I'll assume the ODE is
[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]
Solve the homogeneous ODE,
[tex]y'' - 3y' + 2y = 0[/tex]
The characteristic equation
[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]
has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is
[tex]y = C_1 e^x + C_2 e^{2x}[/tex]
For nonhomogeneous ODE (1),
[tex]y'' - 3y' + 2y = e^x[/tex]
consider the ansatz particular solution
[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]
Substituting this into (1) gives
[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]
For the nonhomogeneous ODE (2),
[tex]y'' - 3y' + 2y = e^{2x}[/tex]
take the ansatz
[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]
Substitute (2) into the ODE to get
[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]
Lastly, for the nonhomogeneous ODE (3)
[tex]y'' - 3y' + 2y = e^{-x}[/tex]
take the ansatz
[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]
and solve for [tex]c[/tex].
[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]
Then the general solution to the ODE is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]
A function has a slope of 3, and one solution is given in the table. identify the missing outputs. x: 5 6 7 8 9 y: -50
The remaining value will increase by the value of the slope. Hence the remaining missing values are -47, -44, -41, -38 and -35
Slope and tablesThe slope of a line is the ratio of the rise to run of a line. It is also defined as the rate of change of coordinate y with respect to x. Mathematically;
slope = change in y/change in x
If the slope of the table given is 3, then using the coordinate points (5, -50)and (6, y)
Substitute
3 = y-(-50)/6-5
3 = y+50/1
y+50 = 3
y = -47
The remaining value will increase by the value of the slope. Hence the remaining missing values are -44, -41, -38 and -35
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A map has a scale of 1cm:4km the actual distance between the two cities is 52km. What is the distance between the two cities on the map
Answer:
13cm
Step-by-step explanation:
Given the map scale:
1cm on the map : 4km actual distance
4km actual distance : 1cm on the map
1km actual distance : [tex]\frac{1}{4} =0.25cm[/tex] on the map
Therefore,
52km actual distance = 0.25 * 52 = 13cm
(n - 1)!, where n = 4
Answer:
6
Step-by-step explanation:
Original Equation
(n-1)!
Plug in 4 as n
(4-1)!
Subtract
(3)!
Rewrite using definition of factorial: [tex]a! = a*(a-1)*(a-2)....*1[/tex]
3! = 3*2*1
You don't really have to write the 1, since it doesn't change the value
6
How to recognize the domain, the range and the axis of symmetry in a graph?
Answer: Read below.
Step-by-step explanation: To recognize the domain of a graph, you have to find out what points does the graph cross the x-axis? For example, consider the equation, y = x. The domain for this graph is all real numbers, or (-∞, ∞). This is because, the graph goes infinitely forever, and eventually hits every single number in the x-axis. This is true for every single linear graph in the form y = mx + b or ax + by = c. However, in a graph that is an inequality, like let's say, x < 4, then there will be an open dot on 4, and the graph will go to the left infinitely, hitting every single number in the negative x-axis eventually. The interval for this would be (-∞, 4).
The range is as easy as the domain to figure out. Instead of all the values that the graph goes on the x-axis, we need to find all the values that the graph goes on the y-axis. Again, for a linear graph in the form y = mx + b or ax + by = c, the range is also (-∞, ∞). For an inequality though, like y ≥ 2, the graph would have a closed plot on 2 in the y-axis, and go infinitely in the direction of the right, hitting every single y value after 2 eventually. The interval would be [2, ∞).
The axis of symmetry can only be found in parabolas. In parabolas, the axis of symmetry is an invisible vertical or horizontal line (depending on if your parabola is sideways or not.) The invisible line cuts through the vertex of the parabola, or the center of the parabola, and splits it into two even and equal pieces. Thus, the axis of symmetry will always be the x-coordinate of the parabola if upwards or downwards, or the y-coordinate of the parabola if sideways.
Hope this helped!
Which equation can be solved by using this system of equations?
[y=3x5 - 5x³ + 2x² - 10x+4
y=4x4 +6x³-11
the equation that we can solve using the given system of equations is:
3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0
Which equation can be solved using the given system of equations?
Here we have the system of equations:
y = 3x^5 - 5x^3 + 2x^2 - 10x + 4
y = 4x^4 + 6x^3 - 11
Notice that both x and y should represent the same thing in both equations, then we could write:
3x^5 - 5x^3 + 2x^2 - 10x + 4 = y = 4x^4 + 6x^3 - 11
If we remove the middle part, we get:
3x^5 - 5x^3 + 2x^2 - 10x + 4 = 4x^4 + 6x^3 - 11
Now, this is an equation that only depends on x.
We can simplify it to get:
3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0
That is the equation that we can solve using the given system of equations.
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the sides of each square have a length of 3 inches. what is the perimeter of Edgar's check boar
Answer:
(b) 96 inches
Step-by-step explanation:
The perimeter of the board is the sum of its four edge lengths.
Edge lengthEach edge of the board is indicated as being 8 squares long. Each square is 3 inches on a side, so the edge of the board is ...
8 × (3 in) = 24 in . . . . board edge length
PerimeterThe perimeter of the board is 4 times the length of one edge, so is ...
P =4s = 4(24 in) = 96 in
The perimeter of Edgar's checkerboard is 96 inches.
__
Scaled geometry (alternate solution)The perimeter of one small square on the board is ...
P = 4s = 4(3 in) = 12 in
The whole board is a dilation of one square by a factor of 8. Its perimeter will be ...
P' = (scale factor) × P
P' = 8×(12 in) = 96 in
The perimeter of Edgar's checkerboard is 96 inches.
Need help with my math please. 31-41. Read the directions carefully please.
Answer:
31. (98,765 x 9) + 3 = 888,888
32. (12,345 x 9) + 6 + 111,111
33. 3367 x 15 + 50,505
34. 15,873 x 28 = 555,555
35. 33,334 x 33,334 = 1,111,155,556
36. 11,111 x 11,111 = 123,454,321
41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2
42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6
Conjecture -> solve these problems and see if they are equal on both ends
EX: 3 + 9 + 27 + 81 + 243 -> 363
3 x 242 = 726 -> 726/2 = 363
Verified
Can you solve and explain how to solve problems like these.
Step-by-step explanation:
there are some formulas to know about this.
I am sure you discussed this in class.
when 2 lines (originating from the same point) cut through the same circle creating some circle segments (such lines are also called Secants), then there is a relationship in the lengths of the different parts of the lines among themselves.
the outer portion of such a line multiplied with the length of the whole line to the second point it intersects the circle is the same for every secant from the same point through the same circle.
that means in our case :
7(x - 6) = 6(x - 3)
7x - 42 = 6x - 18
x = 24
and so,
EG = (x - 3) + 6 = (24 - 3) + 6 = 21 + 6 = 27
When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodness-of-fit test, can you tell exactly how the distribution of observed values over the specified categories differs from the expected distribution? explain your answer.
No. When we reject the null, we can only conclude that the observed distribution differs from the expected distribution.
What do you mean by categories?Any of a number of basic and distinctive classifications to which entities or concepts belong Taxpayers fall into a number of categories.A division within a categorization scheme She entered the contest for the prize in her age group.Foods made of grains are an illustration of this category. Any of the several fundamental ideas that can be used to categorize all knowledge.A high-level business region that aids in organizing business jargon is a business category. Information Governance Catalog (IGC) defines business categories as categories having attributes that convey the meaning of the business category in the business language and are offered with IBM Industry Models.No. When we reject the null, we can only conclude that the observed distribution differs from the expected distribution.
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No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.
What is a null hypothesis?The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.
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Rod waxes two thirds of his car with one fourth bottle of car wax. What fraction of the bottle of car wax will Rod need to wax his entire car?
i,dk how to do this pls help :)
Given the percentage taken off and the reduced price, the original price of the item is $142.
What was the original price of the item?Given the data in the question;
Percentage off the item = 20%Reduced price of the item = $113.60Original price of the item = ?The original price of the item is at 100%, if the 20% is taken off. The price is now at 80%.
Hence 80% of the original price will give the reduced price.
Let the original price be represented by x
80% × x = $113.60
We solve for x
80/100 × x = $113.60
80x/100 = $113.60
Cross multiply
80x = $11360
x = $11360/80
x = $142
Given the percentage taken off and the reduced price, the original price of the item is $142.
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A bag has marbles labeled ‘4’ and ‘7’ and a spinner has 3 options, What is the probability of drawing a number less than 8 or spinning a 4?
Answer:2
Step-by-step explanation:
im just guessing
The answers are :
P (Drawing a number < 8) = 1
P (Spinning a 4) = 0
There are only 2 numbers in the bag, 4 and 7, both of which are less than 8. Hence, as it is a sure event, the probability of the event is 1.
There are only 3 numbers on the spinner, 1, 2, and 3. As 4 is not on the spinner, it is an impossible event, hence the probability of the event is 0.
The age of a father is three times that of his son. In ten year's time their ages will add up to 68 years. If the son is x years old today write down an algebraic expression for: the present age of the father and the son's age in ten year's time and the father's age in 10 year's time.
Answer:
46 and 22
Step-by-step explanation:
let the father b (f) and d son is (s)
so
f=3s.....(1)
(f+10) +(s+10)=68 .... (2)
substitute f=3s in equation (2)
we have
(3s+10)+(s+10)=68
4s+20=68
4s=68-20
4s=48
s=12 .......(3)
substitute (3) in (1)
f=3*12
which f=36
in 10 year time
f+10 =46
s+10=22
How much is 8000% + 80% =
Answer:
8000/100+80/100=80+0.8=80.8
Step-by-step explanation:
hope this helps (❁´◡`❁)
Identify the area of the figure rounded to the nearest tenth.
Please give an Explanation :)
Answer:
67.5 cm²
Step-by-step explanation:
The figure can be decomposed into figures whose area formulas you know.
DecompositionAs the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.
TrapezoidThe area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the parallel bases, and h is the height.
The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...
A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²
RectangleThe area of a rectangle is given by the formula ...
A = LW
where L and W represent the length and width, respectively.
The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...
A = (15 cm)(3 cm) = 45 cm²
Total areaThe total area of the figure is the sum of the areas of the trapezoid and rectangle:
A = (22.5 cm²) + (45 cm²) = 67.5 cm²
The are of the figure is 67.5 cm².
Emma bought snacks for her team's practice. She bought a bag of chips for $2.27 and a 24-pack of juice bottles. The total cost before tax was $51.23. Write and solve an equation which can be used to determine jj, how much each bottle of juice cost.
Answer:
each bottle of juice costs $2.04
Step-by-step explanation:
we first need to minus the cost of chips so we can focus on just the price of the juice bottles.
51.23-2.27
=48.96
this gives the total cost of all 24 bottles but we need the cost of just one, so we divide 48.96 by 24.
which gives us our answer of $2.04 per bottle.
Which graph represents the polynomial function?
f(x)=−x3+x2+9x−9
The curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)
Graph of a polynomialThe graph of a polynomial function is a smooth continuous curve. The point where the curve intersects the x-axis is the zero of the polynomial.
A polynomial is also known to have a degree of 3 and above. Hence the given polynomial has a leading degree of 3 and expressed as:
f(x)=−x^3+x^2+9x−9
The graph of the function is as plotted below. From the function, you can see that the curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)
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The ratio is: 450g to 1kg
In it's simplest form
Answer:
9:20
Step-by-step explanation:
1kg is 1000g grams and in order to simify we need the units to be equal . 450:1000 would simplify to
45: 100 by divinding both the number by 10 then divide both number by 5 which would give 9: 20
hopefully this helped . if you need any more explanation pls ask
pls give brainliest if you like my answer :) thanks
Answer:
9: 20
Step-by-step explanation:
First, we have to convert both figures into the same unit.Here we can convert both into grams.As 450g is already given in grams, let us convert 1kg into grams.To convert kilograms into grams we have to multiply kilograms by 1000.Therefore,1kg × 1000 = 1000g
Now let us write those as a ratio.450 : 1000g
450 : 1000
To write the ratio in the simplest form we can divide both by 50.9: 20
As this cannot be simplified anymore, the simplest form of 450: 1000 is 9: 20.Someone PLEASE HELP MEE
The exponential growth rate is obtained as 0.1099.
What is the rate of multiplication?Now we know that an exponential function has to do with an exponential increase or decrease. An exponential function could increase or decrease and this means that the constant of the function could be a decay constant or a growth constant.
When we have an exponential function, we have to apply the general formula; P(t) = P(o)e^rt
Po = initial number
P(t) = number at time t
r = rate of growth
t = time taken
Thus;
270=90e^10r
270/90 = e^10r
3 = e^10r
ln3 = 10r
r = ln3/10
r = 0.1099
After 13 hours;
P(t) = 90e^(0.1099 * 13)
P(t) = 376
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If each interior angle of a regular polygon measures 157.5°, how many sides does it have?
Step-by-step explanation:
180(n-2)/n =157.5
180n -360/n=157.5
Cross multiplying
180n -360=157.5n
180n-157.5n=360
22.5n=360
22.5n/22.5=360/22.5
n=16, the number of sides the polygon has is 16
Solve for n.
7+2n = 11
Answer:
2
Step-by-step explanation:
7+2n = 11
2n = 11-7
2n = 4
n = 4/2
therefore n = 2
4 pictures on 1/3 of a page
= ________pictures/page
Step-by-step explanation:
4 pictures correlate to 1/3 page.
how many 1/3 pages do we need to get 1 full page ?
3, as 3 × 1/3 = 3/3 = 1.
so, to keep the ratio, we need to multiply also the pictures by 3 and get
4×3 = 12 pictures per page
A grocery store sells a bag of 7 oranges for $2.03. If Mason spent $1.16 on oranges, how many did he buy?
Answer: 4
Step-by-step explanation:
2.03 / 7 = 0.29
1.16 / 0.29 = 4
Mason will get 4 oranges on spending 1.16$
What is Rate of change?
A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.
Here it is given that a grocery store sells a bag of 7 oranges for $2.03,
Now firstly let calculate for 1$ how many oranges Mason get by dividing 7 with 2.03$ :
For 1$ we get = 7/2.03 = 3.5 oranges
Therefore to calculate for 1.16 $ amount spend by Mason will be multiplication of 3.5 with 1.16$ : 3.5 x 1.16 = 4 oranges
Therefore, Mason will get 4 oranges on spending 1.16$
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i want to solve this problem i forgot maths lol 4/5 + 8/5
Answer:
The correct answer is 2 [tex]\frac{2}{5}[/tex].
Step-by-step explanation:
To get this answer, we first have to add the numerators.
We can easily say that 4 + 8 = 12
That leaves us with the improper fraction, [tex]\frac{12}{5}[/tex].
To make this fraction proper, we must first find out how many times 5 can go into 12.
5 can go into 12 two times which leaves us with 2 left over from the numerator.
Now all that's left to do is add 2 (the amount of times 5 can go into 12) and [tex]\frac{2}{5}[/tex] (the left over fraction) to get the answer 2[tex]\frac{2}{5}[/tex].
Hope this helps:) Goodluck!
What's the volume of a pipe that's 4 feet in diameter and 24 feet long? (Use π = 3.1416.)
Answer:
301.5936 cubic ft
Step-by-step explanation:
Formula for the volume of a cylinder is V = pi*r*r*h, where r represents the radius and h represents the height of the cylinder. Since radius is half the length of diameter, the pipe has a radius of 4/2 = 2 ft.
V = pi*r*r*h = 3.1416*2*2*24 = 301.5936 cubic ft
What are the domain and range of the function?
domain:
range:
domain:
range:
domain:
range:
domain:
range:
The domain of f(x) = √(x - 7) +9 is x ≥ 7 and the range of f(x) = √(x - 7) +9 is y ≥ 9
How to determine the domain and the range?The function is given as:
f(x) = √(x - 7) +9
Set the radicand greater than or equal to 0
x - 7 ≥ 0
Add 7 to both sides
x ≥ 7
The above represents the domain
Set the radicand to 0
f(x) = 0 +9
So, we have
f(x) = 9
This represents the minimum value of the range.
So, the range is y ≥ 9
Hence, the domain of f(x) = √(x - 7) +9 is x ≥ 7 and the range of f(x) = √(x - 7) +9 is y ≥ 9
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Answer:
Step-by-step explanation:
Its A
A scale measured a 4.5-pound brick as weighing 5.3 pounds. which measurement is more accurate but less precise than 5.3 pounds? 4.98 pounds 5 pounds 5.52 pounds 6 pounds
The correct option is B.
5 pound
The number (5.3) after Decimal is <5 so it round off to 5.
What is the property of rounding off numbers to one decimal place?It is the same to round a number to one decimal place as to the nearest tenths. At this instance, it is known which numeral is in the hundredths position. When the number in the hundredths place is higher than or equal to 5, the tenths digit is raised by one unit.
How do you round off decimals examples?A typical rule of thumb is to glance at the digit immediately to the right of the place value you want to round to and make your choice. For instance, rounding 5.1837 to the closest hundredth would result in 5.18 (because 3<5), whereas rounding 5.184 to the nearest thousandth would result in 5.184 (because 7>5).
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I understand that the question your are looking for is:
A scale measured a 4.5-pound brick as weighing 5.3 pounds. which measurement is more accurate but less precise than 5.3 pounds?
A. 4.98 pounds
B. 5 pounds
C. 5.52 pounds
D. 6 pounds
-10(1 - 9x) + 6(x - 10)
Pics pls
Answer:
[tex]\boxed{\sf{96x-70}}}[/tex]Step-by-step explanation:
Use the distributive property.
What is a distributive property?Distributive property is a serving to distribute or allot or disperse.
Distributive property:
A(B+C)=AB+AC
A(B-C)=AB-AC
-10(1-9x)+6(x-10)
Expand.
-10(1-9x)
-10*1=-10
-10*9x=90x
[tex]\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}[/tex]
6(x-10)
6*x=6x
6*10=60
6x-60
Rewrite the problem down.
= -10+90x+6x-60
Combine like terms.
90x+6x-10-60
Add the numbers from left to right.
90x+6x=96x
96x-10-60
Finally, subtract the numbers from left to right.
-10-60=-70
[tex]\Longrightarrow \boxed{\sf{96x-70}}[/tex]
Therefore, the final answer is 96x-70.
I hope this helps, let me know if you have any questions.
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Distributive Property :
[tex]-10(1-9x)+6(x - 10)[/tex]
[tex]-10(-9x+1)+6(x - 10)[/tex]
[tex]90x-10+6x-60[/tex]
[tex]90x-70+6x[/tex]
[tex]96x-70[/tex]
[tex]answer : \boxed{\pink\star\tt{96x-70}}[/tex]
━━━━━━━━━━━━━━━━━━━━━━━━
Common factor :
[tex]- 10(1 - 9x) + 6(x - 10)[/tex]
[tex]96x - 70[/tex]
[tex]2(48x - 35)[/tex]
[tex] answer : \boxed{ \pink \star\tt{2(48x - 35)}}[/tex]
please answer this question I f0ll0w u and mark brainiest and give many thanks
Answer:
look above
Step-by-step explanation:
hope it helps
Julia bought stock at $281/8 per share. The value of each share increased by $65/8. How much is each share of stock now worth?
The worth of the share of stock is $[tex]34\frac{3}{4}[/tex].
What is the worth of the stock now?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.
A mixed fraction is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a number where the numerator is less than the denominator.
The worth of the stock now = purchase price + increase in the share price
28 1/8 + 6 5/8
[tex]34 \frac{1 + 5}{8}[/tex]
[tex]34\frac{6}{8}[/tex] = [tex]34\frac{3}{4}[/tex]
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