Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).
The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:
The equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x or constants, this is called Bernoulli's equation.
Now, we have to substitution using
\(v = {y}^{1 - n} \)
Differentiating both side with respect to 'x'
\(v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'\)
we get,
\(= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)\)
Now, by using
\(v' = {y}^{1 - n} \)
The given equation is expressed as:
\(v + (1 - n)p(x)v = (1 - n)q(x)\)
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.
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Work out the size of angle a and angle b
Answer:
a = 120°
b = 60°
Step-by-step explanation:
Angle a and 60° are suplementary. The sum of supplementary angles is 180° (straight angle).
a + 60° = 180°
a = 180° - 60°
a = 120°
The sum of angles in the quadrilateral is 360°. Notice how two of the angles in the quadrilateral are marked as right angles (angles marked with a square). Each of them is 90°.
b + 90° + a + 90° = 360°
Substitute a with the value calculated in the previous step.
b + 90° + 120° + 90° = 360°
Solve for b.
b + 300° = 360°
b = 60°
pls help me with this i’ve been stuck on it for a while but i did it on paper and it doesn’t look right
i will fill the boxes from top down
4(-2)-5=-13
4(1)-5=-1
4(2)-5=3
4(3)-5=7
[y=-z+2
y=-2²+z+1
Which ordered pair is the solution of the system?
The graph shows the system
0 (0, 2)
O (1,2)
(1,1)
(0, 1)
+
Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).
What exactly are ordered pairs?"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.
Here, The formulae are as follows:
=>y = -z + 2 ...(1)
=> y = -2x² + z + 1 ...(2)
Equation (1) can be substituted for equation (2) to find the value of z:
=> Z = x² + 1/2 - z + 2 = -2x² + z + 1
=> 2z = 2x² + 1
We can now enter this value of z into equation (1) and find the value of y:
=> y = -z + 2
=> y = -(x² + 1/2) + 2
=> y = -x² + 3/2
As a result, the equation system can be expressed as:
=> z = x² + 1/2
=> y = -x² + 3/2
When x=0:
=> z = 0² + 1/2 = 1/2
=> y = -0² + 3/2 = 3/2
Therefore, there is no answer for the ordered pair (0, 3/2).
When x=1:
=> z = 1² + 1/2 = 3/2
=> y = -1² + 3/2 = 1/2
The answer is the ordered pair (1, 1/2).
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:Jonathan is incorrect.
Step-by-step explanation:A quadrilateral has 4 straight sides is a four sided shape which means 4 straight sides.The image you have showed me does not have 4 straight sides nor 4 edges nor 4 verticals.So Jonathan is incorrect.
someone please help me
Answer:
A. 20ft
Step-by-step explanation:
Answer:
d. 98.5
Step-by-step explanation:
Triangles:
5 x 4 = 20/2 = 10
Circle:
5² x 3.14 = 78.5
Add both of them 98.5
A bag contain 8 blue balls, 7 green balls and 5 red balls.What is the probability that the ball is red?
Answer:
A bag contains:
8 blue balls.
7 green balls.
5 red balls.
The probability that the ball is red would be:
P = Red balls/Total balls = 5/(5+7+8) = 5/20 = 1/4 =0.25
Hope this helps!
:)
Answer:
0.25
Step-by-step explanation:
Total balls: 8 + 7 + 5 = 20
Red balls: 5
P(red) = 5/20 = 0.25
Please Help im am so lost on this one
Answer:
2 and 3
Step-by-step explanation:
:)
Question Andre bought 8 bagels and ate 2/3 of them. Sandra bought 20 bagels and ate 1/4 of them. Who ate more bagels?
Answer:
Andre
Step-by-step explanation:
Andre ate 2/3 of 8 bagels, so to get the number of bagels-
8 *2/3
8/1*2/3 = 16/3 = 5 1/3
Meanwhile Sandra ate 1/4 of 20, so,
20*1/4 = 20/4 = 5
PLEASE HELP FAST Which gives the solution of this inequality?
7m - 2 >_ 61
btw the arrow that is pointing right is supposed to be on top of the underscore
A triangle has side lengths of 5 units, 11 units and 6 units. Tell whether the triangle is a right triane
Answer:
triangle isn't right angled
Step-by-step explanation:
For a right tangled triangle :
Length of the longest side, hypotenus is given by :
Hypotenus = √(opposite² + adjacent ²)
From.the question :
Hypotenus = 11
Opposite and adjacent = 5 units and 6 units
Let's test :
Hypotenus = √(5² + 6²)
Hypotenus = √(25 + 36)
Hypotenus = √61 units
Hypotenus = 7.8
Hypotenus for a right angled triangle = 7. 8 units and not 11.
Hence, triangle isn't right angled
At a baseball game, 14% were supporting the visiting team. If total number of people
attending the game was 3800, how many people were supporters of the home team?
Answer: 532
Step-by-step explanation:
14% of 3800 is 532
A solid with surface area 50units^2 is dilated by a scale factor of K to obtain a solid surface area 200units^2. Find the value of K.
The value of K is 2.
Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.
We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.
Using the formula for the surface area, we have:
Initial surface area * (scale factor)^2 = Final surface area
50 * K^2 = 200
Dividing both sides of the equation by 50:
K^2 = 200/50
K^2 = 4
Taking the square root of both sides:
K = √4
K = 2
Therefore, the value of K is 2.
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first sequence: 3 8 13 18 23 second sequence: -2 4 10 16 . find the TWO numbers that are in both number sequences.
\(a(n) = 3 + 5n\)
\(b(n) = - 2 + 6n\)
\(a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)\)
\(a(5) \: or \: b(5) = 3 + 5(5) = 28\)
Use the graphical method to solve the following Linear Programming model.
max = x1 + 3x2
s.t.
5x1 + 2x2 ≤ 10
x1 + x2 ≥ 2
x2 ≥ 1
x1, x2 ≥ 0
The given linear programming model needs to be solved using the graphical method. The objective function is to maximize the expression x1 + 3x2, subject to three constraints. The first constraint is 5x1 + 2x2 ≤ 10, the second constraint is x1 + x2 ≥ 2, and the third constraint is x2 ≥ 1. The decision variables x1 and x2 must be non-negative.
To solve the linear programming model using the graphical method, we start by graphing the feasible region determined by the constraints. Each constraint is represented by a linear inequality, and the feasible region is the area where all constraints are satisfied. By plotting the feasible region on a graph, we can identify the region where the optimal solution lies.
Next, we evaluate the objective function, which is to maximize the expression x1 + 3x2. We identify the corner points or vertices of the feasible region and calculate the objective function value at each vertex. The vertex that yields the highest objective function value represents the optimal solution.
In this case, without having specific values and the graphical representation, it is not possible to provide the exact coordinates of the corner points or the optimal solution. To obtain the precise solution, you would need to plot the feasible region, determine the vertices, and evaluate the objective function at each vertex.
It's important to note that the graphical method is suitable for problems with two decision variables, allowing for easy visualization of the feasible region and identification of the optimal solution.
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A regular heptagon has sides measuring 3.2 inches and an apothem that measures 2.9 inches. What is the area of this heptagon?
Answer:
32.48 square inches
Step-by-step explanation:
The area of a polygon is \(A=\frac{nsa}{2}\) where \(n\) is the number of sides of the polygon, \(s\) is the side length of the polygon, and \(a\) is the length of the apothem.
We are given the polygon is a heptagon, so it has 7 sides, making \(n=7\)
We are given the heptagon's side length is 3.2 inches, making \(s=3.2\)
We are also given an apothem of 2.9 inches, making \(a=2.9\)
Therefore, by using the formula for the area of a polygon, we get\(A=\frac{nsa}{2}=\frac{7*3.2*2.9}{2}=\frac{64.96}{2}=32.48\)
In conclusion, the area of the heptagon is 32.48 square inches
Aaron makes $9 an hour at work. He worked h hours yesterday. Write an expression to represent how much money he made at work yesterday.
Answer:
9h
Step-by-step explanation
If Aaron makes 9 dollars per hour, then we can find out how much money he earned by doing the expression 9h, which means 9 dollars times h (the number of hours.)
Hope this helped!!! :)
Answer:
9h
Step-by-step explanation:
If he makes $9 an hour, and h represents how many hours he worked, the amount of money he made can be represented by 9h.
This will multiply $9 by how many hours he worked, giving us the total amount he made.
For example, if he works 2 hours, he will get $18.
So, the expression that represents how much he made yesterday is 9h.
a%b when a=2 and b=1/2
Answer:
0.01
Step-by-step explanation:
Solve for x. PLZ HELP ASAP!!!
X is a vertical angle to the angle marked as 100 degrees.
Vertical angles are the same so x = 100 degrees
Answer: 100 degrees
PLEASE HELPP SHOW WORK 20 PONITS
The option that correctly describes the domain and range is;
Option B;
D; -4 ≤ x < 5
R; -1 ≤ y < 3
What is the domain and range of the given graph?The domain of a function is a set of all possible input values for which the function is possible.
The range of a function is a set of all possible output values that make a function possible.
Now, in inequalities, Open circles are used for numbers that are less than or greater than (< or >). Whereas, closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).
Now, from the graph, at the coordinate (-4, -1), we see that the circle is closed while at the coordinate (5, 3), we see that the circle is open. Thus, we have the domain and range as;
D; -4 ≤ x < 5
R; -1 ≤ y < 3
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Using only the H NMR spectrum of the crude nitration porduct, determine if the product is mostly ortho-, para-, or para- substituted, and explain how you came to your conclusion. (Note: Jortho= ~8 Hz, Jmeta= ~3 Hz and Jpara = ~1 Hz. Also aromatic protons ortho to NO2 or C=O groups are generally downfield.)
Based on the H NMR spectrum of the crude nitration product, the product is likely mostly para-substituted.
First, we need to identify the peaks in the H NMR spectrum that correspond to aromatic protons. These will appear as peaks in the range of 6-8 ppm, typically.
Next, we need to look for any peaks that are downfield from the expected chemical shift range for the aromatic protons. This indicates that the proton is near an electron-withdrawing group, such as a NO2 or C=O group.
Using the J-coupling constants given in the question, we can determine the splitting pattern for each peak. Peaks that are ortho to each other will have a Jortho coupling constant of around 8 Hz, resulting in a doublet splitting pattern. Peaks that are meta to each other will have a Jmeta coupling constant of around 3 Hz, resulting in a triplet splitting pattern. Peaks that are para to each other will have a Jpara coupling constant of around 1 Hz, resulting in a singlet splitting pattern.
Based on the splitting patterns observed in the H NMR spectrum, we can make some conclusions about the substitution pattern of the aromatic ring. If we observe doublet splitting patterns, we can infer that there is likely ortho substitution present. If we observe triplet splitting patterns, we can infer that there is likely meta substitution present. If we observe singlet splitting patterns, we can infer that there is likely para substitution present.
Finally, we can look at the chemical shifts of the aromatic peaks and any downfield shifts to determine the nature of the substituents. Aromatic protons that are downfield from the expected range and are para to a NO2 or C=O group indicate para substitution. This is because the electron-withdrawing group reduces electron density on the aromatic ring, causing the chemical shift of the nearby protons to shift downfield.
Additionally, the singlet splitting pattern observed in the H NMR spectrum indicates that the para-substituted protons are not splitting with any other protons, which is consistent with the absence of any other substituents in the para position. Therefore, based on the H NMR spectrum, we can conclude that the product is mostly para-substituted.
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please help with this:)
Answer:
\(area = 2 \times 6 \times \pi = 12\pi\)
Phoebe want to invest $10,000.
● Account A earns 9% simple interest.
● Account B earns 9% interest compounded annually.
To determine which account would be a better investment for Phoebe, we need to calculate the future value of each account after one year and compare them.
Account A earns simple interest, which means that the interest is calculated only on the initial investment. After one year, the investment in Account A would be worth:
$10,000 + ($10,000 x 0.09) = $10,900
Account B earns interest that is compounded annually, which means that the interest is calculated on the initial investment plus any previously earned interest. After one year, the investment in Account B would be worth:
$10,000 x (1 + 0.09)^1 = $10,900
As we can see, both accounts would have the same value of $10,900 after one year. Therefore, the choice between the two accounts depends on Phoebe's investment goals and preferences.
If Phoebe wants a simple and straightforward investment that provides a guaranteed return, Account A would be the better choice.
If Phoebe is willing to take on some risk and wants the potential for higher returns, Account B would be the better choice as the compounding of interest can lead to a higher return over a longer period of time.
assuming that the population from which you select your sample is normal, which of the statements about m are true? check all that apply. the expected value of the sampling distribution of m is equal to the value of the population mean divided by the sample size. the standard deviation of the sampling distribution of m is equal to the standard deviation of the population divided by the square root of the sample size. you can assume that the sampling distribution of m is normally distributed for any sample size. you can only assume that the sampling distribution of m is normally distributed for sufficiently large sample sizes.
Answer:
Step-by-step explanation: the sampling distribution of the s score of M is normal for any sample size
you can only assume that the sampling distribution of M is normally distributed for sufficiently large sample sizes
The population mean divided by the sample size gives the expected value of the sampling distribution, or m, in terms of the population. Thus, it is true.
What is the value of the sampling distribution?For every sample size, it is safe to assume that the sampling distribution of m is normally distributed. As long as the population is normal, and the sample size is not too tiny (for example, n>30), this assertion is typically accurate, even for small sample sizes.
With sufficiently large sample sizes, you cannot simply assume that the sampling distribution of m is normally distributed.
This is untrue since, provided the other assumptions are followed, the sampling distribution of m is often normal regardless of the sample size.
Therefore, it is true that the square root of the sample size divided by the standard deviation of the population yields the standard deviation of the m sampling distribution.
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The area of the triangle below is 3/10 square meters. What is the length of the base?
Express your answer as a fraction in simplest form.
2/5 m is the height.
The length of the base of the triangle is 3/2 meters.
To find the length of the base of the triangle, we can use the formula for the area of a triangle, which is given by the formula:
Area = (1/2) * base * height.
We are given that the area of the triangle is 3/10 square meters, and the height is 2/5 meters. Let's denote the length of the base as b.
Plugging in the given values into the formula, we have:
(1/2) * b * (2/5) = 3/10.
To solve for b, we can simplify the equation:
b * (2/5) = (3/10) * 2.
Multiplying both sides of the equation by 5/2 to isolate b, we get:
b = (3/10) * 2 * (5/2).
Simplifying further, we have:
b = (3/10) * 5 = 15/10 = 3/2.
In summary, using the formula for the area of a triangle and the given values, we find that the length of the base of the triangle is 3/2 meters.
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someone please help me
I really need your help guys.
Answer:
The average rate of change from 0 to 20 years old is -2.
Step-by-step explanation:
Average rate of change means slope.
slope = y2 - y1 / x2 - x1
Pick any points between 0-20. They have given on the graph already (0, 112) and (20, 72) so plug it into slope equation.
112 - 72/ 0 - 20
40/-20
= -2
The average rate of change from 0 to 20 years old is -2.
Which are rational and irrational? Thanks in advance :)
Answer:
\(3\frac{1}{2}-rational\)
\(\pi -irrational\)
\(-\frac{2}{3}-rational\)
\(\sqrt{16} -rational\)
\(\sqrt{3} -irrational\)
\(18-rational\)
\(0.625-rational\)
\(0.987987987...-rational\)
Step-by-step explanation:
Rational numbers:
-are all numbers you can write as a quotient of integers \(\frac{a}{b}\) , \(b\neq 0\)
-include terminating decimals. For example, \(\frac{1}{8}=0.125\)
-include repeating decimals. For example, \(\frac{1}{3} =0.33333....\)
Irrational numbers:
-have decimal representations that neither terminate nor repeat. For example, \(\sqrt{2}=1.414213....\)
-cannot be written as quotients of integers
What is the value of 0 in the following image
We will determine the value of theta as follows:
\(\begin{gathered} cos(\theta)=\frac{10}{21}\Rightarrow\theta=cos^{-1}(\frac{10}{21}) \\ \\ \Rightarrow\theta\approx61.6 \end{gathered}\)So, the measurement of the angle is approximately 61.6°.
Select the equation that matches the written description.
A number, y is eight less than negative nine times a number,x.
(А)
y = -4x + 8
B
y = 3x + 8
y = -9x - 8
D
y = 5x + 8
Answer:
C. y = -9x - 8
Step-by-step explanation:
Setting up the equation:
eight LESS (so minus sign before the 8) THAN (so 8 is being subtracted from the -9x) negative (-) nine TIMES (multiplication) a number, (variable) x.
We want to get the variable y alone, so this can be written as y = -9x - 8