find a sinusoidal function with the following four attributes: (1) amplitude is 16, (2) period is 4, (3) midline is y=16, and (4) f(2)=32.
Answers
The required sinusoidal function is: f(x) = -16 sin((π/2)x) + 32 with amplitude 16, period 4, midline y=16, and f(2)=32.
A general form of a sinusoidal function is:
f(x) = A sin(Bx + C) + D
where A is the amplitude, B is the coefficient of x, C is the phase shift, and D is the vertical shift.
Using the given attributes, we can determine the values of A, B, C, and D as follows:
Amplitude = 16, so A = 16.
Period = 4, so B = (2π)/4 = π/2.
Midline is y = 16, so D = 16.
f(2) = 32, so we can use this information to find the phase shift C.
We know that when x = 2, the value of the function is 32. Plugging these values into the general form of the function, we get:
32 = 16 sin((π/2)*2 + C) + 16
Simplifying this equation:
16 sin(π + C) = 0
sin(π + C) = 0
π + C = kπ, where k is an integer
C = kπ - π, where k is an integer
To satisfy the condition f(2) = 32, we need to choose k = -1. Therefore,
C = -π
Now, we have all the required values to write the sinusoidal function:
f(x) = 16 sin((π/2)x - π) + 16
Simplifying this expression, we get:
f(x) = -16 sin((π/2)x) + 32
Therefore, the required sinusoidal function is:
f(x) = -16 sin((π/2)x) + 32
with amplitude 16, period 4, midline y=16, and f(2)=32.
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Related Questions
rob is asked to graph this system of equations: 6x + 2y = 5; y + 3x =2; how many times will the lines intersect? A. there is no way to tell without graphing the lines first. B. the lines will not intersect, cuz the system only has one system. C. the lines will intersect once. D. the lines will intersect more than once.
Answers
Answer:
C
Step-by-step explanation:
A and B are wrong and with D they wouldn't be lines so imma go with C.
Sorry if it's wrong.
What is the next fraction in this sequence.
Answers
Samantha is starting a test that takes 3/5 of an hour to complete but she only has 1/2 of an hour to work on it if she works and it even pays what fraction of the test will she complete.
Answers
Step-by-step explanation:
The fraction she will complete is 1/2 / 3/5 = 1/2 * 5/3 = 5/6 completed
36 + (12 - 8) + 2 × 5
Answers
Answer:
50
Step-by-step explanation:
To answer this we need to use the PEMDAS strategy, first solve any questions in parentheses, next solve all multiplication and division problems from left to right. Next, solve all addition and subtraction problems from left to right.
36 + (12 - 8) + 2 × 5
36 + 4 + 2 x 5
36 + 4 + 10
40 + 10
50
Answer:
\(50\)
Step-by-step explanation:
Follow the PEMDAS order of operations:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction.
Calculate the Parentheses- (12-8)
This will equal 4.
\(36+4+2x5\)
(x= times)
Multiply and divide, left to right.
\(2x5=10\)
\(36+4+10=50\)
Question 1 (2 x 12 = 24 marks) Analyze and discuss the performance (in Big-O notation) of implementing the following methods over Singly Linked List and Doubly Linked List Data structures: To be submitted through Turnitin.Maximum allowed similaritv is 15% Operation Singly Linked List Doubly Linked List add to start of list Big-O notation Explanation add to end of list Big-O notation Explanation add at given index Big-O notation Explanation
Answers
In analyzing the performance of implementing the given methods over Singly Linked List and Doubly Linked List data structures, we consider the Big-O notation, which provides insight into the time complexity of these operations as the size of the list increases.
Add to Start of List:
Singly Linked List: O(1)
Doubly Linked List: O(1)
Both Singly Linked List and Doubly Linked List offer constant time complexity, O(1), for adding an element to the start of the list.
This is because the operation only involves updating the head pointer (for the Singly Linked List) or the head and previous pointers (for the Doubly Linked List). It does not require traversing the entire list, regardless of its size.
Add to End of List:
Singly Linked List: O(n)
Doubly Linked List: O(1)
Adding an element to the end of a Singly Linked List has a time complexity of O(n), where n is the number of elements in the list. This is because we need to traverse the entire list to reach the end before adding the new element.
In contrast, a Doubly Linked List offers a constant time complexity of O(1) for adding an element to the end.
This is possible because the list maintains a reference to both the tail and the previous node, allowing efficient insertion.
Add at Given Index:
Singly Linked List: O(n)
Doubly Linked List: O(n)
Adding an element at a given index in both Singly Linked List and Doubly Linked List has a time complexity of O(n), where n is the number of elements in the list.
This is because, in both cases, we need to traverse the list to the desired index, which takes linear time.
Additionally, for a Doubly Linked List, we need to update the previous and next pointers of the surrounding nodes to accommodate the new element.
In summary, Singly Linked List has a constant time complexity of O(1) for adding to the start and a linear time complexity of O(n) for adding to the end or at a given index.
On the other hand, Doubly Linked List offers constant time complexity of O(1) for adding to both the start and the end, but still requires linear time complexity of O(n) for adding at a given index due to the need for traversal.
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Which expression gives the correct volume of the steps?
Math item stem image
CLEAR CHECK
4×4×1 cubic feet
(4×4×1)+(3×3×3) cubic feet
(4×4×1)+(3×3×1)+(2×2×1)+(1×1×1) cubic feet
(4×4×4)+(3×3×3)+(2×2×2)+(1×1×1) cubic feet
Answers
Answer:
(4×4×4)(3×3×3)(1×1×1) Cubic feet
x(t)=at
4
+bt
3
+ct Where a,b, and c are constants. (a) What are the dimensions of the constants in the position equation? (b) What is the acceleration of the body? (c) What is the time-dependent force acting on the body?
Answers
a) [a] = LT⁻⁴, [b] = LT⁻³, and [c] = L T⁻².
b) The acceleration of the body is 12at² + 6bt
c) The time-dependent force acting on the body is 12ma.
Given equation:
x(t)=at⁴+bt³+ct
where a, b, and c are constants.
(a) Dimensions of the constants in the position equation.The dimensions of the constants in the position equation are
[a] = LT⁻⁴, [b] = LT⁻³, and [c] = L T⁻².
(b) Acceleration of the body
The velocity of the body v(t) is given by taking the derivative of position equation with
respect to time t.
v(t) = x'(t) = 4at³ + 3bt²
The acceleration of the body is given by taking the derivative of velocity equation with respect to time t.
a(t) = v'(t)
= 12at² + 6bt
(c) Time-dependent force acting on the body.
The time-dependent force acting on the body is given by taking the derivative of acceleration equation with respect to time t.
F(t) = m a'(t)
= m (12a)
where m is the mass of the body.
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what are the coordinates of the projection of the point q(−3, 5, 4) onto the xy-plane?
Answers
The coordinates of the projection of point Q(-3, 5, 4) onto the xy-plane are (-3, 5, 0).
To find the projection of a point onto the xy-plane, we need to drop a perpendicular line from the point to the plane. This perpendicular line will intersect the plane at the projected point. The projected point will have the same x and y coordinates as the original point, but its z-coordinate will be zero since it lies on the xy-plane.
In this case, we have the point Q(-3, 5, 4), and we want to find its projection onto the xy-plane. Since the xy-plane is defined by the equation z = 0, the z-coordinate of the projected point will be zero.
Therefore, the coordinates of the projected point can be written as (x, y, z), where x and y are the same as the coordinates of the original point, and z is zero.
For point Q, the x-coordinate is -3, the y-coordinate is 5, and the z-coordinate of the projected point is 0. Hence, the coordinates of the projected point are (-3, 5, 0).
To visualize this, imagine a vertical line dropping from the point Q(-3, 5, 4) down to the xy-plane. The point where the line intersects the plane will have the same x and y coordinates as Q, but its z-coordinate will be zero.
In conclusion, the projection of point Q(-3, 5, 4) onto the xy-plane has coordinates (-3, 5, 0). This means that the point lies on the xy-plane, with its z-coordinate being zero.
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What is the value of (3^6)^3
Answers
Answer:
3^18
Step-by-step explanation:
\((3^6)^3\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\left(3^6\right)^3=3^{6\times\:3}\\\\=3^{6\times\:3}\\\\=3^{18}\\\\=387420489\)
What is a 2-digit special number?.
Answers
A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.
In the given question we have to explain about 2-digit special number.
A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.
Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.
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Can someone explain this or help me plss .
Answers
Answer:I'll explain this to you, It's a chart with lined down margin math equation.
Step-by-step explanation:
So the first up/down line margin is X*X, the second is X numbers, third is x^x numbers, fourth is explain the left to right's math solutions into words. Just imply your following numbers into X's and onto your chart. Hopefully this helps.
Some nations require their students to pass an exam before earning their primary school degrees or diplomas. A certain nation gives students an exam whose scores are normally distributed with a mean of 41 4141 points and a standard deviation of 9 99 points. Suppose we select 2 22 of these testers at random, and define the random variable d dd as the difference between their scores. We can assume that their scores are independent. Find the probability that their scores are within 10 1010 points of each other. You may round your answer to two decimal places.
Answers
The probability that the scores of the two randomly selected testers are within 10 points of each other is approximately 0.78 (rounded to two decimal places).
To find the probability that the scores of the two randomly selected testers are within 10 points of each other, we need to calculate the probability that the absolute difference between their scores (denoted as |d|) is less than or equal to 10.
Let X and Y be the scores of the two testers, with X ~ N(\(41, 41^2\)) and Y ~ N(\(41, 41^2\)) (since both have a mean of 41 and a standard deviation of 9).
We want to find P(|X - Y| ≤ 10).
Since X and Y are independent and normally distributed, the difference X - Y is also normally distributed with a mean of (41 - 41) = 0 and a variance of \((9^2 + 9^2) = 162.\)
Now, we can calculate the standard deviation of X - Y as √(162) ≈ 12.73.
Thus, P(|X - Y| ≤ 10) can be calculated using the standard normal distribution as follows:
Z = (10 - 0) / 12.73 ≈ 0.785
Using a standard normal table or calculator, we find that the probability corresponding to Z = 0.785 is approximately 0.7838.
Therefore, the probability that the scores of the two testers are within 10 points of each other is approximately 0.78 (rounded to two decimal places).
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if two variables are manipulated in a completely between-subjects experiment, and if there are two levels of each independent variable, then how many total participants would you need to have 15 participants in each experimental condition?
Answers
You would need a total of 60 participants to have 15 participants in each experimental condition.
In a completely between-subjects experiment with two variables, if there are two levels of each independent variable and you want to have 15 participants in each experimental condition, you would need a total of 15 participants in each combination of levels.
Let's break it down step by step:
Number of levels per variable: 2
Number of participants per level: 15
Total number of conditions: 2 levels * 2 levels = 4
To calculate the total number of participants, you multiply the number of participants per condition by the total number of conditions:
Total participants = Number of participants per condition * Total number of conditions
Total participants = 15 * 4
Total participants = 60
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2/3(x+6)=-8 whats the value of x?
Answers
Answer:
x=-18
Step-by-step explanation:
Answer:
The answer is -18
Step-by-step explanation:
STEP 1:
\(3 \times \frac{2}{3} (x + 6) = 3( - 8)\)
2(x+6) = -24
______________________________________
STEP 2:
Divide both sides by 2:
\( \frac{2(x + 6)}{2} = \frac{ - 24}{2} \)
________________________________
STEP 3:
Simplify:
\(x + 6 = - 12\)
Subtract 6 from both sides:
\(x + 6 - 6 = - 12 - 6\)
________________________________
STEP 4:
\(x = - 18\)
Therefore, your answer is -18.
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A philanthropist pledges to donate 13% of a fund each year. If the fund initially has $761,000.00, how much will the fund have after 16 years?
Please type answers with no commas and round to 2 decimal places.
Answers
If the philanthropist pledges to donate 13% of a fund each year, at the end of 16 years, the fund will have $35,517,190.20.
How much would the fund have after 16 years?The formula that can be used to determine the value of the fund after 16 years is:
Initial value of the fund x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
(1.13^16 - 1) / 0.13 = 46.671735
46.671735 x $761,000.00 = $35,517,190.20
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Need help ASAP!!
All exponential functions can be written in many forms. Write the function
f(t) = 750(0.65) ^t\35 in the form f(t) =ab^t. Round all coefficients to four decimal
places.
Answers
The final form of the exponential function is: f(t) = 750(0.8825)raise to the power t
what is exponential function?
An exponential function is a mathematical function of the form f(x) = a to the power x, where "a" is a positive constant (called the base of the exponential function) and "x" is a variable that can take on any real number value.
The key property of an exponential function is that the output value (or "y" value) grows or decays at a constant rate as the input value (or "x" value) increases or decreases. This constant rate of growth or decay is determined by the base "a" of the function.
When the base "a" is greater than 1, the function represents exponential growth, where the output value increases rapidly as the input value increases. When the base "a" is between 0 and 1, the function represents exponential decay, where the output value decreases rapidly as the input value increases.
Exponential functions are commonly used to model natural phenomena such as population growth, radioactive decay, and compound interest. They also have many applications in science, engineering, economics, and finance.
Starting with the given exponential function:
f(t) = 750(0.65)raise to the power (t/35)
We can rewrite 0.65 as 0.65, and 35 as 5 * 7. Then we have:
f(t) = 750(0.65)raise to the power (t/(5*7))
Using the exponent rule that (a to the power b)to the power c = a to the power (bc), we can simplify the expression inside the parentheses:
f(t) = 750(0.65 to the power (t/5))⁷
Letting a = 750 and b = 0.65 to the power(1/5), we can write the function in the desired form:
f(t) = ab to the power , where a ≈ 750 and b ≈ 0.8825 (rounded to four decimal places)
Therefore, the final form of the exponential function is:
f(t) = 750(0.8825) to the power t
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A pie crust recipe calls for 2 cups of butter for each 3 cups of flour. Elliette is making enough crust to use up 8 cups of flour. How many cups of butter will she need?
Answers
pls answer the question with explanation
Answers
Answer:
a) 96m
b) 2 m/s^2
Step-by-step explanation:
The distance travelled in a velocity time graph as shown in the image is the area of the shape. As such, considering the first 14 seconds, the distance covered will be computed by finding the area of the shape.
Note that the shape to be considered ends t the 14 seconds mark. This shape is a trapezium. The area of a trapezium is given as
A = 1/2(a + b) h
where a and b are the parallel sides of the trapezium and h is the height As such, the distance covered in the first 14 seconds
= 1/2 (14 + 10) * 8
= 4 * 24
= 96m
The acceleration after 4 seconds
Acceleration is the rate of change of velocity with time, at time 0 second, the velocity is also 0 but at time 4 seconds, the velocity is 8 m/s hence, the acceleration after 4 seconds
= 8/4
= 2 m/s^2
Is 9.90 greater than or lesser than 9.9
Answers
Answer:
it is equal too.
Step-by-step explanation:
Answer:
it is equal to
Step-by-step explanation:
plzzz help me i will mark you as brainliest
Answers
Answer:
10/12
Step-by-step explanation:
6*2=12 so
5*2=10
Can someone help me give it with this my grade are bad
Answers
Answer:
Your new points are (3,6) (3,3) and (6,3)
That means (3,6) is from (0,0) (lower left corner) - count 3 across then 6 up and make a point
(3,3) from lower left corner count 3 across then 3 up and make a point
(6,3) from lower left count 6 across then 3 up and make a point
Connect the points, the shape will match the other but it will be smaller
someone pls help
asap
ty :)
Answers
Answer:
56%
Step-by-step explanation:
We know that there are 6 groups of 6 and 4 groups of 5.
6x6 = 36
4x5 = 20
Add them up. 36 + 20 = 56.
Add the percent sign for 56%.
Answer:
56%
Step-by-step explanation:
I Need Help With This Question
Answers
Answer:
Step-by-step explanation:
Dont do it. Just take the detention
What is the slope of the line? *
Answers
Answer:
-2/-5 = 2/5
Step-by-step explanation:
in percent the whole of an amount W is measured by the formula W=100N/P where N=part and P=percent solve the formula for P (SAVVAS MATH XL)
Answers
The equation of P in the given equation is P = 100N/W
How to solve for P in the equation?The equation is given as:
W = 100N/P
Multiply both sides by P
WP = 100N
Divide both sides by W
P = 100N/W
Hence, the equation of P in the given equation is P = 100N/W
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The width of a rectangle measures (2p-5) centimeters, and its length measures (8p+8)centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer: The expression that represents the perimeter, in centimeters, of the rectangle=20p + 11 centimeters
Step-by-step explanation:
Perimeter of a rectangle = 2(l+w)
length measures (8p+8)centimetres.
width measures (2p-5) centimeters,
Such that Perimeter= 2 L +2 W
Perimeter= 2( 8p+8) + 2(2p-5 ) This gives the expression to solve for the Perimeter
Solving
Perimeter= 2( 8p+8) + 2(2p-5 )
Permeter= 16p+ 16+ 4p-5
Perimeter= 16p+4p+16-5
Perimeter= 20p + 11 centimeters
3.46 Informed consent A researcher suspects that traditional religious beliefs
tend to be associated with an authoritarian personality. She prepares a question-
naire that measures authoritarian tendencies and also asks many religious ques-
tions. Write a description of the purpose of this research to be read by subjects in
order to obtain their informed consent. You must balance the conflicting goals of
not deceiving the subjects as to what the questionnaire will tell about them and
of not biasing the sample by scaring off religious people.
Answers
Answer: The purpose of this research is to explore the potential relationship between traditional religious beliefs and authoritarian tendencies. We are administering a questionnaire that will measure your views on various topics and ask about your religious beliefs. It is important to note that this research is not intended to judge or stereotype individuals based on their religious beliefs, but rather to gain a better understanding of how these beliefs may be related to certain personality traits. Your participation in this study is completely voluntary and your responses will be kept confidential. We understand that some of the questions may be sensitive in nature, and we want to assure you that your personal beliefs will not be used in any negative way. Your participation in this research will help us to better understand the relationship between religious beliefs and personality traits, and will contribute to the field of psychology.
i. A continuity correction compensates for estimating a discrete distribution with a continuous distribution.ii. The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when np and n(1 -p)are both greater than five.iii. When a continuity correction factor is used, its value is 1.Multiple Choice(i) and (ii) are correct statements but not (iii).(i), (ii), and (iii) are all correct statements.(i), (ii), and (iii) are all false statements.(i) and (iii) are correct statements but not (ii).(i) is a correct statement but not (ii) or (iii).
Answers
The correct answer is (i) and (ii) are correct statements in the above probability-based question but not (iii).
(i) A continuity correction is needed to account for the fact that we are approximating a discrete distribution with a continuous distribution. It adjusts the endpoints of the interval of the continuous distribution by 0.5 to take into account the discrepancy between the two distributions.
(ii) The normal probability distribution can be used to approximate the binomial probability distribution when the sample size is large (n ≥ 30) and both np and n(1-p) are greater than five. This is because the binomial distribution approaches the normal distribution as the sample size increases.
(iii) The statement that the continuity correction factor is always 1 is false. The value of the continuity correction factor depends on the problem at hand and is calculated by taking into account the specific values of n, p, and x that are being used.
Therefore, the correct answer is (i) and (ii) are correct statements but not (iii).
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Hi Everyone! I need LOTS of help with my math homework. I have 2 questions, and if you could tell me which ones you are answering then that would be great! Thank You So Much!!!
Answers
Answer:
4. 143°
5. x=32°, exterior angle=134°
Step-by-step explanation:
The relation of interest in these two questions is ...
an exterior angle of a triangle is equal to the sum of the remote interior angles.
__
4.The exterior angle is u°. The opposite (remote) interior angles are a right angle (90°) and one marked 53°. The above relation tells you ...
u° = 90° +53°
∠u = 143°
__
5.In this figure, the external angle is marked (4x+6)°, and the opposite internal angles are x° and 102°. Our relation between these tells us ...
(4x +6)° = x° +102°
3x = 96 . . . . . . . . . . . . divide by °, subtract x+6
x = 32 . . . . . . . . . . divide by 3
∠x = 32°
(4x+6)° = (4(32) +6)° = 134°
The function f(x)=x^2+2 is not one to one. Determine a restricted domain that makes it one to one and find the inverse function
Answers
Answer:
Hope it helped
Step-by-step explanation:
The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = \(\sqrt{x-2}\) if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -\(\sqrt{x-1}\) if we restrict the domain to (-∞,0] .
What is inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function.
Now the given quadtratic function is,
f(x) = x² + 2
Now vertex of the given quadratic function is (0,2)
Thus the range of the function is [2,∞)
If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.
Now the inverse function is given as,
y = x² + 2
Upon interchanging x and y, we get:
x = y² + 2
⇒ y² = x - 2
or, y = ±\(\sqrt{x-2}\)
Hence, the inverse function would be f⁻¹ (x) = \(\sqrt{x-2}\) if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -\(\sqrt{x-1}\) if we restrict the domain to (-∞,0] .
Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = \(\sqrt{x-2}\) if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -\(\sqrt{x-1}\) if we restrict the domain to (-∞,0] .
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