distance traveled by the ball is approximately 11.926 feet.
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The more time that I spend reading, the more pages I have read. Which variable is independent?
Answers
Answer:
The more time i spend reading
Step-by-step explanation:
The variable which causes a change to the variable which we intend to measure in an experiment is the independent variable, Hence, the independent variable is the amount of time spent reading.
The Independent variable in an experiment is also called the explanatory variable, which is used to tweak the value obtained for the dependent or measured variable.
In the scenario described, the measured variable is the number of book pages read which is determined by the number of time spent reading (independent variable.)
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assume a fixed cost for a process of $1,000. the variable cost to produce each unit of product is $12 and the selling price for the finished product is $20. which of the following is the number of units that has to be produced and sold to break-even? 75 units 90 units 120 units 125 units 150 units
Answers
The number of units that have to be produced and sold to break-even is 125 units.
To calculate the break-even point, we need to consider the fixed cost, variable cost per unit, and selling price per unit. The break-even point is reached when the total revenue equals the total cost.
Let's assume x represents the number of units to be produced and sold. The total cost is the sum of the fixed cost and the variable cost per unit multiplied by the number of units:
Total Cost = Fixed Cost + (Variable Cost per Unit × Number of Units)
The total revenue is the selling price per unit multiplied by the number of units:
Total Revenue = Selling Price per Unit × Number of Units
At the break-even point, Total Revenue = Total Cost. Using the given values:
$20x = $1,000 + ($12x)
Simplifying the equation:
20x = 1,000 + 12x
8x = 1,000
x = 125
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I need help please!!!!!!!
Answers
Answer:
75°
Step-by-step explanation:
We can assume that the angle shown and an angle that measures 15° makes a complementary angle. A complementary angles is when two angles add up to be 90°. We can create an equation and simplify:
15 + x = 90
x = 75
Best of Luck!
need help with transformations-reflectionsill send a picture of the question
Answers
Given:
The objective is to find the line of reflection at which the triangle carries onto itself.
Explanation:
To obtain the reflection of the rectangle on itself, it must reflect over the midpoint of each parallel side of the rectangle.
The line passing through the midpoint of the rectangle in the x-axis is x= 2.
Similarly, the line passing through the midpoint of the rectangle in the y-axis is y = 1/2.
Thus, the reflecting lines are x = 2 and y = 1/2.
Hence, option (A) is the correct answer.
Determine the value of x1081461019153113
Answers
To calculate the angles of a figure there are different strategies
In this case we can divide into different geometric shapes for example a square and a right triangle
Happy National estúpido question day
What’s 1+1=
Answers
god knows
Bruce has a spinner with four equal sections that are labeled A, B, C and D. He spun the spinner 8 times. It landed on A 3 times, B 1 time, and C 4 times. If he spins the spinner a 9th time, which of the following statements is true?
A. It is equally likely to be A, B, C, or D.
B. It is more likely to be D because it has not been landed on.
C. It is more likely to be C because it has landed on C the most.
D. It is not likely to be D because it has not been landed on.
Answers
All have an equal probability. One letter is not “due” because of previous spins
Answer:
the answer would be A.
Step-by-step explanation:
because it done not matter how many times the spinner has landed on a certain letter it is still always gonna be a 1/4th chance to land on any letter