The general solution of the given differential equation are: [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]
What are differential equations?A differential equation is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the two.Now,
Given: 3y'' + 2y' + y = 0
To find: General solution of the given differential equation.
Finding:
=> [tex]3\frac{d^{2}y}{dx^{2}} + 2 \frac{dy}{dx} + y = 0[/tex]
The characteristic equation of this equation is:
=> 3m² + 2m + 1 = 0
=> m = [tex]\frac{(-2)± \sqrt{4 - 4(3)(1)}}{2(3)}[/tex]
=> m = [tex]\frac{(-2)±\sqrt{4-12}}{6}[/tex]
=> m = [tex]\frac{(-2)±2\sqrt{2}i}{6}[/tex]
=> m = [tex]\frac{(-1)±\sqrt{2}i}{3}[/tex] = [tex]\frac{-1}{3}[/tex] ± [tex]\frac{\sqrt{2}}{3}[/tex]
Thus, For a = -1/3 and b = (√2)/3,
General solution of the differential equation => [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]
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Two motorcyclist start at the same point and travel in opposite directions. One travels 8 miles an hour faster than the other. In 3 hours they are 288 miles apart how fast is each traveling
Answer:
One motorcycle was going 44 miles and hour and the other motorcycle was going 8 miles an hour faster, so it was going 52 miles per hour.
Step-by-step explanation:
Distance = rate times time
Both motorcycles have a time of 3. We do not know the rates, but we know that one motorcycle's rate was 8 miles an hour faster. Let's call motorcycle 1's rate x then motorcycle 2's rate must be (x + 3)
Motorcycle 1
d = 3x
Motorcycle 2
d = 3(x +8)
We know that the total distance together is 288
3x + 3(x+8) = 288 Distribute the 3
3x + 3x + 24 = 288 Combine the 3's
6x + 24 = 288 Subtract 24 from both sides of the equation
6x = 264 Divide both sides by 6
x = 44
One motorcycle was going 44 miles and hour and the other motorcycle was going 8 miles an hour faster, so it was going 52 miles per hour.
Find the coordinates of the midpoint of a segment with the given endpoints.
C(22,4), B(15,7)
The location of the midpoint of the line segment is (37 / 2, 11 / 2).
How to determine the location of the midpoint in a line segment
According to the statement, the position of the two endpoints of a line segment are known and we must determine where the midpoint is, that is, the point such that the line segment is divided into two parts of equal length. The location of the midpoint is found by means of the midpoint formula:
M(x, y) = 0.5 · B(x, y) + C(x, y)
Where M(x, y) is the midpoint.
If we know that B(x, y) = (15, 7) and C(x, y) = (22, 4), then the location of the midpoint is:
M(x, y) = 0.5 · (15, 7) + 0.5 · (22, 4)
M(x, y) = (15 / 2, 7 / 2) + (11, 2)
M(x, y) = (37 / 2, 11 / 2)
The location of the midpoint of the line segment is (37 / 2, 11 / 2).
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Given h(x) = 4x + 2, find h(5).
Answer:
22
Step-by-step explanation:
4(5)=20
20+2=22
jdjdjdiskfjfiodkfjifofo
Answer:
22 is correct
Step-by-step explanation:
write a two-column proof to verity each conjecture. If -3r+1/2=4, then r=-7/6
Answer:
7/6
Step-by-step explanation:
Solve for T
1 < 4 - t
-
Answer:
[tex] \sf \large \: t<3[/tex]
Step-by-step explanation:
Let's solve your inequality step-by-step.
1<4−t
Step 1: Simplify both sides of the inequality.
1<−t+4
Step 2: Flip the equation.
−t+4>1
Step 3: Subtract 4 from both sides.
−t+4−4>1−4
−t>−3
Step 4: Divide both sides by -1.
−t/−1 > −3/−1
t<3
what would be the value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 6.89? a. 19.32 b. 15.32 c. 18.43 d. 31.89
The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 31.89
What is regression?Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).
The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).
Linear regression determines the actual linear relationship between two variables based on a line of best fit. As a result, the slope of a straight line was used to depict linear regression indicating how altering one variable impacts modifying another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.
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Help me help me help me please
Answer:
D. 24
Step-by-step explanation:
The area of a triangle is [tex]\frac{1}{2} (bh)[/tex].
The height is already given: 8
But we need to find the base and since the hypotenuse is given and it's a right triangle, we can use the pythagorean theorem. (Hypotenuse is longest, slanted side of a right triangle)
The pythagoren theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the sides, and c is the hypotenuse.
Plugging in the given values => [tex]8^2+b^2=10^2[/tex]
We have to solve for b. So, squaring 8 and 10 we get [tex]64+b^2=100[/tex].
Next, subtract 64 from both sides to get b by itself: [tex]b^2=36[/tex]
Square root both sides to get [tex]b=6[/tex].
Now that we have our base we can plug it in to the area of triangle formula: [tex]1/2(6*8)[/tex].
Multiply inside the parenthesis: 1/2(48) => 24
Factorise a^2/8 - b^2/18
Step-by-step explanation:
answer=((a/(2× sqrt 2))+(b/(3× sqrt)))((a/(2× sqrt 2))-(b/(3× sqrt 2)))
method-difference of two squares
Malcolm got his first job. His wage in his first year was $12.50 an hour. In year 2, it was raised to $13.20 an hour. What was the percent increase in his hourly wage between year 1 and year 2?
Answer:
5.6%
Step-by-step explanation:
1) Find the difference between the initial and final values
In this case, a man's hourly wage increased from $12.50 to $13.20. The difference between the hourly wages is $13.20 - $12.50 = $0.70.
2) Divide the difference by the initial value
$12.50 is the initial hourly wage
($0.70 ÷ $12.50) = 0.56
3) Convert the quotient to a percentage
0.56 x 100 = 56%
The man's hourly wage increased by 56%.
Hope this helps, have a great day!
The percentage is the change with respect to the original amount increase in his hourly wage between year 1 and year 2 will be 5.6%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given,
The hourly wage in year 1 = $12.50 an hour
The hourly wage in year 2 = $13.20 an hour
Percentage = change / initial
Percentage = (13.20 - 12.50)/12.50
Percentage = 0.7/12.50
Percentage = 0.056
⇒ 0.056 × 100 = 5.6%
Hence "The percentage is the change with respect to the original amount increase in his hourly wage between year 1 and year 2 will be 5.6%".
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7. Mrs. Jackson's class reads for a total
of 1,544 minutes one day. Each of her
32 students read the same number of
minutes. How many minutes did each
student read?
Answer:
48.25 minutes
Step-by-step explanation:
Divide 1544/32 to find the time per student
IMPORTANT HELPP
What type of transformation is this? Be specific
Answer:
Rotation
Step-by-step explanation:
Rotation at the origin (0,0) by 180*
MATH GENUISES HELP ME OUT WITH MY QUESTIONS PLEASE!
Answer:
Equation: P=$2500+$120N
Total pay if Miguel sells 23 copies: $5260
Divide
266 divided by 15
Hint: The remainder is not a decimal it is the number that is leftover and can no longer be divided
17. The remainder is 11
I showed my work here
https://witeboard.com/537d7850-38f8-11ed-b5a9-6540cf185f3a
Answer:
17, remainder 11
____________
Long Division[tex]Borrow\:6\:from\:the\:ones\:place\\=26\\= 26 - 15(15 \cdot 1)\\= 11\\Drop\:the\:borrowed\:6\\= 116\\= 116 - 105(15 \cdot 7)\\= 11\\\\Using\:the\:numbers\:we\:multiplied\:\:the\:divisor\:by,\\we\:got\:17.\:So\:our\:answer\:would\:be\:17\:with\:a\:remainder\:of\:11.[/tex]
____________
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Work out the cost of a) 1 kg of turnips. b) 1 kg of mushrooms.
The solution to the system of linear equations shows that the cost of 1 kg of turnips is £ 1.1 and the cost of 1kg of mushrooms is £ 2.9.
System of EquationsA system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
First, you should convert the text of the problem into equations, thus you can write:
2m + 2.5t = 8.55 (1)
3m + 4t = 13.10 (2)
where: m = mushrooms and t = turnips
For solving this question, you can apply the addition method. Thus, you should follow the steps below:
Multiply equation 1 by 3 and equation 2 by -2, thus you can rewrite the equations as shown below6m + 7.5t = 25.65 (1)
-6m -8t = -26.20 (2)
Sum equations 1 and 2 and find t-0.5t = -0.55
0.5t = 0.55
Finding mFrom equation 1, you have 6m+7.5t=25.65 . If t= 11/10, you have
6m + 7.5*11/10 = 25.65 * (100)
600 m + 825 = 2565
600 m = 2565 -825
600 m = 1740
m = 1740/600
m=29/10
m=2.9
From the previous steps, you have the answers for the letter a ( £ 2.9 ) and the letter b ( £ 1.1).
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All the data collected in a particular study are referred to as the? inference. variable. data set. population.
Inference is referred to as all the data collected in a particular study.
What is inference?Etymologically, the word "infer" means to "carry ahead." Inferences are stages in reasoning that connect premises to logical conclusions. The dichotomy between deduction and induction in inference theory, which dates at least to Aristotle in Europe, is a classic one (300s BCE). Deduction is inference that results in logical conclusions from premises that are known to be true or that are presumed to be true, while the logic of correct inference is investigated. A universal conclusion is inferred by induction from specific evidence. Contradistinguishing abduction from induction, Charles Sanders Peirce is credited with identifying a third sort of inference. Researchers in the domains of logic, argumentation studies, and cognitive psychology traditionally study human inference (i.e., how people draw conclusions); artificial intelligence researchers create automated inference systems to mimic human inference.
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Approximate negative thirteen plus square root of seventy to the nearest tenth.
−8.4
−4.6
4.6
8.4
Answer:-4.6
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
6
Step-by-step explanation:
Solve for x. 4x + 6 = 2(2x + 3)
Answer:
True for all x/infinite solutions.
Step-by-step explanation:
[tex]4x+6=2\left(2x+3\right) < - Base Equation[/tex][tex]4x+6=4x+6 < - Expand-The-Equation-and-Simplify![/tex]
[tex]4x+6-6=4x+6-6 < - Subtract-Six-From-Both-Sides![/tex]
[tex]4x=4x[/tex]
[tex]4x-4x=4x-4x < - Subtract -4x- from- both -sides![/tex]
[tex]0=0[/tex]
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What is the result of adding these two equations?
The value of the linear equation after adding is -5x -8y = -5.
According to the statement
We have to find that the value of the linear equation.
So, For this purpose, we know that the
The linear equation, statement that a first-degree polynomial—that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable—is equal to a constant.
From the given information:
The given equations are:
4x-4y = -2
-9x-4y = -3.
Then
Now, add these equations then
4x-4y = -2 + -9x-4y = -3.
4x-9x-4y-4y = -2-3
-5x -8y = -5
After addition ,the value becomes -5x -8y = -5.
So, The value of the linear equation after adding is -5x -8y = -5.
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While visiting the zoo, Monika has budgeted $10 for lunch at the café. Can she afford a bacon
cheeseburger, large fries and milkshake? Explain.
The total money Monika spent at the cafe to buy a bacon cheeseburger, large fries and milkshake is $9.9.
Given that, while visiting the zoo, Monika has budgeted $10 for lunch at the café.
How to add decimal numbers?To add decimals, write the numbers in a column, and make sure that the decimal points are aligned. To keep the decimal point in your sum, place a decimal point directly below the decimal points in the addends. Align the decimal point in the sum with the decimal point in the addends, and add a zero if necessary.
Cost of a Cheeseburger= $4.75
Cost of a french fries, a large = $1.90
Cost of a milkshake = $3.25.
Now, the total amount spent at the cafe = Cost of a Cheeseburger + Cost of a french fries, a large + Cost of a milkshake
= (4.75+1.90)+3.25
=6.65 + 3.25
=$9.9
Therefore, the total money Monika spent at the cafe to buy a bacon cheeseburger, large fries and milkshake is $9.9.
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"Your question is incomplete, probably the complete question/missing part is:"
While visiting the zoo, Monika has budgeted $10 for lunch at the café. Can she afford a bacon cheeseburger, large fries and milkshake? Explain.
The cost of food items available at cafe are listed below:
Sandwiches Sides Beverages
Hamburger $3.25
Bacon Cheeseburger $4.75
Chicken Fajita Taco $3.50
French Fries, Small $1.55
French Fries, Large $1.90
Onion Rings $2.40
Cole Slaw $1.45
Soft Drink, Small $1.30
Soft Drink, Large $1.65
Milkshake $3.25
Juice $1.80
Solve system of equations.
y=2 x
y=-x+6
The system of equations involving y = 2x and y = -x + 6 has the solution (2 , 4).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
y = 2x (equation 1)
y = -x + 6 (equation 2)
Since both equations are in the form of y in terms of x ans dome constant, substitute the first equation to the second equation.
y = -x + 6 (equation 2)
2x = -x + 6
Combining the all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
2x + x = 6
3x = 6
x = 2
Substituting the value of x in the first equation,
y = 2x (equation 1)
y = 2(2)
y = 4
Writing it as an ordered pair, we got (2 , 4) as the solution of the system of equations involving y = 2x and y = -x + 6.
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Choose the correct numbers in order to have the following output.
31
34
51
54
for numX in [3, +
for numy in [1,
#
print (numX, numy)
The correct number that represents the output of the print statement is 31
How to determine the correct output of the program segment?The program segment is given as
for numX in [3]
for numy in [1]
print (numX, numy)
The program flow of the above program segment is:
Iterate through the first listIterate through the second listPrint the values of both iterationsIn the above iterations, we have the following values
numX = 3
numY = 1
When both values are printed, we have the output to be 31
Hence, the correct number that represents the output of the print statement is 31
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Answer:
answer 1 = 3,5
answer 2 = 1,4
Step-by-step explanation:
SHOW WORK!!!!!!!!!!!!!!!!
AC = x +3, BC= 8, and AB= 2x-11. Find X
ABC are collinear. Point B is between A and C
Answer:
[tex]{ \rm{ac = ab + bc}} \\ { \rm{(x + 3) = (2x - 11) + 8}} \\ { \rm{2x - x = 3 + 11 - 8}} \\ { \rm{x = 6}}[/tex]
Question 7(Multiple Choice Worth 1 points)
(02.01 MC)
One of the factors of 8x3 - 800x is
O 8x
Ox+10
Ox-10
O All of the above
The factor of the given expression 8x³ - 800x is (A) 8x.
What are the factors?A factor is a number that is multiplied by another number to produce the desired result. The answer to a multiplication puzzle is a product. Imagine multiplying the factors in a multiplication problem to get the answer. For instance, factors 2 and 4 add up to 8: Just two factors or a great many factors can affect a number.In mathematics, a factor is a number or algebraic expression that divides another number or expression evenly, leaving no remainder. Due to the fact that 12 ÷ 3 = 4 and 12 ÷ 6 = 2, respectively, they are factors of 12 as well.1, 2, 4, and 12 make up the remaining 12 factors.So, 8x³ - 800x:
8x³ - 800x ⇒ take the common8x(x² - 100)As a result, (A) 8x is the expression's factor.
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The correct question is given below:
Question 7(Multiple Choice Worth 1 point)
(02.01 MC)
One of the factors of 8x3 - 800x is
A. 8x
B. x+10
C. x-10
D.All of the above
39.
Gregory planted a lemon tree in his back yard. When he planted the tree, it was 2 feet tall. He noticed that it has been growing
eTool (Desmos) Homework Help
a. Create multiple representations (→y table, graph, and equation) to represent the relationship between the days that ha
tree.
b. If the tree continues growing at this rate, when will it be 6 feet tall? How can you see this in each of the representations?
c. State the possible inputs and outputs of the graph.
Find the value of the variable and YZ if Y is between X and Z. XY= 11d, YZ=9d-2, XZ=5d+28
Answer:
d = 2
YZ = 16
Step-by-step explanation:
X-Y-Z
so XY + YZ = XZ
11d + (9d -2) = 5d + 28
11d + 9d - 5d = 28 + 2
15d = 30
d = 30/15 = 2
YZ = 9d - 2 = 9(2) - 2 = 18 - 2 = 16
The ratio of the measures of the three sides of a triangle is 3: 7: 5 , and its perimeter is 156.8 meters. Find the measure of each side.
Answer:
31.36m, 73.2m, 52.3m respectively
Step-by-step explanation:
a ball is dropped from rest. after $t$ seconds, the ball has fallen a distance $d$. relative to this location, how much farther does it fall after another 5$t$ seconds?
The ball will fall 35d after 5t seconds.
Equation Of Motion is used to define the basic concept of motion of object at various interval of times.
There are three equation of motion
[tex](i) v=u+at\\ \\ (ii) s=ut+\frac{1}{2} at^{2} \\ \\ (iii)v^{2}=u^{2} +2as[/tex] (where s=distance, v=final velocity, u=initial velocity ,t=time, a=acceleration)
According to the given question
Given distance = d
time=t
Acceleration a=g( gravity)
Using second equation of motion
[tex]d=ut+\frac{1}{2} at^{2}[/tex] ( given u=0 as the ball was at rest, a=g , s=d)
[tex]d=\frac{1}{2} gt^{2}[/tex]........(1)
Using first equation of motion
Speed after t sec
[tex]v=u+at\\ \\ v=0+gt\\ \\ v=gt[/tex] ....... (2)
Using second equation of motion distance after 5t seconds
since ball is moving with velocity "v", t=5t.
[tex]s=ut+\frac{1}{2} at^{2}\\ \\ d=v(5t)+\frac{1}{2} g(5t)^{2}[/tex]
Substituting the value v=gt from equation (2)
[tex]d=(gt)(5t)+\frac{1}{2} g(5t)^{2}\\ \\ =5gt^{2} +\frac{1}{2} g(5t)^{2}[/tex]taking LCM as 2 and solving further we get
[tex]=35(\frac{1}{2}gt^{2} )[/tex]
using equation (1) we get
=35d
Therefore , The ball will fall 35d after 5t seconds.
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Natalie's fifth grade classroom is 900 square feet. The length is 30 feet. What is the width of her classroom?
Answer:
30
Step-by-step explanation:
30*30 is 900
Answer:
30
Step-by-step explanation:
let x =width
900=(×)(30)
900=30×
900/30=30×/30
30=×
= 30 width
Ted works as a travel guide for a mountain resort, earning
$15.72 per hour. Ted is paid weekly, and works 40 hours in
one week. His current federal withholding per week is $69.
He works in a state with a flat-rate income tax of 4.63%. He
will receive a raise of 5% of his hourly rate. Determine the
change in Ted's net pay per paycheck, after taxes, if his new
federal withholding per week is $75.
Ted's net pay per week after the taxes is $559.09
Net Pay:
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.
Given,
Ted works as a travel guide for a mountain resort, earning $15.72 per hour. Ted is paid weekly, and works 40 hours in one week. His current federal withholding per week is $69. He works in a state with a flat-rate income tax of 4.63%. He will receive a raise of 5% of his hourly rate.
Here we need to find the Ted's net pay per paycheck, after taxes, if his new federal withholding per week is $75.
Through the given details we know that,
Per hour pay = $15.72
Total work per week = 40
So, the total amount for a week is
=> 15.72 x 40
=> $628.8
After federal withholding tax, then the amount is
=> $628.8 - 69
=> $559.8
Now the tax is 4.63%, then
=> $559.8 x 4.63%
=> $559.8 x (4.63/100)
=> $25.91
So, the remaining amount is
=> $559.8 - $25.91
=> $533.88
Now, he will receive 5% for his hourly rate,
Then,
=> $15.72 x (5%)
=> $15.72 x (5/100)
=> 0.78
So, the increased amount is
=> $16.5
Now, the net pay is,
=> (16.5 * 40) - (75 + 25.91)
=> 660 - 100.91
=> 599.09
So, Ted's net pay per paycheck, after taxes is $559.09.
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