To plot the direction field associated with the differential equation u^n + 192u = 0, we need to first rewrite the equation as: u' = -192u^(1-n) where u' denotes the derivative of u with respect to some independent variable, such as time. The direction field represents the slope of the solution curve u(x) at each point (x, u(x)) in the xy-plane. To find this slope, we evaluate the right-hand side of the equation at each point: dy/dx = -192y^(1-n)
We can then plot short line segments with this slope at each point in the plane. The resulting picture will show us how the solution curves behave over the entire domain of the equation.To plot the phase plot of the solution corresponding to the initial value problem (IVP), we need to find the specific solution that satisfies the given initial condition. In other words, we need to find u(x) such that u(0) = y0, where y0 is some given constant. The solution to this IVP is: u(x) = (y0^n) / ((y0^n - 192) * e^(192x)) To plot the phase plot, we need to graph this solution as a function of time (or whatever independent variable is relevant to the problem), with u(x) on the vertical axis and x on the horizontal axis. We can then mark the initial condition (0, y0) on this graph and sketch the solution curve that passes through this point.Overall, the direction field and phase plot provide us with a visual representation of how the solution to the differential equation behaves over time. By analyzing these plots, we can gain insight into the long-term behavior of the solution and make predictions about its future behavior.
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applied partial differential equations 7.7.2
The solution of the partial differential equation 7.7.2 is given by
u(x,t) = t^2 sin(2πx) + c,u(0.3,1.5) = 1.96 + c, where c is an arbitrary constant.
Partial differential equations are mathematical equations used to describe how a function changes as its inputs change. The equation 7.7.2 is a linear second order partial differential equation in two independent variables. It has the form of a generalized wave equation, in which a wave propagates through a medium with varying physical properties.
To calculate partial differential equations u(x,t) for given values of x and t:
Let x = 0.3 and t = 1.5
Substituting these values into the equation, we get:
u(0.3,1.5) = (1.5)^2 sin(2π(0.3)) + c
= 2.25 sin(0.6π) + c
= 2.25(0.87) + c
= 1.96 + c
Therefore, u(0.3,1.5) = 1.96 + c, where c is an arbitrary constant.
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Cups are sold in packages of 8. Napkins are sold in packages of 12. How many sets of cups and napkins will there be?
Andrea earns a flat fee of $20 per day plus an additional x dollars for each sale she makes. Andrea made 10 sales last Saturday. The equation 10x + 20 = 80 represents the amount, in dollars, that Andrea earned. How much does Andrea earn for each sale she
makes?
Answer:
x=6
Step-by-step explanation:
10x+20=80
10x=60
x=6
A model train ha a cale of 3 cm : 14 m. If the model train i 57 cm long, then how long i the real train?
If the model train is 57 cm long, then 266 m is the length of real train.
In the given question, a model train has a scale of 3 cm : 14 m.
If the model train is 57 cm long, then we have to find how long the real train is.
The scale of model train is 3 cm : 14 m.
Now firstly convert m in cm. As we know that 1 m = 100 cm
Now, the scale of model train is 3 cm : 1400 cm.
The length of the model train is 57 cm.
So in the scale of the model train 3 cm = 57 cm
Now the scale of the model train 1 cm = 19 cm
Now find the length of the real train by multiplying the 1400 by 19 because in the scale of 1 cm is equal to the 19 cm.
So, the length of the real train = 1400 × 19
The length of the real train = 26600 cm
The length of the real train = 266 m
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Please help me and explain
The value of x in the equation 8 (x - 3) + 7 = 2x (4 - 17) is x = 1/2.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
The given equation is,
8 (x - 3) + 7 = 2x (4 - 17)
Distributive property : p (q + r) = p q + p r
Applying the property here,
8x - (8 × 3) + 7 = 2x × (-13)
8x - 24 + 7= -26x
8x - 17 = -26x
8x + 26x = 17
34x = 17
x = 17/34
x = 1/2
The mistake of Lin happened in the second step where 4 - 17 = -13 but she wrote 13.
Hence the value of x is 1/2 not -1/2 as the solution of Lin.
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Which coordinate comes first?
While writing the coordinates in the coordinate plane the coordinate that comes first coordinate is represented by x-coordinate.
As given in the question,
In the coordinate plane:
We draw two axis named as x-axis and y-axis.x-axis and y-axis intersect at origin with coordinate ( 0,0 ).x-axis is represented by the horizontal axis.y - axis is represented by the vertical axis.First coordinate is of horizontal axis and second one is of vertical axis.Coordinates in the coordinate plane are represented by ( x ,y )First coordinate is represented by x -coordinate.Therefore, the first coordinate in the coordinate plane is represented by x-coordinate.
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Jon has to choose which variable to solve for in order to be able to do the problem below in the most efficient manner.
6 x + 3 y = 27. 5 x + 2 y = 21.
Which variable should he choose so that he can use substitution to solve the system?
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Jon should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Jon should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Jon should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient of y.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given linear equations are,
6x + 3y = 27
5x + 2y = 21
The coefficients of the first equation are multiples of 3.
Hence dividing throughout the first equation by the common factor 3, coefficient of y will be eliminated.
6x/3 + 3y/3 = 27/3
2x + y = 9
y = 9 - 2x
Solving by substitution, the second equation becomes,
5x + 2(9 - 2x) = 21
5x + 18 - 4x = 21
x = 3
y = 9 - 2x = 3
Hence Jon should could solve the problem by eliminating the coefficient of y in the first equation by a common factor 3.
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Help please I need this answer very quick will be very appreciated?
This figure has Line, Point and Rotational Symmetry.
How can you tell if something has rotational symmetry?If a figure can be rotated by an angle between 0° and 360° so that the image coincides with the preimage, it has rotational symmetry. The smallest angle for which the figure can be rotated to coincide with itself is the angle of rotational symmetry.
What exactly is a line of symmetry?A line of symmetry is a line that divides two equal and symmetrical parts of a shape or object. This line is also known as the axis of symmetry or the mirror line because it divides the figure symmetrically and the divided parts appear to be mirror reflections of each other.
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What is the image of (−8,12) after a dilation by a scale factor of 1/4 centered at the origin?
The image of (−8,12) after a dilation is (-2, 3).
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
Point (-8, 12)
scale factor = 1/4
After applying the scale factor then image
= (-8/4, 12/4)
= (-2, 3)
Hence, the image is (-2, 3).
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what is the answer to a=-4, b=-6, and c=5:b^2-4ac
[tex]b^2-4ac[/tex] when a is -4. b is -6, and c is 5
Substitute for variables with given values:
[tex]-6^2-4(-4)(5)[/tex]
[tex]=\fbox{116}[/tex]
How do you describe the behavior of the graph relative to the x axis?
The behavior of the graph relative to the x axis can be described by the equation of the line.
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. The slope of a line represents the rate of change of the graph with respect to the x axis; a positive slope indicates the graph is increasing, while a negative slope indicates it is decreasing. The y-intercept is the point at which the line crosses the y axis. For example, if the equation of the line is y = 2x + 4, then the slope of the line is 2, meaning the graph increases by 2 units every time the x axis increases by 1 unit, and the y-intercept is 4, meaning the line crosses the y axis at the point (0, 4). By analyzing the equation of the line, you can determine the behavior of the graph relative to the x axis.
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What does it mean to dilate by 1 2?
Dilation is a type of transformation in geometry that changes the size of a shape without changing its orientation. When a shape is dilated by 1 2, it means that the shape is multiplied by a factor of 1 2.
This means that the shape is made half of its original size. The shape will be reduced to one-half of its original area and its perimeter will be halved as well. When a shape is dilated by a factor greater than 1, it will be expanded; when a shape is dilated by a factor less than 1, it will be reduced.
When a shape is dilated by 1 2, the center of dilatation is the same as the original shape's center of dilation. The scale factor of the dilation is 1 2, so the coordinates of the center of dilation will not change.
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PLEASEEE HELPP!! i have a lot more problems to go
The equations can be completed by;
1) y^8 - 1/y^8
2) 1/y^8 + 1/y^2
What is the law of the exponents?We have to know that there are laws that can be used when we are dealing with exponents. Two of the laws that we need to know here are the law of multiplication and the law of division.
Note that;
a^m/a^n = a^m - n (division law)
a^m * a^n = a^ m + n (multiplication law)
Having these laws at the back of our minds;
y^5 y^3 - (y^-2)^4 = y^8 - y^-8
= y^8 - 1/y^8
And;
(y^-2)^4 + y^3/y^5
y^-8 + y^-2
1/y^8 + 1/y^2
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Sally's Smoothies makes two flavors: strawberry and banana. The ratio of strawberry
smoothies to banana smoothies is 3:2.
If Sally makes 60 strawberry smoothies, how many total smoothies does she make?
Select
60
, where n is the number of banana smoothies.
Cross multiply to get
Solve to find that n =
Select
smoothies
k
Sally makes 60 strawberry smoothies and
of
banana smoothies.
banana smoothies, for a total
The Total number of smoothies after calculating are 100 .
What is ratio ?
ratio can be defined as the Given value divided by the total value, is called as ratio.
Given ,
Sally's Smoothies makes two flavors: strawberry and banana. The ratio of strawberry
smoothies to banana smoothies is 3:2.
If Sally makes 60 strawberry smoothies, The number of total smoothies does she make are.
let the banana smoothie be x .
so,
3/2 = 60/x
x = 2* 60 / 3
x = 2*20
x = 40
Total number of smoothies are = 60+40 = 100
Hence , The Total number of smoothies are 100 .
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The graph of a linear function passes through the points (-10, -14) and (10, 11). Place (click and drag) a choice from each list into its corresponding b
describe the slope and y-intercept of the function.
Answer:
Slope = 1.25
Y-intercept = -1.5
Step-by-step explanation:
Slope:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-(-14)}{10-(-10)}=\frac{11+14}{10+10}=\frac{25}{20}=1.25[/tex]
Y-intercept:
[tex]y=mx+b\\\rightarrow y=1.25x+b\\\rightarrow 11=1.25(10)+b\\\rightarrow 11=12.5+b\\\rightarrow -1.5=b[/tex]
Final Equation:
[tex]y=1.25x-1.5[/tex]
In a school, all students study one language, French or Spanish.The ratio of girls to boys in Year 11 is 4:3, 3/4 the boys study French There are 168 students in Year 11.How many of the boys study Spanish?
The answer is 72 boys
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The ratio of boys to girls is 4:3 and total students as 168
thus there are 96 boys and 72 girls and also 3/4 th of the boys study french
which is equivalent to 72 boys
Therefore the number of boys that study spanish is equal to 96-72=24
Hence, 24 boys study spanish.
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Twelve less the product of two numbers, ‘a’ and ‘b’. what does it mean.
Answer: (a * b) - 12
Step-by-step explanation:
We will pull details for the sentence given to write an expression representing this situation.
In this case, these words mathematically mean:
less ➜ subtraction
product ➜ multiplication
Using this information, we will write our expression.
(a * b) - 12
How do you know if a domain is all real numbers?
A domain is all real numbers if it includes all of the values on the real number line (including negative and positive numbers, fractions, decimals, and irrational numbers).
1. A domain is the set of all possible values of an independent variable that produces a valid solution to a given equation.
2. To determine if a domain includes all real numbers, you must examine the set of values in the domain and see if it includes all the values on the real number line.
3. This includes negative and positive numbers, fractions, decimals, and irrational numbers.
4. If the domain includes all of these, then it is all real numbers.
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An unusually wet spring has caused the size of a mosquito population in some city to increase by 7% each day. If an estimated 250,000 mosquitoes are in the city on May 11, find how many mosquitoes will inhabit the city on May 23. Use y250,000(1.07)x where x is number of days since May 11
The number of mosquitoes that will inhabit the city on May 23, given the increase in population, is 563, 048 mosquitos
How to find the number of mosquitoes ?The formula for finding the number of mosquitoes after May 11, is given as:
y = 250,000 ( 1. 07 ) ˣ
Given that x is the number of days since May 11, the number of days till May 23 is :
= 23 - 11
= 12 days
The number of mosquitoes is therefore:
= 250, 000 x ( 1. 07 ) ¹²
= 250, 000 x 2.252191588960823337718801
= 563, 048 mosquitos
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Which function could have produced the values in the table? Explain why you chose this answer. i will mark you brainliest!!
Answer:
The answer is (d) y=3x+2
Inserting the given points in the given equation yields the answer. To make the process faster, insert the zero first then you will get y=2. You have to choose whether B and D. Then insert the x values and you will obtain the correct answer which is valid for the given points x and y.
Can someone help me out with this question fast!?!?!
Answer:
x=2
Step-by-step explanation:
2(4x-1)= -10(x-3)+4
(2×4x)-(1×2 )=(-10×x) -(3×-10) +4
8x -2 = -10x -(-30)+4
8x -2 = -10x +30+4
8x-2= -10x+ 34
8x+10x=34+2
18x=36 we do ÷18
x=2
What is f(-3) if f(X) =1/3x
Answer: 1/3x
Step-by-step explanation:
Hey there!
f(x) = 1/3x
f(x) = 1/3(-3)
f(x) = 1/3(-3/1)
f(x) = 1(-3)/3(1)
f(x) = -3/3
f(x) = -1
Therefore, your answer should be:
f(x) = -1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
(a) Write an equation and (b) solve. 7. The mountains received 4 times the snow a nearby valley received. If the difference in snowfall was 21 in., how much snow did the mountains get?
Answer:
I don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and height for all the help and their kids the the other one of it and don't
Somebody help please I don’t understand
The constant of proportionality for respective problems is 2/7, 15, 2.75, 13, 4/3.
A) In the first block,
Using points we can find the equation of line ,
Using the formula (y - y₀) = m (x - x₀)
where m is the slope of the equation
The equation of line becomes 2x = 7y
⇒ y = 2/7x
⇒ 2/7 is the constant of proportionality
B) From the graph given,
Again Using the formula (y - y₀) = m (x - x₀)
If we consider two points,
(2,30) and (4,60)
The equation of line becomes
15x = y
Here, the constant of proportionality is 15.
C) It is given the equation is y = 2.75x
The constant of proportionality here is 2.75
D) It is given that,
The price of 5 games is $65.00
The price of 1 game will be 65 / 5
= $13.00
The equation becomes
y = 13x
So, the constant of proportionality becomes 13.
E) Let us consider 2 points (3,12) and (6,24)
The equation of line using the formula (y - y₀) = m (x - x₀) becomes 4x = 3y
⇒ y = 4/3 x
The constant of proportionality becomes 4/3.
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drew was shopping on amazon on black Friday. he purchased 5 DVDs all at the same price. the tax on his purchase was 6 bring the total cost to 61. what was the price of each DVD?
Based on the information provided, the price of each DVD is $11.
How to calculate the price of the DVD?To calculate the price of the DVD, two main variables must be considered:
Price of the DVD Total of units boughtTaxesWhat is the price of each DVD?Tax is a compulsory amount that is levied on goods and services by the government. Tax serves as a form of transfer of wealth from the private individuals to the government.
Taxes increase the cost of a good or service.
Now, let's calculate the cost of each DVD:
The price of each DVD = (total cost - tax) / number of DVDs bought
The price of each DVD = (61 - 6) / 5
The price of each DVD = 55 / 5
The price of each DVD = $11
Based on this, the price of each DVD was $11, you can double-check this below
$11 x 5 = $55 (prices for the DVDs) + 6 = $61 (total price)
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a right triangle is formed by fbe y-axis, the y = 2x + 4, and another line. if the legs of the right triangle intersect at (2, 8), what is the equation of the line other line of the triangle?
Replace -0.5 with the fraction -1/2 if needed.
======================================================
Explanation:
The legs of any right triangle are always perpendicular. They meet up to form a right angle, aka 90 degree angle.
The line y = 2x+4 goes through (2,8). This can be confirmed with a graph. Or note how plugging x = 2 leads to y = 8.
Therefore, y = 2x+4 forms one of the legs of this triangle.
The slope here is 2 = 2/1; the negative reciprocal is -1/2 = -0.5, which is the slope of the perpendicular line. We want this line to go through (2,8)
So,
y = mx+b
8 = -0.5*2+b
8 = -1+b
8+1 = b
9 = b
b = 9
The equation of the perpendicular line is y = -0.5x+9
Replace -0.5 with the fraction -1/2 if needed.
Check out the graph below.
Evaluate the expression use calculator if needed
Answer:
780.
Step-by-step explanation:
I cant explain Its just the answer.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. Complete the table of inputs and outputs for the given function. g(x)=3−8x
The complete table is,
x 3/8 0 1 3
g(x) 0 3 -5 -21
What are linear equations?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Given equation g(x) = 3 − 8x
1. when g(x) = 0
0 = 3 - 8x
8x = 3
x = 3/8
2. when x = 0
g(x) = 3 − 8x
g(x) = 3 − 8(0)
g(x) = 3
3. when g(x) = -5
-5 = 3 - 8x
8x = 3 + 5
8x = 8
x = 1
4. when x = 3
g(x) = 3 − 8x
g(x) = 3 − 8(3)
g(x) = -21
Hence the missing values of x are 3/8 and 1,
missing values of g(x) are 3 and -21.
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Which description best matches the graph below? please explain why you chose this answer. I will mark you brainliest
the sum of 47 and 39 is 22 more than a number. what is the number?
Answer: 64
Step-by-step explanation:
(47 + 39) - 22
= 86 - 22
= 64