The first property states that the Fourier transform of a function evaluated at a certain frequency is equal to 2π times the inverse Fourier transform of the function evaluated at the negative of that frequency.
The second property states that the Fourier transform of a modulated function is equal to the Fourier transform of the original function shifted by the modulation frequency.
To verify the given properties of the Fourier transform, we can use the definitions and properties of the Fourier transform. Here's how we can verify each property:
1. Property: (Fu)(ω) = 2π (F^-1u)(-ω)
To verify this property, we need to use the definitions of the Fourier transform and its inverse. Let's denote the Fourier transform operator as F and its inverse as F^-1.
According to the definition of the Fourier transform, for a function u(t), its Fourier transform is given by:
(Fu)(ω) = ∫[from -∞ to ∞] u(t) e^(-iωt) dt
Similarly, the inverse Fourier transform of a function U(ω) is given by:
(F^-1U)(t) = (1/2π) ∫[from -∞ to ∞] U(ω) e^(iωt) dω
Now, let's substitute -ω for ω in the inverse Fourier transform:
(F^-1u)(-ω) = (1/2π) ∫[from -∞ to ∞] u(t) e^(i(-ω)t) dt
= (1/2π) ∫[from -∞ to ∞] u(t) e^(iωt) dt
Comparing this with the Fourier transform, we see that (F^-1u)(-ω) is equal to (Fu)(ω) multiplied by 2π, which verifies the first property.
2. Property: (F(e^(iat)u))(ω) = (Fu)(ω + a)
To verify this property, we use the modulation property of the Fourier transform. According to this property, if u(t) has a Fourier transform U(ω), then the Fourier transform of e^(iat)u(t) is given by:
(F(e^(iat)u))(ω) = (Fu)(ω + a)
Applying this property to the given expression, we have:
(F(e^(iat)u))(ω) = (Fu)(ω + a)
This verifies the second property.
In summary, we have verified both properties of the Fourier transform as stated.
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The lengths of the sides of a triangle are 5, 12, and 13. What is the length of the altitude drawn to the side with length equal to 13? (Hint: Use triangle area).
Answer:
h=60/13
Step-by-step explanation:
Δ=1/2(13)(h)
30=13h/2
h=60/13
4c+3d+f c=5 3=d f=-2
Hey there!
• If c = 5; d = 3; f = –2, then SUBSTITUTE it for their values !
• 4(5) + 3(3) + (–2)
4(5) = 20
• 20 + 3(3) + (–2)
3(3) = 9
• 20 + 9 + (–2)
20 + 9 = 29
• 29 + (–2)
➡️ 29 – 2 = 27
Answer: 27 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Answer:
27
Step-by-step explanation:
Consider the two tables T1 and T2 shown.Show the results of the following operations: (9 points each. Total 36 points)
Table T1
P Q R
10 A 5
15 B 8
25 A 6
Table T2
A B C
10 B 6
25 C 3
10 B 5
T1 JOIN T1.P = T2.A T2
T1 (LEFT OUTER JOIN) T1.P = T2.A T2
T1 (RIGHT OUTER JOIN) T1.Q = T2.B T2
T1 JOIN (T1.P = T2.A AND T1.R = T2.C) T2
T1 LEFT OUTER JOIN T2 ON T1.P = T2.A T1.P T1.R T2.A T2.C10 B 6 NULL NULLNULL NULL NULL 7 C T2 JOIN (T1.P = T2.A AND T1.R = T2.C) T2 T1.P T1.R T2.A T2.CNULL NULL NULL NULL NULL NULL NULL NULL
Consider the two tables T1 and T2 and the operations performed on them. The results of the operations are shown above. In the first operation, a LEFT OUTER JOIN is performed on T1 and T2, where the join is made on the basis of T1.P = T2.A. In the second operation, a JOIN is performed on T1 and T2, where the join is made on the basis of T1.P = T2.A AND T1.R = T2.C. The keyword 'LEFT OUTER JOIN' has been bolded in the main answer, while 'JOIN' has been bolded in the supporting explanation.
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How do I figure out X in this equation URGENT!!!
Step-by-step explanation:
p = 2(L+W)
98 < 2(x-2cm + 3x+5cm)
98 < 2x - 4 + 6x + 10
98 < 2x + 6x -4 +10
98 < 8x + 6........the inequality
98 - 6 < 8x
92 < 8x
11.5 < x.......the value of x
let f(t)f(t) be the number of us billionaires in year tt. in 1985 there were 13 us billionaires, and in 1990 there were 99 us billionaires. assuming the yearly increase remains constant, find a formula predicting the number of us billionaires in year tt.
The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.
The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).
The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b
where
t is the year and f(t) is the number of US billionaires in that year (t).
m is the slope of the line and b is the y-intercept.
The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)
Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.
Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.
The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129
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Can someone help ASAP? I will give lots of points
Three-part question:
A: The height of the street sign is obtained by indirect measurement method as 15 feet.
B: The two proportions Betsy can use is 5/1.5 = x/4.5 and 5/.x = 1.5/4.5
C: Using both the proportions height of the street sign is obtained as 15 feet.
What is indirect measurement?
A mathematical technique called as an indirect measurement is used to discover unknown measures of items that are challenging to measure. A direct measurement is something that can easily be measured, like a toddler's height.
The height of Betsy is h = 5 feet.
The shadow of Betsy is h' = 1.5 feet.
The height of the street sign is H = x feet.
The height of the shadow of street sign is H' = 4.5 feet.
The two proportions are -
h/h' = H/H' and h/H = h'/H'
These two can be used to find the measurement of the street sign.
To find the height of the street sign use the method of indirect measurement -
h/h' = H/H' h/H = h'/H'
Substitute the values in the given equation -
5/1.5 = x/4.5 5/x = 1.5/4.5
1.5 × x = 5 × 4.5 5 × 4.5 = 1.5 × x
1.5x = 22.5 22.5 = 1.5x
Simplify the equation further -
x = 22.5/1.5 x = 22.5/1.5
x = 15 x = 15
Therefore, the value of the x is obtained as 15 feet.
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I’ll mark brainliest if correct lol
Wilbur landed his plane.
The plane’s elevation relative to the ground (in meters) as a function of time (in seconds) is graphed.
How long was each descent by 50 meters?
Answer:
10 seconds
Step-by-step explanation:
mark two points on the line the use the slope rule to calculate it you'll find it's -5 m/s
The answer is bellow, with all the steps
Answer:1700
what is the range of Dan’s car? It’s highway EPA rating is 40mpg and the tank holds 12 gallons
The range at which Dan's car can go is 3.33 miles
What is range of a car?A car's range is the distance it can travel with the current amount of fuel in the tank.
The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.
The range of a car can be measured in the unit of distance.
Therefore the range of a car can be calculated as;
R = distance per gallon/ number of gallon.
Dan's car is 40mpg and has 12 gallons in it's tank.
Therefore it's range = 40/12
= 3.33miles.
therefore the range of Dan's car is 3.33miles
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help asap will give brainliest!!!
The exact volume of the cone is 3,087.18 cubic inches.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. The curving surface of it slopes upward towards the apex and has a round base. The radius of the base is the distance from the centre of the base to its edge, and the height of the cone is the separation between the base and the apex.
The formula for the volume of a cone is:
V = 1/3 * πr²h
Substituting the given values, we get:
V = 1/3 * 3.14 (9²) (11)
V = 1/3 * 3.14 (81)(11)
V = 1/3 (9,261.54)
V = 3,087.18 cubic inches
Hence, the exact volume of the cone is 3,087.18 cubic inches.
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Read the case study below and answer ALL the questions that follow. The topic of a research proposal submitted by a Bachelor of Business Administration Honours student at a prestigious Business School in South Africa is: An investigation into the determinants of the sustainability of small and medium-sized enterprises in Soweto The student has proposed a quantitative approach to achieve the three research objectives below: * To determine the sustainability of Small and medium-sized enterprises (SMEs) in Soweto; * To determine the factors (determinants) of SME sustainability in Soweto, and * To make practical recommendations to owner-managers of SMEs in Soweto on how to enhance the sustainability of their businesses Answer ALL the questions in this section. QUESTION 1 (20 Marks) On the basis of the student's research topic and research objectives specified above, answer the following questions: 1.1 With reference to the 5W criteria (What? Who? Why? Where? When?), critically analyse the topic (10 marks) of the research proposal. 1.2 State the aim of the proposed study. (2 marks) 1.3 (3 marks) Formulate three (3) research questions for the proposed study (Hint: the research questions should be based on the student's research objectives ). 1.4 For the proposed study, choose an appropriate research design and motivate your choice. (5 marks) QUESTION 2 (20 Marks) Based on the design you have chosen above in question 1.4 above, discuss the methodology you would follow with regard to the following:
The research proposal focuses on investigating the determinants of the sustainability of small and medium-sized enterprises (SMEs) in Soweto. The research objectives are to determine the sustainability of SMEs, identify the factors that contribute to their sustainability, and provide practical recommendations to enhance their sustainability.
1.1 The research proposal addresses the "what" by examining the determinants of SME sustainability in Soweto. It focuses on "who" by targeting owner-managers of SMEs in Soweto. The "why" is to understand the factors that influence SME sustainability. The "where" is in Soweto, South Africa, and the "when" refers to the time period during which the research will be conducted.
1.2 The aim of the proposed study is to explore and analyze the determinants of sustainability for small and medium-sized enterprises in Soweto, with the ultimate goal of providing practical recommendations to enhance their sustainability.
1.3 Three research questions for the proposed study could be:
What are the key indicators of sustainability for SMEs in Soweto?
What factors contribute to the sustainability of SMEs in Soweto?
How can owner-managers of SMEs in Soweto improve the sustainability of their businesses?
1.4 An appropriate research design for the proposed study could be a mixed-methods approach. This design would involve both quantitative and qualitative data collection and analysis methods. Quantitative data could be collected through surveys or questionnaires to measure indicators of sustainability and assess the relationship between various factors. Qualitative data could be collected through interviews or focus groups to gain a deeper understanding of the experiences and perspectives of owner-managers. The mixed-methods approach would provide a comprehensive and holistic understanding of the determinants of SME sustainability in Soweto and enable practical recommendations to be formulated based on both quantitative and qualitative insights.
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In a data set, the number of elements will always be the same as the number of: a. data point b. independent variable c. dependent variable d.observation
The number of elements will always be the same as the number of observations.
How to find the mean of a data set?
Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.
Thus, we get;
\(\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}\)
We are given that;
the number of elements=number
Now,
From observation we can say that the number of elements is equal to the number of observations.
Therefore, by mean the answer will be observation.
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in a binomial experiment, the number of successes can never exceed the number of trials. true/false
Answer:
True
Step-by-step explanation:
An expected value is another term for the mean of a probability distribution. The number of successes in a binomial experiment must range from zero to n. In a binomial experiment, the number of successes can never exceed the number of trials. The probability of a success must exceed the probability of a failure.
Suppose that: f(x) = 6x - 3
Find the average rate of change of f(x) from 1 to 3
Answer:
6
Step-by-step explanation:
The average rate of change is the same as the slope. Since the slope is the same no matter what interval you choose, the answer is 6.
Answer:
6
Step-by-step explanation:
The average rate of change is the same as the slope. Since the slope is the same no matter what interval you choose, the answer is 6.
Polygon B is a scaled copy of Polygon A using a scale factor of 5.
Polygon A’s area is what fraction of Polygon B’s area?
Answer:
1/5
Step-by-step explanation:
A: 1
B: 5
Scale is 1:5
Answer:
\(\frac{1}{25}\)
Step-by-step explanation:
Given the scale factor is 5 , then
the scale factor of areas is 5² = 25
Then A is \(\frac{1}{25}\) of B's area
Michelle's car needs repairs. The mechanic said it will be $144 for parts plus $80 an hour to repair the car. How many hours can Michelle afford to pay the mechanic if she can spend no more than $384?
Answer:
3 hours
Step-by-step explanation:
Total cost = 144 + 80h
Where h = number of hours
How many hours can Michelle afford to pay the mechanic if she can spend no more than $384?
384 = 144 + 80h
Subtract 144 from both sides
384 - 144 = 144 + 80h - 144
384 - 144 = 80h
240 = 80h
Divide both sides by 80
h = 240 / 80
= 3
h = 3 hours
Choose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 − 7x 1
5x² + 9x - 1 is the expression that represents a quadratic expression.
What is quadratic expression?
Quadratic expression is an expression with the variable with the highest power of 2. The word quadratic is derived from the word quad which means square. The expression should have the power of two and not higher or lower.A quadratic expression is of the form
ax² + bx +c = 0 where a ≠ 0
The give options are-
9x - 2
5x² + 9x - 1
-2x³ + 8x² - 7x +1
\(x^{4} - 12 x^{3} + 8x^{2} - 7x +1\)
From the given options, the only expression which is quadratic is
5x² + 9x - 1
wChoose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 −here a =5, b=9 and c=-1
Therefore, 5x² + 9x - 1 is the expression that represents a quadratic expression.
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Rhea sold 6 boxes of blueberry muffins and 8 boxes of corn muffins at the bake sale. Each box contained 18 muffins. The muffins cost $0.50 each. What is the total amount raised by the sale of the muffins?
Please help me (and thanks if you are, I very much appreciate it :))
Answer:
$126.00
Step-by-step explanation:
1 you Multiply .50×18=9
so the ratio is 9 per box
you add 6+8=14 and then 14×9=126
Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town Hall.
The length of the straight line calculated between school and the fire station is equal to 4.6 miles ( nearest tenth ).
Location of town hall is 4.3 miles directly east of the middle school.
Location of fire station is 1.7 miles directly north of town hall.
To find the length of the straight line between the school and the fire station,
Apply the Pythagorean theorem,
Which states that in a right triangle the square of the length of the hypotenuse the longest side is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance between the school and Town Hall, and the distance between Town Hall and the fire station form a right triangle,
So, we can calculate the length of the hypotenuse as,
√(4.3² + 1.7²)
≈ √(18.49 + 2.89)
≈ √21.38
≈ 4.62
≈ 4.6 miles ( Rounding to the nearest tenth)
Therefore, the length of the straight line between the school and the fire station is approximately 4.6 miles.
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The above question is incomplete, the complete question is:
Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town Hall. What is the length of a straight line between the school and the fire station? Round to the nearest tenth.
The city of London, England, has an
elevation of 11 meters.
Which of these describes the elevation
of London?
below sea level
at sea level
above sea level
Answer:
above sea level
Step-by-step explanation:
Write an equation in the slope-intercept form for the line with slope - 3/2 and y-intercept 6
Answer:
\(y = -\frac{3}{2} +6\)
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope: \(-\frac{3}{2}\)
Y-Intercept: \(6\)
\(y = -\frac{3}{2} +6\)
Marking brainliest
What do you thinks this means and why does it matter
Answer:
You didnt put anything for me to see lol
Step-by-step explanation:
Suppose that each country currently has 90 workers and each decides to transfer some amount of labor toward its area of comparative advantage. The United States transfers 10 workers away from socks toward producing cell phones. Thailand transfers 18 workers away from cell phones toward producing socks. What will be the new total output of cell phones for both countries combined?
Answer:
I got 41000 cell phones.
Step-by-step explanation:
Step 1: I figured out the amount of each workers from 90
US Sock Production: 18 workers
Thailand Sock Production: 15 workers
US Cell Production: 27 workers
Thailand Cell Production: 30 workers
Step 2: I adjusted the workers amounts to the question's changes
US Sock Production: 18 - 10 = 8 workers
Thailand Sock Productions: 18 + 15 = 33 workers
US Cell Production: 27 + 10 = 37 workers
Thailand Cell Production: 30 - 18 = 12 workers
Step 3: Find the total amount of cell phones produced
4(1000) + 37(1000) = 41000 cell phones
*12/3 = 4 because 3 workers are needed to make 1000 cell phones
Help please
9- 2x< -5 or 1/2x+13<15
The solution for the given linear equalities is x < 7 (or) x < 4.
What is linear equality?
A linear inequality is a mathematical inequality that involves a linear function. A linear inequality contains one of the inequality symbols. It shows the data which is not equal in graph form.
The given equalities are
9 - 2x < -5 (or) 1/2x + 13 < 15
Let's solve your inequality step-by-step.
9 − 2x < −5
Simplify both sides of the inequality.
−2x + 9 < − 5
Subtract 9 from both sides.
−2x + 9 − 9 < − 5 − 9
−2x < −14
Divide both sides by -2, and we get
x < 7
Let's solve your inequality step-by-step.
1/2x + 13 < 15
Subtract 13 from both sides.
1/2x + 13 − 13 < 15 − 13
1/2x < 2
Multiply both sides by 2.
x < 4
Hence, the solution for the given linear equalities is x < 7 (or) x < 4.
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Scenario 1A Calculate the following amounts for a participating provider who bills Medicare and has no deductible left. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Coinsurance amount (20% paid by) $ Medicare payment (80 percent of the PFS) $ Provider write-off $ Scenario 1B Calculate the following amounts for a participating provider who bills Medicare and remaining annual deductible for the patient. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Patient pays $100 remaining on their deductible $ Remaining amount for Insurance and patient to pay $ (PFS - $100) Coinsurance amount (20% of remaining amount) $ Total paid by patient (deductible & 20% of remaining) $ Medicare payment (80 percent of the remaining amount) $ Provider write-off $
Scenario 1A:
Coinsurance amount is $90
Medicare payment is $360
Provider write-off is $290
Scenario 1B:
Remaining amount for Insurance and patient to pay is $350
Coinsurance amount is $70
Total paid by patient is $170
Medicare payment is $280
Provider write-off is $370
Scenario 1A:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Coinsurance amount (20% paid by patient): $
Medicare payment (80% of the PFS): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Coinsurance amount (20% paid by patient):
Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)
Coinsurance amount = 0.2 * $450 = $90
Medicare payment (80% of the PFS):
Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)
Medicare payment = 0.8 * $450 = $360
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $360 = $290
Scenario 1B:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Patient pays $100 remaining on their deductible
Remaining amount for Insurance and patient to pay: $
Coinsurance amount (20% of remaining amount): $
Total paid by patient (deductible & 20% of remaining): $
Medicare payment (80% of the remaining amount): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Remaining amount for Insurance and patient to pay:
Remaining amount for Insurance and patient to pay = PFS - remaining deductible
Remaining amount for Insurance and patient to pay = $450 - $100 = $350
Coinsurance amount (20% of remaining amount):
Coinsurance amount = 20% of the remaining amount
Coinsurance amount = 0.2 * $350 = $70
Total paid by patient (deductible & 20% of remaining):
Total paid by patient = remaining deductible + coinsurance amount
Total paid by patient = $100 + $70 = $170
Medicare payment (80% of the remaining amount):
Medicare payment = 80% of the remaining amount
Medicare payment = 0.8 * $350 = $280
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $280 = $370
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help me for brainitest pls
Answer:
3/6+4/6=7/6 (or 1 1/6)
Step-by-step explanation:
Multiply 1/2 by 3, add the top and bottom numbers together
Then I simplified 7/6 to 1 1/6 because 7 goes into 6, 1 time and there is still 1 remaining
I NEED HELP!!! What is is this ----> 3x - 3y = 3 12x + 8y = -8
x = what
y = what
Answer:
3x = 3 + 2y -------------> 3x - 2y = 3 {subtracted 2y from each side of top equation}
(-4/3)x + y = -2/3 ------> -4x + 3y = -2 {multiplied bottom equation by 3}
3x - 2y = 3 ------> 12x - 8y = 12 {multiplied top equation by 4}
-4x + 3y = -2-----> -12x + 9y = -6 {multiplied bottom equation by 3}
12x - 8y = 12
-12x + 9y = -6
--------------
y = 6 {added the two equations}
3x = 3 + 2y {original top equation}
3x = 3 + 2(6) {substituted 6, in for y, into top equation}
3x = 3 + 12 {multiplied}
3x = 15 {added}
x = 5 {divided each side by 3}
x = 5 and y = 6
Step-by-step explanation:
Answer:
x= 0
y= -1
Step-by-step explanation:
Hope this helps.
Albertostart color #28ae7b, start text, A, l, b, e, r, t, o, end text, end color #28ae7b and \blue{\textrm{Bianca}}Biancastart color #6495ed, start text, B, i, a, n, c, a, end text, end color #6495ed run a 50\text{ km}50 km50, start text, space, k, m, end text race. The illustration below shows the graph of the position of the two runners as a function of time.
Complete the following sentences based on the graph of the function.
Early in the race,
runs faster.
Alberto maintains a speed of
\text{ km/h} km/hstart text, space, k, m, slash, h, end text during the first hour of the race.
However, after one hour he gets tired and must take a break. Unfortunately, he falls asleep!
Meanwhile, Bianca's running speed
.
The first person to cross the finish line is
.
Bianca is the first to reach the finish line with her speed.
What is speed?
The quantity of the change in an amount that exceeds over time or the quantity of the change in that amount that exceeds per unit of time makes the speed of that object, also abbreviated as v in kinematics, a scalar number. As the length of the time period approaches 0, the instantaneous speed represents the upper bound of the average speed. The distance measured by an object in a time interval is divided by the length of the interval to determine its average speed. Speed and velocity are not quite the same thing.Alberto runs faster in the beginning of the race.
For the first hour of the race, Alberto keeps a 50 km/h pace.
Bianca's running pace is exponential in the meantime.
Bianca is the first to reach the finish line with her speed.
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Answer: Initially,
Alberto
Albertostart runs faster.
Alberto maintains a speed of
20km/h during the first hour of the race.
Meanwhile, Bianca's running speed is increasing
The first person to cross the finish line is Bianca
Step-by-step explanation:
The following are house prices in Southern California:
$750,000 $680,000 $600,000 $880,000 $1,200,000 $760,000 $480,000
What is the median house price?
Answer:
$750,000
Step-by-step explanation:
$750,000 $680,000 $600,000 $880,000 $1,200,000 $760,000 $480,000
Write the prices in increasing order and choose the middle one.
$480,000 $600,000 $680,000 $750,000 $760,000 $880,000 $1,200,000
Answer: $750,000
The largest Easter Basket ever made in out city was in the shape of a huge circle and had a circumference of 20 feet. How many feet wide was the Easter Basket? (Round to the tenths place)
Answer:
13
Step-by-step explanation:
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.,kjhuilk;jk;lk'
write the equation that is best represented by the graph? (look at the picture attached)
The Equation of the Line is \(y=1.5x+0.5\)
How to find the Equation of the line ?
the Equation of the line is described by the following Relation.
\(\frac{y-y_{1}}{x-x_{1}} =\frac{y_{2}-{y_{1}}}{x_{2}-x_{1}} \\\\\frac{y-0.5}{x-0} =\frac{2-0.5}{1-0} \\\\y-0.5=1.5x\\\\y=1.5x+0.5\)
There are different methods to find the equation of line like
1.) point slop form
2.) intercept form
3.) parametric form
in this problem i have used the concept of point slop form.
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The equation of the line best represented by the graph is y = 1.5x + 0.5. The solution has been obtained by using the slope - intercept form.
What is the slope - intercept form?
When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
We are given a graph with a line drawn.
The coordinates of the line are (0, 0.5) and (1, 2).
Using this, we will find the slope.
⇒ m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)
⇒ m = \(\frac{2 -0.5 }{1 -0}\)
⇒ m = 1.5
We know that the general form of slope - intercept form is y = mx + b.
So, by substituting (0, 0.5) in the equation, we get
⇒ b = 0.5
Thus, the equation comes out to be y = 1.5x + 0.5.
Hence, the equation of the line best represented by the graph is
y = 1.5x + 0.5.
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