The critical points are y = 0 and y = 4.
What do you mean by differential equation?A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.
The critical points of the differential equation dy/dx = y^2 - 4y are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:
y² - 4y = 0
y(y - 4) = 0
So the critical points are y = 0 and y = 4.
For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.
At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.
At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.
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The critical points are y = 0 and y = 4.
What do you mean by differential equation?A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.
The critical points of the differential equation [tex]\frac{dy}{dx} = y^{2} - 4y[/tex] are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:
[tex]y^{2} - 4y[/tex]= 0
[tex]y(y-4)[/tex] = 0
So the critical points are y = 0 and y = 4.
For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.
At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.
At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.
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nasa launches a rocket at seconds. suppose its height, in meters above sea-level, as a function of time is given by . how high above sea-level does the rocket get at its peak? round your answer to 2 decimal places. the rocket peaks at meters above sea-level.
The rocket peaks at 5000 meters above sea-level.
The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:
h'(t) = -10t + 1000
h'(t) = 0 => t = 100
So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:
h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000
Therefore, The rocket peaks at 5000 meters above sea-level.
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The rocket peaks at 5000 meters above sea-level.
The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:
h'(t) = -10t + 1000
h'(t) = 0 => t = 100
So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:
h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000
Therefore, The rocket peaks at 5000 meters above sea-level.
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Write the next three terms of the geometric sequence -2, 4, -8, 16, …
Answer:
-32, 64, -128
Step-by-step explanation:
Each term is -2 times the previous term. This means the next term is
(-2) x 16 = -32
Then,
(-2) x (-32) = 64
and lastly,
(-2) x 64 = -128
A single die is rolled 100 times. List the probabilities below from leat to greatest. P(odd), P(>4), P(prime), P(8)
The probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).
What is probability?
Calculating probability is a method of determining how likely something is to occur. The probability scale runs from 0 to 1, where 0 denotes impossible and 1 denotes certainty.
We are given that a single die is rolled 100 times.
So, the outcomes can be {1,2,3,4,5,6}
Now,
P(odd) = Probability of odd numbers
Odd numbers are 1, 3 and 5
So, P(odd) = 3/6 = 1/2
P(>4) = Probability of numbers greater than 4
Numbers greater than 4 are 5 and 6
So, P(>4) = 2/6 = 1/3
P(prime) = Probability of prime numbers
Prime numbers are 1, 2, 3 and 5
So, P(prime) = 4/6 = 2/3
P(8) = Probability of number 8
In a dice, the maximum number is 6
So, P(8) = 0
Hence, the probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).
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What is the Side Angle Side Formula?
Side angle side formula is used to prove congruent triangles.
What are congruent triangles?
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has a symbol ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
Side angle side rule:
The triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
There are four rules of congruent triangles.
1) Side angle side
2) Side side side
3) Angle angle angle
4) Angle side angle
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Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Let x be a random variable representing time to failure (in hours) at 90% breaking strength.
0. 52 1. 80 1. 52 2. 05 1. 03 1. 18 0. 80 1. 33 1. 29 1. 12
3. 34 1. 54 0. 08 0. 12 0. 60 0. 72 0. 92 1. 05 1. 43 3. 05
1. 81 2. 17 0. 63 0. 56 0. 03 0. 09 0. 18 0. 34 1. 51 1. 45
1. 52 0. 19 1. 55 0. 02 0. 07 0. 65 0. 40 0. 24 1. 51 1. 45
1. 60 1. 80 4. 69 0. 08 7. 89 1. 58 1. 64 0. 03 0. 23 0. 72 (a) Find the range.
(b) Use a calculator to calculate ?x and ?x2. (Round your answers to two decimal places. )
?x =
?x2 =
On the NASA space shuttles, a substance called kevlar epoxy is employed. This epoxy's strands underwent testing for 90% breaking strength.
The range is: 7.87The values of ∑X and ∑X² are respectively: 62.12 and 164.3516The values of the sample mean, variance and standard deviation are respectively: 1.24, 1.78 and 1.334The coefficient of variation is: 107.356Mean, Range, variance, standard deviation
A) Formula for range is;
Range = Highest term - Lowest term
Range = 7.89 - 0.02
Range = 7.87
B) Sum of all the given 50 epoxy samples is gotten to be;
∑X = 62.12
From online statistics calculator, we have; ∑X² = 164.3516
C) Formula for sample mean here is;
x' = ∑x/n
x' = 62.12/50
x' = 1.24
Formula for variance is;
σ² = [∑x² - [(∑x)²/n]]/(n - 1)
σ² = (164.3516 - (62.12²/50))/(50 - 1)
σ² = 1.78
Formula for the standard deviation is;
σ = √variance = √1.78
σ = 1.334
D) Formula for coefficient of variation is;
CV = (σ/x') * 100
CV = (1.33379/1.2424) * 100
CV = 107.356
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50 points, PLS HELp!
Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid. (50 points)
The equivalent ratios are given as follows:
21/7 = 3.24/8 = 3.27/9 = 3.Hence the coordinates are given as follows:
(7,21).(8,24).(9, 27).As the constant of the proportional relationship is of 3, starting from the origin, the points are plotted always moving one unit right (x) and three units up (y).
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
Then the constant is obtained as follows:
k = y/x.
For this problem, the constant is given as follows:
k = 21/7 = 24/8 = 27/9 = 3.
(representing the equivalent ratios).
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State the converse of the inscribed angle theorem do you think the converse is true
The given statement can be justify by using angle inscribed theorem. The angle inscribed theorem define as the angle inscribed in a circle is half of the center angle which subtends same arc of the circle.
What is inscribed angle?
When two chords intersect on a circle, an inscribed angle is the angle that is created inside the circle. It can alternatively be described as the angle formed at a particular point on a circle by two specified points. Alternatively, two chords of the circle sharing an endpoint define an inscribed angle.
Angle inscribed theorem
As per the inscribed angle theorem angle inscribed in a circle is half of the center angle so the angle would be or .
In geometry right angle is
Thus, the second corollary, that an angle inscribed in a semicircle is a right angle.
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Given the graph below, find the length of the segment. Round to the nearest hundredth.
The length of the segment MN = 5.4 unit
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The length of the segment MN = The distance from (-1, 2) and (4, 0).
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
The length of the segment MN = √{(4+ 1)² + (0 - 2)²}
The length of the segment MN = √{5)² + (2)²}
The length of the segment MN = √{29} = 5.385
Therefore, the length is 5.4 unit.
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what does -4xy equal to
Answer: I can not give an answer because you have not given enough information to answer it. If you could add a picture it would be greatly appreciated.
A cla recorded the mae,in gram,of 20 bag of rice. Their reult are hown on the right. Explain how all three tudent could be correct?
All three students could be correct if they recorded the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces.
In order for all three students to be correct, they would have to be recording the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces. This would explain why each student has a different answer, as they are all measuring the mass in different units. The only way to ensure accuracy would be to measure the mass in the same unit of measurement, so that all students have the same answer.
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What is the formula for the arc length of the sector of a circle?
If PQ subtends angle at the circle's center, then let PQ be an arc with radius r and a center at O. Thus, the arc length of PQ is given by PQ = /360° (2r), where is a degree.
What is angle?A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. From the Latin word "angulus," which meaning "corner," comes the English term "angle." The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.Two lines intersect at a shared point to produce an angle. Degrees, denoted by the symbol °, are used to measure them. Acute, right, obtuse, and reflex angles are among the four crucial types of angles. 360° makes up a full circle. It has completed two full rotations if the angle is more than 720°.To learn more about angle, refer to:
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Evaluate the function at the specified values of the independent variable. Simplify the results. f(x) = 5x + 7 (a) f(-8) (b) f(0.6) (c) f(x + 9)
At the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
Given that the function is:
f(x) = 5x + 7
To evaluate the function at the specified values substitute the value in x:
a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33
b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10
c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52
Hence, at the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.
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Alex drew two lines and two transversals. He wants to know the measures of angles 1, 2, and 3. Identify the measure of each angle and the relationship used to find the angle measure.
2 vertical parallel lines, M and N, intersected by 2 transversal lines P and Q. Lines P and Q intersect each other on line N. Between lines M and N, the 2 angles formed by lines M and P are labeled 1 and one hundred thirty-five degrees, and the smaller angle formed by lines M and Q is labeled 3. The non-adjacent angles formed by lines P and Q are labeled 2 and ninety-five degrees.
m∠
1=
° because ∠
1 and the angle measuring 135° are
Choose...
angles.
m∠
2=
° because ∠
2 and the angle measuring 95° are
Choose...
angles.
m∠
3=
° because ∠
1, ∠
2, and ∠
3 form a
Choose...
.
<1 = 45 degrees- are supplementary angles.
<2 = 95 degrees - vertical angles.
<3 = 40 degrees because 1, 2, and 3 form a triangle.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Using the provided figure, we can
Because <1 and the angle with a measure of 135 degrees are supplementary angles, m<1 = 45 degrees.
and, Because <2 and the angle measuring 95 degrees are vertical angles, m<2 = 95 degrees.
Also, Because 1, 2, and 3 make a triangle, m<3 = 40 degrees.
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4 in
6 in.
4 in
Find the area of the unshaded region
The area of the unshaded region in the given diagram is 64π in²
Calculating the area of the unshaded regionFrom the question, we are to determine the area of the unshaded region in the given diagram
Area of the unshaded region = Area of the medium circle - Area of the small circle
The formula for calculating the area of a circle is given as
A = πr²
Where A is the
and r is the radius
From the diagram,
Radius of the medium circle = 6 in + 4 in
Radius of the medium circle = 10 in
and
Radius of the small circle = 6 in
Thus,
Area of the unshaded region = π(10)² - π(6)² in²
Area of the unshaded region = 100π - 36π in²
Area of the unshaded region = 64π in²
Hence, the area is 64π in²
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A park is rectangular with a length of 2/3 miles. If the area of the park is 1/2 square mile, what is its width? Input your answer as a fraction
Answer: 3/2 miles
Step-by-step explanation: Area of Park = Length * Width
Width = Area / Length= (6/8) / (1/2) = (6/8) * (2/1) = 3/2 miles.
The measures of the angles in triangle UVW are shown in the diagram.
What is the value of x ?
Answer:
3x-9+34+24=180 (because the sum of angle of triangle is 180 )
3x+49=180
3x=180-49
3x=131
x=131÷3
x=43.67
Show whether each logical expression is a tautology, contradiction or neither.
(a) (p ⨠q) ⨠(q â p)
(b) (p â q) â (p ⧠¬q)
(c) (p â q) â p
(d) (p â q) ⨠p
(e) (¬p ⨠q) â (p ⧠¬q)
(f) (¬p ⨠q) â (¬p ⧠q)
The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.
(a) Neither - This expression can be written as ¬(p ∨ q) ∧ (q ∨ ¬p), which is neither a tautology nor a contradiction.
(b) Contradiction - This expression can be written as (p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.
(c) Tautology - This expression can be written as (p ∨ q) ∧ p, which is a tautology because it is equivalent to p, which is always true.
(d) Contradiction - This expression can be written as (p ∨ q) ∧ ¬p, which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.
(e) Contradiction - This expression can be written as (¬p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (¬p ∨ q) ∧ (¬p), which is a false statement.
(f) Tautology - This expression can be written as (¬p ∨ q) ∧ (¬p ∨ q), which is a tautology because it is equivalent to (¬p ∨ q), which is always true.
The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.
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Two friends shop for fresh fruit. Jackson buys a watermelon for $7.85 and 3 pounds of cherries. Tim buys a pineapple for $3.25 and 2 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Jackson spent.
(please its due Wednesday!!!!)
Jackson spent 4.60+p more than Tim in buying fruits.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, two friends shop for fresh fruit. Jackson buys a watermelon for $7.85 and 3 pounds of cherries.
Let the variable p to represent the price, in dollars, per pound of cherries.
So, the total cost is 7.85+3p
Tim buys a pineapple for $3.25 and 2 pounds of cherries.
Here, the total cost is 3.25+2p
Difference in there price is 7.85+3p -(3.25+2p)
4.60+p
Therefore, Jackson spent 4.60+p more than Tim in buying fruits.
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Please help me with math problem!! Will give brainliest!! :) It's due tonight!! 20 POINTS!!!
Answer:
Step-by-step explanation:
im sorry Im only in 6th grade and I cant help you
Solve for x. Give a reason for each step in the process.
5(-3a - 6) = 5a + 30
A woman drives to her office 10 km away from her house at 9 a. M. And reaches her office at 9:20 a. M. She stays in the office until 6 p. M. And then returns home at 6:25 p. M. Which answer gives the correct distance and displacement at 6:25 p. M. ?.
Distance is a scalar quantity that represents the total length of the path traveled by an object . It can be thought of as the magnitude of the displacement, which is the change in position of an object.
Displacement, on the other hand, is a vector quantity that represents the change in position of an object, taking into account the direction of travel. It is the shortest distance between the initial and final position of an object.
The distance traveled by the woman is the total length of her trip from her house to her office and back. It is equal to 2 * 10 km = 20 km.
Displacement is the final position of an object relative to its initial position, taking into account only the direction, and not the distance traveled. At 6:25 PM, the woman is back at her house, which is her initial position, so her displacement is 0 km.
So the correct answer is:
Distance traveled = 20 km
Displacement = 0 km
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Erin was shopping and saw that 30oz of milk cost $2.45. Calculate the unit price for 1 oz of milk. $____
Stuck on this question
Answer:
ABD =30 +45
ABD=75
75°is the answer
10). A Pizza Hut driver can travel a radius of 20 miles in all
directions. What is the area the drivers will cover? Use
3.14 for pi.
Answer:
1256 miles
Step-by-step explanation:
the Pizza Hut driver has a circle with a radius of 20 which is the area he can cover. you're looking for the area of the circle, and the formula for the area of a circle is pi * r * r
If you substitute, you have 3.14*20*20, which is 1256
The recurrence T(n) = 7T(n/2)+n2 describes the running time of an algorithm ALG. A competing algorithm ALG has a running time of T (n) = aT (n/4)+ n2 log n. What is the largest value of a such that ALG is asymptotically faster than ALG?
48 will be the value to ensure that A′ is asymptotically faster than A.
The recurrence relation T(n)=7T(n/2)+n2 is given by the question, and its answer is the asymptotic complexity master theorem T(n)=(nlog49base4).
Therefore, the recurrence relation T′(n)=T′(n/4)+n2 can be used to express the complexity in general.
As a result, the relationship is as follows: a=, b=4, f(n)=n2.
For a value of the >16, nloga base b=nlog base 4, and the >0, f(n)=O(nlog).
As a result, for n > 16, T′(n) = (n log base 4)
Now since A is getting asymptotically faster than A', A must hold:
Base 4 (nlog) nlog49 base 4 Since the base is equal to e, we can calculate the power as follows: log base 4 log49 base 4. Thus, after solving, we will obtain 49.
Therefore, 48 will be the value to ensure that A′ is asymptotically faster than A.
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use the root test to determine whether the series is convergent or divergent. [infinity] n = 1 4 1 1 n n2 identify an. evaluate the following limit. lim n → [infinity] n |an| since lim n → [infinity] n |an| ? 1,
In this case, the limit is 0, so the series is indeed convergent.
The Root Test is used to determine the convergence or divergence of a series. and it is used the Root Test, we start by finding the nth root of each term in the series.
In this case, the series is
=> [∞] n = 1 4 1 1 n n²,
so we calculate the nth root of each term:
[tex]= > (1/n^{2} )^{1/n}[/tex]
Then, we take the limit of this expression as n approaches infinity, to find the value of the root.
If this limit is less than 1, the series is convergent. If the limit is greater than or equal to 1, the series is divergent.
In this case, the limit of [tex](1/n^{2} )^{1/n}[/tex] as n approaches infinity is 0, which is less than 1. This means that the series is convergent.
To confirm this, we can evaluate the limit of the absolute value of each term as n approaches infinity, using the formula
=> lim n → [∞] n |aⁿ|.
If this limit is finite, then the series is convergent.
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Find the values of the trigonometric functions of t from the given information. tan(t) = -12/5 , sin(t) > 0 ,sin(t),cos(t),csc(t),sec(t),cot(t).
Find the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5
π
/7 rad. (Round your answer to two decimal places.)
The values of the trigonometric functions of t are Sin(t)=0.2, Cos(t) = -5/12, Csc(t) = 5,Sec(t) = -12/5, Cot(t) = -5/12 and the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5π/7 rad is 8.86 m
To find the values of the trigonometric functions of t, the tan(t) value was used to calculate the sin(t) value by using the relationship sin²(t) + cos²(t) = 1. The other trigonometric functions were calculated by using the relationship among the trigonometric functions.
Sin(t) = √(1 - (tan(t))^2) = √(1 - (-12/5)^2) = √(1 - 144/25) = √(25/25 - 144/25) = √(1/25) = 0.2
Csc(t)= 1/0.2= 5
The radius of the circle was then determined by using the arc length and the angle subtended at the center. The arc length was divided by the subtended angle to find the radius. The result was rounded off to two decimal places.
Radius r = (20m)/(5π/7) = (20m*7)/(5π) = 28/π = 8.86 m
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What is the boundary condition at a perfectly insulated surface expressed mathematically? (Check all that apply.) Check All That Apply эт (0,) k 0 эт (0, ) -k- 1 эт (0,) -k = 0 эт (),) 1
the boundary condition at a perfectly insulated surface is expressed mathematically as (0) -k = 0 depending on the physical characteristics of the surface.
A boundary condition is a mathematical expression that describes the behavior of a physical system at its boundaries, such as a surface.
Mathematically, a perfectly insulated surface is represented as an isothermal surface, meaning that the temperature is constant across the surface.
This is described by the equation (0) = 0, where эт represents the rate of heat transfer at the surface.
In other words, a perfectly insulated surface does not allow heat to flow through it.
This equation shows that the heat transfer is in the opposite direction of the temperature gradient at the surface.
Finally, the boundary condition at a perfectly insulated surface can also be expressed as эт (0,) -k = 0, which means that the heat transfer at the surface is equal to zero and there is no net heat transfer at the surface.
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refers to nondisclosure of the treatment an experimental unit is receiving.
Blinding refers to the nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.
What is Blinding?Blinding is a technique used in experimental design to reduce bias and improve the validity of results. It refers to the practice of not revealing to the experimental units (e.g., participants, animals) or the experimenters which treatment they are receiving in a controlled experiment. Blinding is used to eliminate potential sources of bias that might influence the results of the experiment.
For example, if the participants are aware of the treatment they are receiving, they might behave differently and affect the results. Similarly, experimenters might unconsciously treat participants differently based on their knowledge of the treatment, which could also affect the results.
Blinding is the practice of keeping the therapy that an experimental unit is getting a secret. In a single-blind experiment, the experimental unit (also known as the subject) is kept in the dark regarding the therapy that he or she is getting.
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Complete question:
refers to nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.
collection of n < min{m, n −m } is taken out at random without replacement. for k = 0, . . . , n, give a formula for the probability that exactly k balls are red.
The formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).
Given n balls, m of which are red and n - m are blue, if a collection of n < min{m, n - m} balls is taken out at random without replacement, the probability that exactly k balls are red can be calculated using the Hypergeometric Distribution. The formula for the probability that exactly k balls are red is given by: P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n)
where C(n, k) denotes the number of combinations of n things taken k at a time, and is given by: C(n, k) = n! / (k! * (n - k)!).
Therefore, the formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:
P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).
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