Answers
Answer:
\( \sqrt{32} \)
Step-by-step explanation:
in order to find the length of the diagonal you need to first find the the side lenths. perimeter of a square = 4x were x is the side length so we know that 16=4x we can the sovle for x by divided by 4 so x=4 then if you cut a square diagonaly it makes a triangle. so since we know that the length and with of the triangle our 4 and 4. we just need to find c aka the missing lenth so we can use Pythagorean Theorem a^2+b^2=c^2 a and b our 4 so we can plug those in to our equation. 4^2+4^2=c^2 now we jus have to solve for c and we get our answer. 4^2 is 16 so 16 +16 = 32 so 32=c^2 and the square root both sides and we get that c=
\( \sqrt{32} \)
hopefully that helps
have a nice one
Related Questions
Southeastern Bell stocks a certain switch connector at its central warehouse for supplying field service offices. The yearly demand for these connectors is 15,400 units. Southeastern estimates its annual holding cost for this item to be $24 per unit. The cost to place and process an order from the supplier is $74. The company operates 300 days per year, and the lead time to receive an order from the supplier is 2 working days.
Answers
The economic order quantity (EOQ) for the switch connectors is approximately 97 units.
To determine the economic order quantity (EOQ) for the switch connectors, we can use the following formula:
EOQ = √((2 * Annual Demand * Order Cost) / Holding Cost)
Given the following information:
Annual Demand = 15,400 units
Holding Cost = $24 per unit
Order Cost = $74 per order
Plugging in the values into the formula, we get:
EOQ = √((2 * 15,400 * 74) / 24)
EOQ = √(227,200 / 24)
EOQ = √(9,466.67)
EOQ ≈ 97.28
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A population has a current size of 150. if λ is 1.2, what will the expected population size be after two generations? group of answer choices a. 144 b. 180 c. 200 d. 216
Answers
The expected population size after two generations is 216.
To calculate the expected population size after two generations using the given value of λ, we can use the formula:
\(Nt = N0 * lemda ^{t}\)
where Nt is expected population size after t generations,
N0 is the initial population size, and lemda (λ) is the geometric growth rate.
Here, initial population size is N0 = 150, and the growth rate is λ = 1.2. We want to find the expected population size after two generations, so t = 2.
Putting these values into the formula, we get:
\(Nt = 150 * (1.2)^{2} \\Nt = 150 * 1.44\\Nt = 216\)
Therefore, the expected population size after two generations is 216.
So, the correct answer is option (d) 216.
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Please help me with my Math homework (about Angles)
Answers
The measures of all the numbered angles are:
m<1 = 60 degrees
m<2 = 65 degrees
m<3 = 55 degrees
m<4 = 55 degrees
m<5 = 60 degrees
m<6 = 60 degrees
m<7 = 65 degrees
m<8 = 65 degrees
m<9 = 60 degrees
m<10 = 55 degrees
m<11 = 65 degrees
m<12 = 65 degrees
What are intersecting angles ?
In geometry, an angle is a figure formed by two rays (or line segments) that have a common endpoint, called the vertex of the angle. The rays are called the sides of the angle. Angles are typically measured in degrees or radians, and are used to describe the amount of turn or rotation between the two sides.
The measure of an angle is the amount of rotation between the two sides, usually measured in degrees. One complete rotation is equal to 360 degrees. An angle can be classified as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees but less than 360 degrees).
According to the question:
We are given that angle 1 is 60 degrees.
We are given that angle 2 is 65 degrees.
Angles 1, 2, and 3 form a straight line, so the sum of angles 1 and 2 is equal to 180 - angle 3. We can use this to find angle 3:
angle 1 + angle 2 + angle 3 = 180
60 + 65 + angle 3 = 180
angle 3 = 180 - 60 - 65 = 55 degrees
Angles 3 and 4 form a straight line, so angle 4 is also 55 degrees.
Angles 2, 4, and 5 form a straight line, so the sum of angles 2 and 4 is equal to 180 - angle 5. We can use this to find angle 5:
angle 2 + angle 4 + angle 5 = 180
65 + 55 + angle 5 = 180
angle 5 = 180 - 65 - 55 = 60 degrees
Angles 1, 5, and 6 form a straight line, so angle 6 is also 60 degrees.
Angles 3, 6, and 7 form a straight line, so the sum of angles 3 and 6 is equal to 180 - angle 7. We can use this to find angle 7:
angle 3 + angle 6 + angle 7 = 180
55 + 60 + angle 7 = 180
angle 7 = 180 - 55 - 60 = 65 degrees
Angles 2, 7, and 8 form a straight line, so angle 8 is also 65 degrees.
Angles 4, 8, and 9 form a straight line, so the sum of angles 4 and 8 is equal to 180 - angle 9. We can use this to find angle 9:
angle 4 + angle 8 + angle 9 = 180
55 + 65 + angle 9 = 180
angle 9 = 180 - 55 - 65 = 60 degrees
Angles 5, 9, and 10 form a straight line, so angle 10 is also 60 degrees.
Angles 6, 10, and 11 form a straight line, so the sum of angles 6 and 10 is equal to 180 - angle 11. We can use this to find angle 11:
angle 6 + angle 10 + angle 11 = 180
60 + 60 + angle 11 = 180
angle 11 = 180 - 60 - 60 = 60 degrees
Angles 7, 11, and 12 form a straight line, so angle 12 is also 65 degrees.
Therefore, the measures of all the numbered angles are:
m<1 = 60 degrees
m<2 = 65 degrees
m<3 = 55 degrees
m<4 = 55 degrees
m<5 = 60 degrees
m<6 = 60 degrees
m<7 = 65 degrees
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Counting jails and prisons, approximately how many citizens are incarcerated? a. 1 million b. 2.3 million c. 3 million d. 4.3 million.
Answers
In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.
It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.
These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.
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Draw a line from (2,3) to (21,12) using DDA?
Answers
DDA (Digital Differential Analyzer) is a line drawing algorithm that works by dividing the line into several small segments and then determining the endpoints of each segment by calculating the difference between the coordinates.
To draw a line from (2,3) to (21,12) using DDA, follow these steps:
Step 1: Calculate the slope of the line Using the formula slope (m) = (y2 - y1) / (x2 - x1), we can determine the slope of the line between the two points:(12 - 3) / (21 - 2) = 0.5625
Step 2: Determine the number of pixels to be drawn
We need to determine the number of pixels required to draw the line. The distance between the two points can be calculated using the Pythagorean theorem.√\(((21-2)² + (12-3)² )= √(19² + 9²) = √(361 + 81) = √442 = 21.03\)
Step 3: Determine the increment values for x and y
Since we know the slope and the number of pixels required to draw the line, we can determine the increment values for x and y.
d\(x = (x2 - x1) / n = (21 - 2) / 21 = 0.9524dy = (y2 - y1) / n = (12 - 3) / 21 = 0.4286\)
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Use the information provided to answer Part A and Part B for question 11.
Three congruent figures are shown in the coordinate plane.
8
-7
-5
9-3-7 65
A
N
-4
-5
-6
-7
-8
3
11. Part A
Which statement describes a possible sequence of transformations that
transforms figure 1 into figure 2?
A. a reflection across the x-axis, followed by a translation 2 units to the left
B. a reflection across the x-axis, followed by a translation 3 units to the right
C. a rotation 180° clockwise about the origin, followed by a translation
2 units to the left
D. a rotation 180° clockwise about the origin, followed by a translation
3 units to the right
Answers
B. A reflection across the x-axis followed by a translation 3 units to the right.
The correct statement about the congruent figures is,
⇒ a reflection across the x-axis, followed by a translation 3 units to the right.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Three congruent figures are shown in the coordinate plane.
Now, From figure A and figure B,
Figure B is reflection across the x-axis, followed by a translation 3 units to the right across the figure A.
Thus, The correct statement about the congruent figures is,
⇒ a reflection across the x-axis, followed by a translation 3 units to the right.
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Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
Answers
The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.
To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.
On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.
Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.
Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.
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a simple random sample of 1000 americans found that 62% were satisfied with the service provided by the dealer from which they bought their car. a simple random sample of 1000 canadians found that 59% were satisfied with the service provided by the dealer from which they bought their car. the sampling variability associated with these statistics is
Answers
The sampling variability associated with these statistics is option(A) not exactly same, but very close
Random sampling variability is expected to occur in both samples, but the exact amount of variability may differ due to chance
The size of sampling variability depends on the sample size and the variability in the population, not on the sample proportion alone.
The size of the population does not affect the amount of sampling variability, but it can affect the margin of error and the precision of the estimate.
The dispersion of the population does not necessarily lead to more variable views, and it does not affect the amount of sampling variability. Sampling variability is caused by chance fluctuations in the sample, not by the geographic distribution of the population.
Therefore, correct option is option (A) not exactly same, but very close
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URGENTTT PLEASE!! in middle of test help!
I WILL MARK BRAINIEST! if you answers in under 5mins!
Answers
Answer:
equation: 2(2w + 2) = 60
length = 16
width = 14
Step-by-step explanation:
width = w
length = w + 2
perimeter = 2(w + w + 2) = 60
equation: 2(2w + 2) = 60
4w + 4 = 60
4w = 56
w = 14
width = 14
length = w + 2 = 14 + 2 = 16
length = 16
A company uses paper cups shaped like cones for its water cooler. Each cup has a height of 8cm, and the base has a radius of 3cm . How much water is needed to fill 225 cups?
Answers
The Little Twelve Football Conference has two
divisions, with ten teams in each division. Each team
plays each of the other teams in its own division twice
and every team in the other division once. How many
conference games are scheduled?
Answers
The number of conference games scheduled is 280.
What is a combination?A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.
Given:
The Little Twelve Football Conference has two divisions,
with ten teams in each division.
Each team plays each of the other teams in its own division twice, and every team in the other division once.
The number of conference games scheduled,
= ¹⁰C₂ x 2 + 10 x 10
= 90 x 2 + 100
= 280 games.
Therefore, 280 games are scheduled.
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The function f(x) = x^2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)^2?
Answers
We are given the following parent function f(x)
\(f(x)=x^2\)The transformed function g(x) is
\(g(x)=(x+1)^2\)Notice that the change is done in the horizontal direction.
Recall that the transformation rule for the horizontal translation to the left is given by
\(f(x)\rightarrow f(x+c)\)Where c is the number of units by which the graph is shifted to the left.
So, we should expect that the graph is horizontally shifted to the left by 1 unit.
Therefore, the above is graph represents the transformed function g(x) which is horizontally shifted to the left by 1 unit.
The summer and winter solstices are the longest day and night of the year, respectively. The summer solstice happens between June 20 and June 21, while the winter solstice is between December 21 and December 23. At a latitude of 28° the summer solstice is 14.5 hours long and the winter solstice is 14 hours long. Write a sinusoidal equation modeling the hours of daylight in a year. Use t for the variable and measure t in weeks. For the purposes of this problem, idealize a year to be 52 weeks long, with the winter solstice a week before the new year. h(t) = __________
Answers
The correct answer is h(t) = 14.25 + 0.25 * sin((π/26) * t)
To model the hours of daylight in a year using a sinusoidal equation, we can consider the average length of daylight, the amplitude of the variation, and the period of the function.
Given:
Summer solstice (longest day) is 14.5 hours
Winter solstice (longest night) is 14 hours
Let's analyze the information:
Average daylight: The average daylight throughout the year would be the average of the summer and winter solstices. It can be calculated as:
Average daylight = (14.5 + 14) / 2 = 14.25 hours
Amplitude: The difference between the average daylight and the longest day or night is the amplitude. In this case, the amplitude is half the difference between the summer and winter solstices. It can be calculated as:
Amplitude = (14.5 - 14) / 2 = 0.25 hours
Period: We are modeling the function over a year, which we'll consider as 52 weeks. Since we want to measure time in weeks (t), the period of the function is 52 weeks.
Putting all the information together, we can write the sinusoidal equation:
h(t) = Average daylight + Amplitude * sin((2π / Period) * t)
Substituting the values we calculated:
h(t) = 14.25 + 0.25 * sin((2π / 52) * t)
Simplifying further, the sinusoidal equation modeling the hours of daylight in a year is:
h(t) = 14.25 + 0.25 * sin(π/26 * t)
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Assuming the shapes are similar, find the value of the variable. PLEASE HELP
Answers
Alguien me ayuda .
(please help).
Answers
1) note that when graphed, 3x - 4y = 7 will show a straight line. This means that it is a linear equation.
2) when written in standard form, the above equations will become:
3x+y = 1 and4x -5y =23) the linear equation for the above is y = (-1/2)x + 150. See the graph attached.
What is a linear equation?A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it.
A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant.
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What is the domain? I need help on this problem
Answers
The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x ≥ -6
How to determine the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
\(f(x) = \sqrt{\frac{1}{3}x + 2\)
Set the radicand greater than or equal to 0
So, we have
1/3x + 2 ≥ 0
Next, we have
1/3x ≥ -2
So, we have
x ≥ -6
Hence, the domain of the function is (d) x ≥ -6
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for the following exercise, consider the following scenario: a town has an intial population of 50000 . it grows at a constant rate of 5000 per year. find the linear function that model's the town's population p as a function of the year, t , where t is the number of years since the model began.
Answers
The required function is P(t)=50000 + 5000t.
In this problem we need to form the function of the population in a town.
Here it is given that the initial population of the town is 50000.
the rate at which the population increases is 5000 per year.
So, the increase for the first year will be 5000. And the population will be 55000.
Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)
= 60000
So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.
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Molly ate 1/4 pint of ice-cream. Her sister did not want the last 2/4 pint of her own ice-cream, so Molly ate it. How much ice-cream did Molly eat? Pint
Answers
Answer:
3/4 a pint
Step-by-step explanation:
1/4 + 2/4 = 3/4
John has 4 yards of fabric. Jane has 120 inches of fabric. Who has more fabric? How much more? divied
Answers
Answer:
John has more fabric.
Step-by-step explanation:
There are 36 inches in one yard so I multiplied 36x4 and got 144 inches, this is more than 120 inches.
Answer:
John has more fabric
24 more inches
Step-by-step explanation:
Let's convert John's 4 yards of fabric into inches so we can compare with the same units
1 yard = 3 feet
So 4 yards are equivalent to 12 feet
1 feet = 12 inches
Therefore 12 feet has 144 inches
John has 144 inches of fabric and Jane has 120 inches of fabric
144>120
John has more
How much more?
We can subtract to find the difference: 144-120=24
24 more inches of fabric
The earth travels one full rotation around the sun in approximately 365.25 days.
How many minutes does it take for the earth to travel one full rotation around the sun?
Show your work. Make sure to include units in your answer.
Answers
===================================================
Work Shown:
1 full rotation = 1 year
1 year = 365.25 days (approximate)
1 day = 24 hours
1 hour = 60 minutes
Converting from 1 year to minutes gives
\(1 \text{ year} = \left(1 \text{ year}\right)*\left(\frac{365.25 \text{ days}}{1 \text{ year}}\right)*\left(\frac{24 \text{ hrs}}{1 \text{ day}}\right)*\left(\frac{60 \text{ min}}{1 \text{ hr}}\right)\\\\1 \text{ year} = \left(1*365.25*24*60\right)\text{ min}\\\\1 \text{ year} = 525,960 \text{ min}\\\\\)
So basically we just multiply out 365.25, 24, and 60 to get the answer.
On January 1st, 2017, your great uncle creates an account in your name and invests $20,000 in treasury bills. The nominal rate on the T-bills is 1.95% compounded every 73 days. Exactly 6 months later, your mother deposits $10,000 into an investment account, compounding continuously at 4% per year. What is the combined value of these two accounts on January 1st, 2019 ?
Answers
The combined value of the two accounts on January 1st, 2019, is approximately $31,642.05.
To solve this problem, we'll calculate the value of each investment separately and then combine them.
First, let's calculate the value of your great uncle's investment in treasury bills. The nominal rate of 1.95% compounded every 73 days can be converted to an effective rate per year using the formula:
Effective rate = (1 + (nominal rate / m)) ^ m - 1
Where "m" is the number of compounding periods per year. In this case, there are approximately 365 days in a year, so the number of compounding periods is:
m = 365 / 73 = 5
Effective rate = (1 + (0.0195 / 5)) ^ 5 - 1 = 0.0200
Now, let's calculate the value of the treasury bills investment after 2 years (from January 1st, 2017, to January 1st, 2019):
Value of treasury bills = $20,000 * (1 + 0.0200)^(2 * 365/73) = $20,000 * (1.0200)^(10) ≈ $20,825.40
Next, let's calculate the value of your mother's investment, which is compounding continuously at a rate of 4% per year:
Value of mother's investment = $10,000 * e^(0.04 * 2) ≈ $10,816.65
Finally, let's calculate the combined value of these two accounts:
Combined value = Value of treasury bills + Value of mother's investment
= $20,825.40 + $10,816.65 ≈ $31,642.05
Therefore, the combined value of the two accounts on January 1st, 2019, is approximately $31,642.05.
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If you vertically compress the exponential parent function f(x)=2^x by a factor of 3
Answers
Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.
If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.
Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).
This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.
The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.
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Please help a girl out:
Answers
Answer:
Look at the image.
Step-by-step explanation:
If 12 is 24%, then half of the percent is the actual number.
36% = 18
24% = 12
18% = 9
22% = 11
18 + 12 + 9 + 11 = 50
18 students would like to learn Spanish.
m+n+ex=2m-x find x pls help me
Answers
Answer:
x = \(\frac{m-n}{e+1}\)
Step-by-step explanation:
m + n + ex = 2m - x ( add x to both sides )
m + n + ex + x = 2m ( subtract m + n from both sides )
ex + x = 2m - m - n = m - n ( factor out x from each term on the left side )
x(e + 1) = m - n ← divide both sides by (e + 1)
x = \(\frac{m-n}{e+1}\)
x +ex=2m -m-n
x(1+e)/(1+e) =2m-m-n/(1+e)
X= 2m-m-n/(1 +e)
una caja de 25 newtons se suspende mediante un cable con diámetro de 2cm¿cuál es el esfuerzo aplicado al cable?
Answers
El cable experimenta un esfuerzo axial de 79577.472 pascales por el peso de la caja.
¿Cómo calcular el esfuerzo aplicado sobre el cable?
La caja tiene masa y está sometida a un campo gravitacional, por tanto, tiene un peso (W), en newtons. Por el principio de acción y reacción (tercera ley de Newton), encontramos que el cable es tensionado debido a ese peso y su área transversal experimenta un esfuerzo axial (σ), en pascales.
Asumiendo una distribución uniforme de la fuerza sobre toda la superficie transversal de la cuerda, tenemos que el esfuerzo axial se calcula mediante la siguiente expresión:
σ = W / (π · D² / 4)
Donde:
W - Peso de la caja, en newtons.D - Diámetro del área transversal de la caja, en metros.Si sabemos que W = 25 N y D = 0.02 m, entonces el esfuerzo axial aplicado a la cuerda es:
σ = 25 N / [π · (0.02 m)² / 4]
σ ≈ 79577.472 Pa
ObservaciónLa falta de problemas verificados en español sobre esfuerzos axiales obliga a buscar uno equivalente en inglés.
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a lottery consists of selecting 5 numbers out of 45 numbers. you win $10 if exactly three of your 5 numbers are matched to the winning numbers chosen. what is the probability of winning the $10? round your answer to six decimal places.
Answers
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
first number: 1/25 chance because we only want 1 out of the 25 possibilities.Second number: 1/24 because 1 number was already taken out.Third: 1/23Fourth: 1/22Fifth: 1/21Sixth: 1/20The chance of all of these events happening right after another is 1/25 x 1/24 x 1/23 x 1/22 x 1/21 x 1/20 = 1/127512000, or about 1 in a hundred million.learn more about probability click here:
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The newly connected LRT2 line is being tested for public used a week after. The train is made to accelerate very slowly from rest, giving its 0.30 m radius wheels an angular acceleration of 0.20 rad/s2. After testing, the wheels have made 200 revolutions. Express the angular displacement in radians per second.
Answers
The given problem involves the angular kinematics of a train's wheels during its acceleration. Angular kinematics is a branch of physics that deals with the motion of objects in circular motion, and it includes concepts such as angular displacement, velocity, and acceleration. In this problem, we are given a specific scenario where a train is being tested for public use, and its wheels have a radius of 0.30 m and an angular acceleration of 0.20 rad/s2. We are asked to find the angular displacement of the wheels in radians per second after they have made 200 revolutions. To do this, we need to first find the total angular displacement of the wheels, which is equal to the product of the number of revolutions and the angle covered by each revolution. By applying the appropriate formula and converting the angle to radians, we can solve for the angular displacement in radians. The concept of angular kinematics is important in many areas of physics and engineering, including the design and analysis of rotating machinery and vehicles.
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The angular displacement after testing is approximately 12.73 radians per second.
To answer your question, we need to first convert the number of revolutions to radians and then use the given angular acceleration to find the angular velocity.
1. Convert revolutions to radians:
200 revolutions * (2π radians/revolution) = 400π radians
2. Use the angular displacement (θ) and angular acceleration (α) to find the angular velocity (ω):
θ = 0.5 * α * t^2
400π = 0.5 * 0.20 * t^2
Solve for t:
t^2 = (400π) / 0.1
t ≈ 63.66 seconds
3. Calculate angular velocity (ω) using angular acceleration (α) and time (t):
ω = α * t
ω = 0.20 rad/s² * 63.66 s
ω ≈ 12.73 rad/s
The angular displacement after testing is approximately 12.73 radians per second.
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Determine if the following functions are Well-Defined or Not Well-Defined 1. f(x)=x/12 2. g(x)=1/(x−3)
3. h(x)=5/(1+∣x∣) 4. i(x)=sqrt(−5)
Answers
Function 1, 2 and 3 are well-defined while function 4 is not well-defined.
A function f : A -> B is well-defined if f(a) is unique for all a in A. If a function is not well-defined, then it assigns different values to the same input, which violates the fundamental definition of a function. Here are the solutions to the given question:
1. f(x) = x/12
This function is well-defined since each input (x) is mapped to a unique output (x/12). Therefore, the function is well-defined.
2. g(x) = 1/(x - 3)
This function is well-defined since each input x is mapped to a unique output (1/(x-3)) that exists for all x ≠ 3. Therefore, the function is well-defined.
3. h(x) = 5/(1 + |x|)
This function is well-defined since each input x is mapped to a unique output (5/(1 + |x|)) that exists for all x. Therefore, the function is well-defined.
4. i(x) = √(-5)
This function is not well-defined because there is no real number whose square is negative. Therefore, the function is not well-defined.
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If Albert owns x model airplanes and Maxim owns x + 13 model airplanes, then Albert and Maxim own___ model airplanes together. Albert owns ___ less model airplanes than Maxim.
Answers
Answer:
2x + 13
13
Step-by-step explanation:
Albert and Maxim own
x + (x + 13) = 2x + 13 model airplanes together
Albert owns
(x + 13) - x = 13 less model airplanes than Maxim.
Answer:
They own 2x+13 model airplanes together
Albert owns 13 less model airplanes than Maxim
What is the product of |(−12)3 ÷(14)2|
Answers
Answer:
1.29
Step-by-step explanation:
-12x3=-36
14x2=28
-36/28=-1.29
I-1.29I
Answer:
0.428571428571
Step-by-step explanation:
|-36/84|
|-0.428571428571|
0.428571428571