The system of first-order equations for the equation u" + 0.5u' + 2u = 0 is u' = v and v' = -0.5v - 2u.
The system of first-order equations for the equation tu" + tu' + (12 - 0.25)u = 0 is u' = v and v' = -(1/t)v - (12-0.25)/t u.
The system of first-order equations for the equation u(4) - 1 = 0 is w = v', v = u', and u(4) = 1.
To transform given equations into a system of first-order equations, new variables are introduced to represent the derivatives of the unknown function, allowing the original equation to be expressed as a system of first-order equations.
To transform each of these given equations into a system of first-order equations, we can introduce new variables.
Let v = u' and w = v'. Then, we can rewrite the given equations as follows:
1. u' = v
v' = -0.5v - 2u
2. u' = v
v' = -(1/t)v - (12-0.25)/t u
3. w = v'
v = u'
u(4) = 1
Note that in the third equation, we introduced a new variable w to represent the second derivative of u. This is because the original equation only had a single derivative, so we needed to introduce a new variable to represent the second derivative.
In general, to transform a given equation of order n into a system of first-order equations, we introduce n new variables to represent the first n-1 derivatives of the unknown function. This allows us to rewrite the original equation as a system of n first-order equations.
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Make x the subject
y = 5x + 3
Answer:
x=y-3/5
Step-by-step explanation:
y=5x+3
y-3=5x
y-3/5=x
x=y-3/5
hii please help i’ll give brainliest if you give a correct answer!
Answer:
8
Step-by-step explanation:
What equation below is a perpendicular line to the line y=-4x+8
How many vehicles are at Nam's Gas Station?
Answer:
23
Step-by-step explanation:
The number of car are in the y-intercept line so just add each one of the for every different bar.
3 + 4 + 5 + 6 + 3 + 2 = 23
So there are 23 vehicles in total.
The number of vehicles are at Nam's Gas Station is 23
Calculation of the number of vehicles:Since The number of cars are in the y-intercept line
So here the no of vehicles should be
= 3 + 4 + 5 + 6 + 3 + 2
= 23
Here we added according to the given graph
Therefore, we can conclude that The number of vehicles are at Nam's Gas Station is 23
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simplify -8-(12)+(-2)
Answer:
-22
Step-by-step explanation:
-8-(12)+(-2)
-8-12-2
-20-2
-22
HOPE THIS HELPS!
Hi! I am Khushi
can you all please tell me the answer of this question.
The question is:
Convert 4:1 into percentage
the options are:
(a) 80%:20%
(b) 75%:25%
(c) 60%:40%
(d) 20%:80%
Answer:
80%:20%
Step-by-step explanation:
100 divided by 5 = 20
20 x 1 = 20
20 x 4 = 80
Meaning 80%(4):20%(1)
A container of bread contains: 8 red beads, 6 yellow beads, and 6 green beads. A bread will be drawn from the basket and replaced 60 times. What is a reasonable prediction for the number of times a green or red is drawn?
Guys please help
which phrase has the same meaning as 12y - 2?
Answer:
subtract 2 from the product of 12 and y
Step-by-step explanation:
what is 1/6x + 3/4(1/2x - 4)?
Answer:
13x/24-3
Step-by-step explanation:
Answer:
hello! :) have a good day!
[tex]\frac{13x}{24\\} -3[/tex]
please helppppp please asap
Answer:
126.8
Step-by-step explanation:
angles opposite each other when two lines cross are always equal
Evaluate x=-3, y=4, z=-5
Answers suggested below
-17
41
23
-40
-58
-16
Answer:
2. -16
6. 23
7. -40
8. -17
9. 41
10. -58
I NEED HELP ASAP, AND PLZ DONT SPAM
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the indices,
After applying the log rules we get the equation as,
===> 3-x = 1/2
===> x = 5/2
4 minutes 53 seconds to seconds
Answer: 293 Seconds
Step-by-step explanation:
Answer:
293 seconds
Step-by-step explanation:
one minute = 60 seconds
4 x 60 = 240 seconds -------> use the equation above to multiply per min
240 + 53 = 293 seconds -------> add the remaining seconds to find total
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 4 if she rolls the two number cubes 216 times?
Answer:
18 times
Step-by-step explanation:
Sample space ; roll of 2 number cubes = 6^2 = 36
Sum of 4 in 2 cube rolls = 3
Probability = required outcome / Total possible outcomes
P(sum of 4) = 3 / 36 = 1 / 12
If number cube is rolled 216 times :
Probability on 1 roll * Number of rolls
(1 / 12) * 216
0.0833333 * 216
= 18
How many turning points are there in the graph of y = x^3 - 2x^2 - 2 ?
A. 1
B. 2
C. 3
D. 4
Answer:
D, i think
Step-by-step explanation:
Determine the geometric mean of 11 and 8.
Answer:
[tex]\sqrt{88}[/tex]
Step-by-step explanation:
The geometric mean of 11 and 8 is equal to [tex]\sqrt{88}[/tex].
According to the question it is clear that we have to calculate the geometric mean of two positive numbers 11 and 8.
The geometric mean of two positive numbers a and c is the positive number b in such a way that it satisfies the condition
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
The geometric mean of a and b is √ab if a and b are both positive numbers and it will be −√ab if a and b are negative numbers.
The geometric mean is the positive square root of the product of two numbers.
For a square the geometric mean of two numbers a and b, is the length of one side of a square whose area is equal to the area of a rectangle with the sides of a and b lengths.
If we talk about the n numbers then the geometric mean is the nth root of the product of n numbers. If n positive values are given then the geometric mean is the nth positive root of the product of that n numbers.
So, the geometric mean is equal to [tex]\sqrt{a.b}[/tex]
Here, a = 11 and b = 8
The geometric mean of this is equal to = [tex]\sqrt{11.8}[/tex] = [tex]\sqrt{88}[/tex]
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2(3x-9)=2x+10 what's x
Answer:
x = 7
Step-by-step explanation:
2(3x-9)=2x+10
6x - 18 = 2x + 10
4x = 28
x = 7
Answer:
x = 7
Step-by-step explanation:
In order to find the value of x, isolate it in the equation.
1) First, distribute the 2 to the terms inside the set of parentheses.
[tex]2 (3x - 9) = 2x + 10 \\6x - 18 = 2x + 10 \\[/tex]
2) Next, move all the x terms to one side and all the other terms to the other side. Subtract both sides by 2x and add both sides by 18.
[tex]6x - 18 = 2x + 10 \\4x = 28[/tex]
2) Divide both sides by 4 to finally isolate x.
[tex]4x = 28 \\x = 7[/tex]
Thus, x = 7.
[tex] \frac{4}{5 } + \frac{3}{20} = [/tex]
Answer:
Step-by-step explanation:
[tex]\frac{4}{5}+\frac{3}{20}\\ \\ \frac{4}{5}\left(\frac{4}{4}\right)+\frac{3}{20}\\ \\ \frac{16+3}{20}\\ \\ \frac{19}{20}[/tex]
Desmond spends $800 per month on fixed expenses. Desmond earns $10,00 per hour,
How many hours does Desmond need to work each month to spend 50% of his/her income
on fixed expenses?
Answer: 160 hours
============================================================
Explanation:
He earns $10.00 an hour. Let x be the number of hours worked in a month. So 10x represents how much he earns after working x hours.
If he spends $800 per month on fixed expenses, and wants this to be 50% of his total earnings, then this must mean that the other 50% is for other things (eg: spending on a vacation or putting it to savings). So his goal is to earn 800+800 = 1600 dollars per month.
Set 10x equal to this and solve for x
10x = 1600
x = 1600/10
x = 160
He needs to work 160 hours a month.
-------------------------------
Extra info:
Divide 160 over 4 (the approximate number of weeks in a month) and we see that he'll need to work 160/4 = 40 hours a week
If he only works Monday through Friday, that's 5 days of the week. So he'll put in 40/5 = 8 hours per day.
So his goal of working 160 hours per month is reasonable. Keep in mind that this doesn't include factors like him missing time from work due to being sick (unless he has paid sick leave).
If the radius is 10 ft, what will the area of the circle be?
Answer:
A=πr2=π·102≈314.15927ft²
Step-by-step explanation:
Answer:
314.16
Step-by-step explanation:
The formula is [tex]\pi rx^{2}[/tex]
how do you find the x-intercepts if given the following polynomial in factored form?
X(x-2)^2(x+4)(x+1)
Answer:
Step-by-step explanation:
You know the intercepts occur at x = 0, so set each part of the factored form equal to zero and solve for x.
The first part, plain X = 0, so X = 0 is a root, an x-intercept
The second part (X-2)^2 = 0, so X = 2 is another root. Since the function is being squared, this root will happen twice. The function crosses this root twice.
The third part (x+4) = 0, so x = -4 is another root.
Finally, (x+1) so x = -1 is another root.
So you have X = 0, X = 2, X = -4, X = -1 as your x-intercepts
Find y. Simplify completely.
y = [?]
Enter the number that belongs in the green box.
Please helpppp
Answer:
181?
Step-by-step explanation:
I saw a thing that it was A-squared plus B-squared=C.
9 squared=81. 10 squared=100. 100+81=181.
(If you have checks, I would definetely try it. But if you don't, and it's like a quiz or test, I wouldn't try it cuz I'm not 100% sure.
Answer:Y=190
Step-by-step explanation:I finished my exam and this answer was y=190 :) I hope I helped
In the triangle below x= cm round to the nearest tenth 15 is the hypotenuse 35 is a angle and 90 in an angle. Please help
Answer:x= 38.079
Step-by-step explanation:
655 + (6.3 x 170) + (4.7 x 58) - (4.7 x 18)
Answer:
1914
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
655 + (6.3 × 170) + (4.7 × 58) - (4.7 × 18)
Step 2: Evaluate
(Parenthesis) Multiply: 655 + 1071 + (4.7 × 58) - (4.7 × 18)(Parenthesis) Multiply: 655 + 1071 + 272.6 - (4.7 × 18)(Parenthesis) Multiply: 655 + 1071 + 272.6 - 84.6Add: 1726 + 272.6 - 84.6Add: 1998.6 - 84.6Subtract: 1914how do I solve this
Answer:
113
Step-by-step explanation:
DQ= 180-112= 68
and sum of ang in quad add to 360 so
lets call what we have to find x
so x+ 68+56+123= 360
x+247=360
x= 113
help i have this question and i’m not sure what the answer would be
Answer:
2 10 or 100 2
Step-by-step explanation:
Answer:
The second one
Step-by-step explanation:
Which of the following best describes the solution to the system of equations below?
6x + 5y=8
6x + 5y=15
A. The system of equations has infinitely many solutions.
B. The system of equations has exactly one solution where x=0 and y =8/5
C. The system of equations has no solution.
D. The system of equations has exactly one solution where x = 8 and y= 15.
Answer:
the correct answer is C the system of equations has no solution.
What is the answer to this question? x−7≤−5
Answer:
x<=2
Step-by-step explanation:
x-7<=-5
x<=-5+7
x<=2
(5x-8)
+
(2x+19)
Find the value of x.
OA.5
B.7
C.9
D.11
Answer:
x=9 option C
Step-by-step explanation:
explanation above
Please mark me as brainlist
8 + 3n ≥ 38 do yall know??? solve please
Answer:
n ≥ 10
Step-by-step explanation:
Given
8 + 3n ≥ 38 ( subtract 8 from both sides )
3n ≥ 30 ( divide both sides by 3 )
n ≥ 10