Answer:
1/4
Step-by-step explanation:
I assume the original H-shaped polygon is the one on the left, and the scaled copy is the smaller one on the right.
To find the scale factor, find a dimension in the original polygon and the corresponding dimension in the scaled copy. Then divide the dimension of the scaled copy by the corresponding dimension of the original one.
For example, use the upper width of the left rectangle of the H shape.
A) original polygon: 4 units
B) scaled polygon: 1 unit
scale factor = (1 unit)/(4 units) = 1/4
The scale factor is 1/4. That means that if you multiply every linear dimension of the original polygon by 1/4, you find the corresponding dimension in the scaled copy.
Answer: The scale factor is 1/4
Function to find smallest Write a function def smallest (x,y,z) that returns the smallest of the three arguments. Ex. The call to smallest (10,4,−3) would return the value −3 Write only the function. Unit tests will be used to access your function. \begin{tabular}{l|l} \hline LAB & 5.2.1: LAB: Function to find smallest \\ ACTiviry & . Funt \end{tabular} 0/10 main.py 1
The `smallest` function takes three arguments (`x`, `y`, and `z`) and uses the `min` function to determine the smallest value among the three. The `min` function returns the minimum value from a given set of values.
Here's the implementation of the `smallest` function in Python:
```python
def smallest(x, y, z):
return min(x, y, z)
```
You can use this function to find the smallest value among three numbers by calling `smallest(x, y, z)`, where `x`, `y`, and `z` are the numbers you want to compare.
For example, if you call smallest(10, 4, -3), it will return the value -3 since -3 is the smallest value among 10, 4, and -3.
To read more about function, visit:
https://brainly.com/question/29631554
#SPJ11
Need answers quickly need it step by step
(−5)2 −2×(−9)+6=
(−9)−(−8)+2×42=
8÷(−4)×(−6)2 +7=
10×5−(−6)2 +(−8)=
(10 ÷ (−5) − (−2)) × (−3)3=
3×10+8−42=
(−3)3 −2+8÷(−8)=
4×(−8)+6−(−2)3=
(−5)2 ×3÷5+9=
4 × (−6) ÷ 8 + 33=
Thanks
Answer:
Step-by-step explanation:
1. -10+18+6=8+6=14
2. -1+84=83
3. -2×(−6)2 +7=12×2+7=24+7=31
4. 50-(−6)2 +(−8)=50+12-8=62-8=54
5. (-2+2)× (−3)3=0× (−3)3=0
6. 30+8-42=38-42=-4
7. -9-2-1=-12
8. -32+6+6=-20
9. -10×3÷5+9=-30÷5+9=-6+9=3
10. -24÷ 8 + 33=-3+33=30
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).
option C.
Which ordered pair can be plotted together?The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;
The four points include;
A = (1, 2)
B = (2, - 3)
C = (-2, - 2)
D = (-3, 1)
The ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;
(2, - 1)
Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).
Learn more about ordered pairs here: https://brainly.com/question/30467126
#SPJ1
16. Coach Murphy has an end of the season celebration for his basketball team. He provided a pizza lunch and
distributed a homemade DVD of the season's highlights to each player. It cost him $5 per player for the pizza
lunch and $2 per player for the DVD. If there were 8 players on the team, use the Distributive Property to find
the total cost for the celebration.
Answer:
$56.00
Step-by-step explanation:
8(5 + 2) Distribute the 8
8(5) + 8(2)
40 + 16
56
If X=6and Y=4 work out the value of 2Y ²
Answer:
64
Step-by-step explanation:
Graph the equation y=−x 2 −8x−7 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
The graph of the given quadratic function is shown below
Graph of Quadratic equationsFrom the question, we are to graph the given quadratic function.
The given quadratic equation is
y = −x² −8x −7
The graph of the given quadratic function is shown below
Learn more on Graph of quadratic equations here: https://brainly.com/question/9028052
#SPJ1
if p and q vary inversely and p is 30 when q is 6, determine q when p is equal to 60.
using inverse relation, If p= 60, then q= 3x because i find the constant value is 180.
What is the p increases inversely as q equation?P is approximately equal to 1/Q since P has an inverse relationship to Q. x=k/3 for P=x and Q=3. P = k/x when Q = x.
The correlation between bond prices and interest rates is a prime illustration of an inverse connection. Bond prices normally fall with an increase in interest rates, whereas bond prices often rise with a decrease in interest rates.
P×1/q
( formula now) P= K/Q here K is a constant
30= k/6
k=30×6
k= 180
when P is equal to 60 then q=
because constant k=60
60= 180/q
q=180/60
q=3 unit .
To know more about inverse visit:
brainly.com/question/29423037
#SPJ1
HELP
The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.
|t − 1.8| ≥ 98.6
|t − 1.8| ≤ 98.6
|t − 98.6| ≥ 1.8
|t − 98.6| ≤ 1.8
The inequality which is used to represent normal "temperature-range" for "human-body", is (d) |t − 98.6| ≤ 1.8.
The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.
The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.
This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.
Which means, the temperature cam range from :
⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,
⇒ 96.8 ≤ t ≤ 100.4;
Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.
Learn more about Inequality here
https://brainly.com/question/29053875
#SPJ1
The given question is incomplete, the complete question is
The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.
(a) |t − 1.8| ≥ 98.6
(b) |t − 1.8| ≤ 98.6
(c) |t − 98.6| ≥ 1.8
(d) |t − 98.6| ≤ 1.8
Answer: |t − 98.6| ≤ 1.8
Step-by-step explanation: If takes then takes then takes then takes then takes.
Let the Universe be the real number system. Let A−{x:x>0},B−{2,4,8,16,32}, C={2,4,6,8,10,12,14}
D={x:−3
Calculate the following sets. The formats are either an unordered list like 1;2;3, an interval like (1,2) (use "Inf" without quotes to refer to [infinity] ) or "empty" (without the quotes) for the null set. a) B∩C A b) B∪C Q c) A∩(D∪E) A d) A∪(B∩C) Q e) (A∩C)∪(B∩D) Q f) A∩(B∩(C∩(D∩E)))
Consider the universe to be the real number system
Let A = {x:x>0}, B = {2,4,8,16,32}, C = {2,4,6,8,10,12,14}
D = {x: −3}
To calculate the sets, let's go through each of the given expressions:
a) \(BnC:\)
\(B n C\) : Refers to the intersection of sets B and C.
The intersection comprises elements shared by both sets B and C.
B = {2, 4, 8, 16, 32}
C = {2, 4, 6, 8, 10, 12, 14}
The common elements between B and C are {2, 4, 8}. So, \(B n C\) = {2, 4, 8}.
b) \(B U C\):
\(B U C:\) Refers to the union of sets B and C.
Without repetition, the union contains all of the elements from both sets.
B = {2, 4, 8, 16, 32}
C = {2, 4, 6, 8, 10, 12, 14}
The union of B and C is {2, 4, 6, 8, 10, 12, 14, 16, 32}. So, \(B U C\) = {2, 4, 6, 8, 10, 12, 14, 16, 32}.
c) \(A n (D u E)\):
We can't calculate this formula because E isn't specified in the query. As a result, it is undefined.
d) \(A u (B n C)\):
\(A u (B n C)\): Refers to the union of set A and the intersection of sets B and C.
A = Universe - {x: x > 0} (The set of all real numbers except positive numbers)
B = {2, 4, 8, 16, 32}
C = {2, 4, 6, 8, 10, 12, 14}
The intersection of B and C is {2, 4, 8}.
The union of A and {2, 4, 8} includes all the elements from both sets without repetition.
So, A ∪(B ∩ C) = Universe - {x: x > 0} ∪ {2, 4, 8} (The set of all real numbers except positive numbers, along with 2, 4, 8)
e) \((A n C) u (B u D):\)
We can't calculate this formula because D isn't specified in the query. As a result, it is undefined.
f) \(A n (B n (C n (D n E))):\)
We can't calculate this formula because D and E aren't specified in the question. As a result, it is undefined.
Learn more about the Intersection:
https://brainly.com/question/28278437
#SPJ11
The measurement of the supplement of an angle is 39 more than half the angle. find the measure of the angle and its complement
Answer: 94, 86
Step-by-step explanation:
x + x/2 + 39 = 180
x + x/2 = 180 - 39
x = 94
Other angle is 180 - 94 = 86
Pls help, mathmatics 50 points
The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106
What is a rectangle and its Properties ?A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.
Rectangles' essential characteristics are as follows:
A rectangle is a parallelogram.
Each inner angle is equal to 90 degrees and the opposite sides are parallel and equal to one another.360 degrees is the total of all interior angles.The diagonals cut each other in half, and both of them are equal in length.The perimeter of a rectangle with side lengths a and b is equal to 2a+2b units.The Perimeter of the rectangle is 2a + 2b where a and b are the two sides
Now , if w is the width of the rectangle then, the length is 4w given in problem.
Perimeter,
2w + 2* 4w
As it is given in the problem
2w + 2* 4w ≤ 106
The first model of inequality satisfy the problem.
To learn more about inequatity refer to :
brainly.com/question/2456006
#SPJ1
The Cubs are playing the Red Sox in the World Series. To win the world series, a team must win 4 games before the other team does. If the Cubs win each game with probability $\dfrac{3}{5}$ and there are no ties, what is the probability that the Cubs will win the World Series
The probability that the Cubs will win the World Series is approximately 0.21048 or 21.05% (in percent form).
How to find the probability?To calculate the probability that the Cubs will win the World Series, we need to consider the different possible outcomes.
In order for the Cubs to win the World Series, they must win 4 games before the Red Sox do. This can happen in several ways:
The Cubs win in exactly 4 games: The Cubs win the first 4 games and the Red Sox win 0 games.The Cubs win in 5 games: The Cubs win 4 games and the Red Sox win 1 game, with the Cubs winning the last game.The Cubs win in 6 games: The Cubs win 4 games and the Red Sox win 2 games, with the Cubs winning the last two games.The Cubs win in 7 games: The Cubs win 4 games and the Red Sox win 3 games, with the Cubs winning the last three games.Let's calculate the probability for each scenario and then add them up to find the total probability.
Probability of the Cubs winning in exactly 4 games: (3/5)⁴ = 0.1296Probability of the Cubs winning in 5 games: (3/5)⁴ * (2/5) = 0.05184Probability of the Cubs winning in 6 games: (3/5)⁴ * (2/5)² = 0.020736Probability of the Cubs winning in 7 games: (3/5)⁴ * (2/5)³ = 0.0082944Now, we can add up these probabilities to find the total probability of the Cubs winning the World Series:
Total probability = 0.1296 + 0.05184 + 0.020736 + 0.0082944 = 0.21048
Learn more about probability at:
https://brainly.com/question/25870256
#SPJ4
The probability that the Cubs will win the World Series is approximately 0.3456 or 34.56%.
Explanation:To calculate the probability that the Cubs will win the World Series, we can consider the different possible outcomes of the series. If the Cubs win a game with a probability of 3/5, then the Red Sox win a game with a probability of 2/5. The Cubs need to win 4 games in total to win the series, so the probability can be calculated using the binomial distribution.
The probability that the Cubs win the World Series can be found by summing the probabilities of each possible outcome where the Cubs win 4 games before the Red Sox. The formula for this is:
P(Cubs win the World Series) = (4 choose 4) * (3/5)^4 * (2/5)^0 + (4 choose 3) * (3/5)^3 * (2/5)^1 + (4 choose 2) * (3/5)^2 * (2/5)^2 + (4 choose 1) * (3/5)^1 * (2/5)^3
Simplifying this expression, the probability that the Cubs win the World Series is approximately 0.3456 or 34.56%.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
What is an example of a complex number in standard form?
An example of a complex number in standard form is (5 + 4i), where i is the imaginary unit.
example to solve (x + 5i)(2x - 3i):
Step 1: Multiply the real numbers together:
x × 2x = 2x²
Step 2: Multiply the imaginary numbers together:
5i × -3i = -15i²
Step 3: Multiply the real and imaginary parts together:
x × -3i = -3ix and 2x × 5i = 10xi
Step 4: Add all the terms together:
2x² - 15i² + -3ix + 10xi = 2x² - 15i² - 3ix + 10xi
Step 5: Simplify the terms:
2x² - 15i² - 3ix + 10xi = 2x² - 18ix - 15i²
The product of two complex numbers (x + 5i)(2x - 3i) can be found by multiplying the real numbers together, the imaginary numbers together, and the real and imaginary parts together, then adding all of the terms together and simplifying.
Learn more about unit here
https://brainly.com/question/19866321
#SPJ4
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments: investigate further whether the proportions of furnished apartments differ be- tween apartments with different numbers of bedrooms, it is useful to test formally whether the number of bedrooms in an apartment and whether it is furnished or not are independent (a) State the null hypothesis the relevant form of the test statistic and the approximate distri- bution of the test statistic for carrying out this text (b) Provide cross-tabulation of the apartment data by these two factors (you should generate this table using R)
(c) Carry out a formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv. the resulting p-value for the test, or rejection region You should also ensure that you conclude your formal test by interpreting the p-value (or rejection region and your observed test statistic) in terms of the original question discussed above:'
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000
formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
I bedroom = x
2 bedroom = y
3 bedroom = z
All the condition s gjvbbs'
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
learn more about of apartment here
https://brainly.com/question/22674586
#SPJ4
Please help! Easy question, answer pls, 15 pts.
Answer:
360 in
Step-by-step explanation:
To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:
\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)
So, the dressmaker has 360 in of ribbon.
an electronic store receives shipment of 12 graphing calculators of which 4 are defective. six of the calculators are selected to be sent to a local high school. what is the probability that exactly one is defective?
The probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.
The probability of selecting exactly one defective calculator out of the 6 sent to the local high school can be calculated using the binomial probability formula. The binomial probability formula is \(P(x) = nCx * p^x * q^(n-x)\). For this problem, n = 6 (the number of calculators sent to the local high school), x = 1 (the number of defective calculators selected), p = 4/12 (the probability of selecting a defective calculator from the shipment of 12 calculators), and q = 8/12 (the probability of selecting a non-defective calculator from the shipment of 12 calculators). Plugging these values into the formula gives \(P(x) = 6C1 * 4/12^1 * 8/12^5\), which simplifies to 0.29166. This means that the probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
20% of the 6th graders at ce king middle school. There are 250 sixth grade students. How many sixth graders ride the bus to school
Answer:
50 sixth graders ride the bus to school.
Step-by-step explanation:
250= total amount of 6th grade students.
20% of the total = ?
Use this equation:
0.20=20%
250*0.20 = 50
So, 20% of 250 is 50
Hope this helps!
Estimate 0.03415 to the nearest hundredth. Express your answer as a single digit times a power of ten
Answer:
3 raise to power -100
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
What is the probability that a randomly chosen young adult has at least a high school education? which rule of probability did you use to find the answer?
The probability that a randomly chosen young adult has at least a high school education can be found using the rule of probability called the "complement rule".
To find the answer, we need to subtract the probability that a randomly chosen young adult does not have at least a high school education from 1. In other words:
Probability of having at least a high school education = 1 - Probability of not having at least a high school education.
By using this rule, we can calculate the probability.
To know more about probability refer here:
https://brainly.com/question/31828911
#SPJ11
I have 8 edges.
Four of my faces are
triangles.
I am a solid figure.
What is the answer to this question?
The solid figure that has 8 edges and four triangular faces is a pyramid.
Look at the steps used when solving 3(x - 2) = 3 for X.
3(x - 2) = 3
3x - 6 = 3
3x - 6 + 6 = 3 + 6
3x = 9
Write the original equation.
Use the Distributive Property.
Step 1
Step 2
3x 9
3
3 3
Step 3
x = 3
Step 4
Which step is the result of combining like terms?
Which step is justified by division property of equality?
Answer in at least TWO COMPLETE SENTENCES.
Answer:
3×-6=3
3×=3+6
3×=9
×=3
Step-by-step explanation:
multiply 3 by the variables in the bracket.
then you will get 3×-6=3.
take the -6 to the right hand side and it becomes+6
then you get 3×=3+6 therefore =3×=9
then divide both sides by 3.
3×÷3 and 9÷3
×=3
A flat rectangular piece of aluminum has a perimeter of 60 inches. The
length is 14 inches longer than the width. Find the width.
please add all the steps and explanation thank you.
Answer:
width = 8 inches
Step-by-step explanation:
⭐ What is the formula for the perimeter of a rectangle?
perimeter = 2(length) + 2(width)We are given that the length is 14 inches longer than the width, and the perimeter of the rectangle is 60 inches.
So, let's substitute these values into the perimeter formula and solve for the width. Let w = width.
\(60 = 2(14 + w) + 2(w)\) Multiply the 2 into the parentheses
\(60 = 28 + 2w + 2w\) Add like terms (terms with the same variable)
\(60 = 28 + 4w\) Subtract 28 on both sides
\(32 = 4w\) Divide both sides by 4 to isolate the variable
\(8 = w\)
∴ The width is 8 inches.
Which is the correct way to find the length of a line segment with endpoints (0,4) and (7,-9)?
Answer:
0 is Y 7 is X 4 is Y and -9 is X
Step-by-step explanation:
you can use Y and X to pin point the spots
Ms. Hawkins is taking her science classes on a field trip to a museum. She has $ 1,900 spend on the trip. The bus company will charge $ 175 for travel. The museum charges $6.50 for admission per student and $ 2.25 for lunch per student. Ms. Hawkins gets free admission and lunch. Let s represent the number of students that could go on the trip while Ms. Hawkins stays within her budget .
Write an inequality that models this situation.
Determine how many students Ms. Hawkins can bring with her on her field trip and stay in her budget.
The inequality is ;
175 + 6.50s + 2.25s ≤ 1900Number of students = 197Total amount to spend = $1900
Bus charge = $175
Admission fee per student = $6.50
Lunch fee per student = $2.25
Number of students = s
Writing out the total cost :
Bus charge + (admission fee × s) + (lunch fee × s) ≤ 1900
175 + 6.50s + 2.25s ≤ 1900
Using the equation defined, we can find s ;
175 + 6.50s + 2.25s ≤ 1900
Solve for s
8.75s ≤ 1900 - 175
8.75s ≤ 1725
s ≤ 1725 / 8.75
s ≤ 197.14
The number of students she can bring along is 197 and still stay within her budget.
Learn more : https://brainly.com/question/24513103
If f(x)=2x+3, find the following value of f(x)=11.
Please help me understand this problem and the answer please.
find the x-coordinates of the inflection points for the polynomial p(x)= x^5/20
The inflection point of the polynomial p(x) = \(x^5/20\) is at x = 0. This is the only one inflection point.
To find the x-coordinates of the inflection points for the polynomial p(x) = \(x^5/20\), we'll need to follow these steps:
1. Find the first derivative, p'(x), to determine the slope of the function.
2. Find the second derivative, p''(x), to determine the concavity of the function.
3. Set p''(x) equal to zero and solve for x to find the inflection points.
Step 1: Find the first derivative, p'(x):
p'(x) = \(d(x^5/20)/dx = (5x^4)/20 = x^4/4\)
Step 2: Find the second derivative, p''(x):
p''(x) = \(d(x^4/4)/dx = (4x^3)/4 = x^3\)
Step 3: Set p''(x) equal to zero and solve for x:
\(x^3\) = 0
x = 0
There is only one inflection point, and its x-coordinate is 0.
For more such questions on Inflection points.
https://brainly.com/question/31484498#
#SPJ11
15 first-year algebra students are learning how to solve two-step equations. the teacher notices that the students are not using precise mathematical language. which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? choose 2 answers
Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.
However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.
So the list goes as
1. Exponents
2. Roots
3. Multiplication
4. Division
5. additional
6. Subtraction
However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.
Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.
Furthermore, the preferred behavior norm for division and multiplication is different.
Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.
Know more about algebra
https://brainly.com/question/22399890
#SPJ4
Find the Laplace transform where of the function f(t) =
{ t, 0 < t < {π + t π < t < 2π where f(t + 2 π) = f(t).
The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...
= (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]
Given function is,f(t) ={ t, 0 < t < π π < t < 2π}
where f(t + 2 π) = f(t)
Let's take Laplace Transform of f(t)
L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)
∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}
⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0
when e^{2πs} ≠ 1 ⇒ s ≠ 0
∴ The Laplace Transform of f(t) is
L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...
= (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...
= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]
The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...
= (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]
Learn more about Laplace Transform
brainly.com/question/30759963
#SPJ11
Maste
1) 2,000 pounds of sand is to be put into 100-pound bags. Each bag will sell
for $5.00. How much is the sand worth altogether?
Answer: 100$
Step-by-step explanation:
What is a great answer for 5 plus negative 4