The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)
This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.
The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.
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In a recent survey, three out of every five students said they would prefer going to a water park for the class trip.
If 105 students were surveyed, how many can be expected to prefer the water park?
here. hope this helps....
hellllllllllllllllpppppppppppppp
Answer:
32m^2
Step-by-step explanation:
Please help me with my HW
Answer:
Step-by-step explanation:
(9a⁴b⁷) x (6a³b⁸)
(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)
54 x a⁷ x b¹⁵ = 54a⁷b¹⁵
Answer:
(9a⁴b⁷).(6a³b⁸)
=54a⁷b¹⁵
if A={1,2,3}, find the relation in A×S satisfying the condition x+y<5.
Answer: This is copied from the internet:
Step-by-step explanation:
Answer:
For function, every element of the domain must have a unique image in co-domain...
(A)Let us redefine each function as a set of ordered pairs
and see if they satisfy the above condition (A) of a function f1={(1,2),(2,3),(3,4)} ; (4,5) cannot be an ordered pair as 5 does not belong to co-domain , Thus the element 4 of domain does not have an image.
f2={(1,4),(2,3),(2,4),(3,2)(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
The uniqueness is violated as the elements have not one but many images.
f3={(2,1),(3,2),(3,1),(4,1),(4,2),(4,3)} Not a function as in f2 uniqueness is violated.
f4={(1,4),(2,3),(3,2)(4,1)} It is a function as each element has a unique image.
The perimeter of a square is 48. If the perimeter is 4 times than before then find the number of times the area becomes of what it was before.
Answer:
12?
Step-by-step explanation:
Lowkey don't understand the last part of your q but if it's 4 times then if the original was 12 48 is four times bigger
Please help me! I don't understand
Answer: 12
Step-by-step explanation:
The smaller triangles on the right can be proven congruent, so the other side also equals 6. 6+6=12
You borrowed $59,000 for 2 years at 11% which was compounded annually. What
total will you pay back?
Answer:
$72693.9
Step-by-step explanation:
To get this answer you need to use the compound interest formula, which will be A=P(1+r/n)^n(t). P=59,000 r=11%=0.11 n=1 (annually) t=2 years. From there you should be able to figure the rest out and get the answer. Hope this helps!
How do you calculate the number of seeds per acre?
1. Convert lb./acre to grams/acre
2. Use the TKW to calculate seeds per acre.
What is acre?The imperial system and US customary systems both use acres as a measure of land area.
According to traditional definitions, it is the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1640 of a square mile, 4,840 square yards, or 43,560 square feet, and roughly 4,047 m2, or roughly 40% of an acre.
A declared acre is equal to 4,046.8564224 square metres according to the 1959 international yard and pound agreement. Although the word "acre" is typically spelled out, the abbreviation "ac" is sometimes used instead.
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Brian has 64 flowers for a big party decoration. In addition, he is considering buying flower arrangements that have 18 flowers each. All of the arrangements cost the same. Brian can buy up to 5 arrangements given the amount of money he has. Let x represents the number of flower arrangements Brian buys. Write a function rule to describe how many flowers Brian will have based on the number of arrangements he buys. Find a reasonable range for the function.
The function which can which can define the number of flowers in the arrangement is f(x) = 64 + 18x. The domain is found to be [ 0 , 5 ] and the range is [ 64 , 154 ].
Let the number of flowers which is to be calculated be x,
now we know that she already have 64 flowers and that each arrangement will have 18 flowers.
Therefore, the number of flowers can be given by the function , f(x) = 64 + 18x.
Now , we know that the maximum number of flowers which she can buy externally is 5 , which means the domain becomes [0,5] .
To find the range we will put the value of domain in the given function.
when x = 0 ,
f(0) = 64
when x = 5,
f(5) = 154
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Gabe and Bridgette are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare.
p = the number of people Gabe and Bridgette will be able to serve
m = the number of meals Gabe and Bridgette prepare
Which of the variables is independent and which is dependent?
Answer:
The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.
Step-by-step explanation:
In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.
Answer:
independent variable = m
dependent variable = p
Step-by-step explanation:
The number of people they are able to serve depends on the number of meals they prepare.
please help and explain
Answer:
look at the picture I sent
PLEASE HELP ASAP! 55 POINTS Jackie wraps a sheet of paper tightly around a wax candle whose diameter is two inches, then cuts through them both with a sharp knife, making a 45° angle with the candle's axis. After unrolling the paper and laying it flat, Jackie sees the wavy curve formed by the cut edge, and wonders whether it can be described mathematically. Sketch this curve, then show that it is sinusoidal. It is very helpful to use radian measure to describe angles in this problem.
Which number will have the same result, when rounded to the nearest hundred or thousand? (3-5) A 1,049 B 1,118 and 5 C 1,179 D 2,149
Answer:
The answer is "Option A".
Step-by-step explanation:
In this question except for choice "A", all the value is not nearest about the hundred or thousand, that why the correct answer is "1,049".
which answer? (multiple choice).
Rasheen and Eric went to Taco Express. Rasheen bought seven tacos and two fajitas and paid $12.65. Eric bought four tacos and one fajita and paid $6.95. Find the cost of one taco.
Question 8 options:
$1.35
$1.45
$1.25
$1.95
Please help. Worth 30 points.
Answer:
y = -3x + 5)
Step-by-step explanation:
We see immediately that the line crosses the y-axis at (0, 7). The line also goes through (4, -5). As we move from the first to the second point, x increases by 4 and y decreases by 12. Thus, the slope of this line is m = -12/4, or m = - 3.
Using the slope-intercept form,
y = -3x + 5)
Answer: y=3x+7
Step-by-step explanation: You need to remember y=mx+b. M is the slope and b is the y intercept. The y intercept is easy as it's were the line touches the y axis or in this case 7. The slope is rise over run meaning you find a point on the graph like (2,1) and you count how many spaces up until your next to a point, and then you see how many spaces you have to move over or run. In this case you rise 3 and run 1 meaning the slope is [tex]\frac{3}{1}[/tex] or just 3.
Please find the perimeter of this irregular shape. NO LINKS!
Answer:
36
Step-by-step explanation:
Starting at the uppper left and counting the blocks
3 + 2 + 3 + 2 + 4 + 6 + 4 + 2 + 6 + 4 = 36
What is the slope of the line through the points (-8, 4) and (4,4)?
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-4)/(4-(-8))
m=0/(4+8)
m=0/12
m=0
NO FILES AT ALL JUST HELP ME
Answer:
4/20
Step-by-step explanation:
6x10^-3 x 2 x 10^-4 =
Please help
Answer:
0.0000012
Step-by-step explanation:
I hope this helps you! :D
which system of equations has only one solution
4x+2y=8 -4x-2y=3
A rectangular prism and its dimensions are shown in the diagram.
26
6.5 in.
5 in.
7.5 in.
What is the total surface area of this prism in square inches?
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.
Answer: 21
Step-by-step explanation: you add and subtract
Answer:
21
Step-by-step explanation:
What is the perimeter?
Help plz...
And No links!!I repeat No links!!
Answer:
b= 8
Step-by-step explanation:
you use Pythagorean theorem to solve this problem
a² + b² = c²
since you already have a and c and you're missing b you rearrange the formula to:
[tex]c^{2}[/tex]-[tex]a^{2}[/tex] = b²
17² - 15² = b²
64² = b²
[tex]\sqrt{64}[/tex] = b
8 = b
Step-by-step explanation:
To find side b use Pythagoras theorem:
Hypotenuse²=Base²+Height ²
17²=B²+15²
289-225=B²
64=B²
√8=B²
So,
8 yards is Side B
Now,
We can use Heron's Formula
√S(S-A) (S-B) (S-C)
Let's find semi perimeter
17+15+8/2
40/2=20
So, S=20
Let A=8,B=15,C=17
√20(20-8) (20-15) (20-17)
√20×12×5×3
√2×2×5×5×2×2×3×3 (Factorising the numbers)
2×5×2×2×3
120 yards Answer
hope it helps...
108% of 75.5 is what number
Answer:
81.54
Step-by-step explanation:
% of a # = (% * #)/100
% = 108
# = 75.5
(108 * 75.5)/100
8,154/100
81.54
OR
% of a # = (%/100) * #
% = 108
# = 75.5
(108/100) * 75.5 = 1.08 * 75.5
81.54
Is Avogadro's number the same for all elements?
The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.
What is an atom?
Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.
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Find the measure of MN
Answer:
The measure of arcMN is 60°
Step-by-step explanation:
All the way around the circle is 360°. Two marked arcs are 100° and 140°. AngleMON and AngleNOP are marked equal, which means that ArcMN and ArcNP are also equal. So we can write an equation:
100+140 + x+x =360
combine like terms.
240 + 2x = 360
subtract 240.
2x = 120
divide by 2
x = 60
ArcMN is 60°
What is '__ main __'?
In Python, __main__ is the name of the environment where top-level code is run.
We know that in Python, the main function acts as the starting point of execution for any software program.
As we know the program executes only when it runs directly, and if it is imported as a module, then it will not run, the execution of the program starts only when the main function is defined in Python.
__main__ is the name of the top-level scope in which top-level code executes.
Also, all the functions and modules will be executed in the top-level scope __main___ in the interpreter shell.
Using the top-level scope __main__ increases the reusability.
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John has the option to take the bus or a taxi to work each
day.
.
The bus costs $3. 00 per mile.
The taxi has a flat rate of
$4. 00 plus $1. 00 per mile.
Complete the blanks:
At _____miles, both the bus and the taxi will cost _____ dollars.
At 2 miles, both the bus and the taxi will cost $6.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that the fare on bus is $3 per mile.
The taxi fare of taxi is $4. 00 plus $1. 00 per mile.
Assume that at x miles both fare will be the same.
The fare for x miles in bus is $3x.
The fare for x miles in taxi is $4 + $x
Equate to the fares:
3x = 4 + x
Subtract x from both sides:
3x - x = 4
2x = 4
Divide both sides by 2:
x = 4/2
x = 2.
The fare for 2 miles in bus is $3×2 = $6.
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Solve Similar Triangles (advanced)
Solve for X.
Given:
[tex]m\angle B=90^\circ, m\angle D=90^\circ, AB=6, BD=4, BC=2, DE=x[/tex].
To find:
The value of x.
Solution:
In triangles ABC and ADE,
[tex]\angle B\cong \angle D[/tex] (Right angles)
[tex]\angle A\cong \angle A[/tex] (Common angles)
[tex]\Delta ABC\sim \Delta ADE[/tex] (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{AB}{AD}=\dfrac{BC}{DE}[/tex]
[tex]\dfrac{6}{(6+4)}=\dfrac{2}{x}[/tex]
[tex]\dfrac{6}{10}=\dfrac{2}{x}[/tex]
[tex]\dfrac{3}{5}=\dfrac{2}{x}[/tex]
On cross multiplication, we get
[tex]3\times x=5\times 2[/tex]
[tex]3x=10[/tex]
[tex]x=\dfrac{10}{3}[/tex]
Therefore, the value of x is [tex]\dfrac{10}{3}[/tex] units.
i need this answered
Answer:
69 pi is your answer.