I'm going to assume that you mean to say that i = √(-1) is a root of the auxiliary equation. That is, if the Cauchy-Euler DE is
x ²y'' + axy' + by = 0
then the auxiliary equation obtained by substituting y = xᵐ is
x ² (m (m - 1) xᵐ ⁻ ²) + ax (m xᵐ ⁻ ¹) + bxᵐ = 0
which reduces to
m (m - 1) + am + b = 0
or
m ² + (a - 1) m + b = 0
By the fundamental theorem of algebra, we can write the quadratic in terms of its roots r₁ and r₂,
(m - r₁) (m - r₂) = 0
Given that one root is the imaginary unit i, and the coefficients of the aux. equation are real, it follows that the other root is -i, because complex roots must occur with their conjugates. So we have as our aux. equation,
(m - i ) (m + i ) = 0
or
m ² + 1 = 0
Then a - 1 = 0 and b = 1, so that the given root and general solution correspond to the DE,
x ²y'' + xy' + y = 0
What is the height of a cylinder if the radius is 6 cm and volume is 904.78
Answer:
8 cm
Step-by-step explanation:
h = v/(pi r^2)
h = 904.78/ (3.1415 * 6^2)
CAN SOMEONE HELP ME WITH THIS?
Answer:
d
Step-by-step explanation:
Jackie runs and dances for 75 minutes every day.
She dances 25 minutes more than she runs.
What is the greatest amount of time she could spend dancing every day,
given she will take a run.
Answer:
I think it is 50 because 75-25=50
America says that the point (0,0) on the graph below means that you use no sugar if you make 1 pie. Is America correct?
Answer:
America is correct
Step-by-step explanation:
it says 0,0 and then it would mean it wouldn't have any sugar in the pies
Answer:
No, America's wrong.
If you look on the graph, as the line increases you can see one pie needs around 3/4(not accurate). (0,0) is the origin point. No sugar is used, and no pie was made.
If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?
Answer:
17 and a half days OR 18 days
Step-by-step explanation:
7 books : 8 days
20 books: x days
cross multiply
x = (8×20)÷ 7
x = 17.5
therefore
17 and a half days or 18 days
What type of association does the graph show between x and y
Answer:
Nonlinear positive association
Step-by-step explanation:
It is nonlinear because it does not form a straight line.
It is positive because it is going up to the right.
I hope this helps!
A pair of pants costs $24.60 when it is on sale for 25% off. What was the
original cost of the pants? (still....no labels!)
well, we know the pants are 25% off, that means the current sale price is only 75% of the original price, say the original price is "x" or 100%. So we know that $24.60 is 75%, what is the 100%?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 24.6&75\\ x&100 \end{array}\implies \cfrac{24.6}{x}=\cfrac{75}{100}\implies \cfrac{24.6}{x}=\cfrac{3}{4} \\\\\\ 98.4=3x \implies \cfrac{98.4}{3}=x\implies 32.8=x[/tex]
write a two column proof. given: ab is congruent to ed, ca is congruent to ce; ac bisects bd. Prove abc is congruent edc.
Given that, AB ≅ ED, CA ≅ CE, and AC bisects BD, the two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.
What is the SSS Congruence Theorem?The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information:
AB ≅ EDCA ≅ CEAC bisects BDSince AC bisects BD, therefore the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
Therefore, it implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), which meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
The two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.Learn more about the SSS Congruence Theorem on:
https://brainly.com/question/19262620
Find the volume of a pyramid with a square base, where the perimeter of the base is 18.1 ft and the height of the pyramid is 28.1 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
191.8
Step-by-step explanation:
Hope this helps!
Step-by-step explanation:
the volume of a pyramid is
base area × height / 3
the base area here is a square.
we know its perimeter : 18.1 ft, which is 4 times the side length.
so, one side of the square is :
18.1/4 = 4.525 ft
the area of the square is side² = 4.525² = 20.475625 ft²
we also know the height of the pyramid, so the volume is :
Vp = 20.475625 × 28.1 / 3 = 191.7883542 ft³
the rounded volume of the pyramid is 191.8 ft³
which statement about decision making analysis is false
Answer: Id personally say D
Step-by-step explanation:
04.03 HC)
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
(10 points)
Part A:
To find the average rate of change, let us first write out the equation to find it.
Δy/Δx = average rate of change.
Finding average rate of change for Section A
Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5
Δx = 1- 0 = 1
Plug the numbers in: Δy/Δx = 5/1 = 5
Therefore, the average rate of change for Section A is 5.
Finding average rate of change for Section B
Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36
Δx = 3 - 2 = 1
Plug the numbers in: Δy/Δx = 36/1 = 36
Therefore, the average rate of change for Section B is 36.
Part B:
(a) How many times greater is the average rate of change of Section B than Section A?
If Section B is on the interval [2,3] and Section A is on the interval [0,1].
For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.
(b) Explain why one rate of change is greater than the other.
Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.
If Janet earned e extra credit points. Mona earned 32 fewer extra credit points than Janet.
What is the expression that shows how many extra credit points Mona earned?
How many terms are in the expression?
subtract 8 and 1/5 - 4 2/5
Answer: = -3
Step-by-step explanation:
a tube has a radius of 4 inches and a height of 4 inches. what's its approximate volume?
Step-by-step explanation:
that is the same as the volume of a cylinder :
pi×r²×height = pi×4²×4 = pi×64 = 201.0619298... in³
≈ 201 in³
Volume is a three-dimensional scalar quantity. The volume of the tube is 201.0619 inches³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a cylinder is given by the formula as shown below,
Volume of a cylinder = πr²h
where r is the radius of the cylinder while h is the height of the cylinder.
Given that a tube has a radius of 4 inches and a height of 4 inches. Therefore, the volume of the tube will be,
The volume of the tube = π × R² × h
= π × (4 inches)² × (4 inches)
= 64π inches³
= 201.0619 inches³
Hence, the volume of the tube is 201.0619 inches³.
Learn more about Volume:
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Simplify the expression 16+(−5)−6/7j−2/7j+6
If you have to fly from JFK airport in New York to LAX airport in Los Angeles, you will fly 2,475 miles. If the average amount of time for a plane to fly from JFK to LAX is 5 hours and 30 minutes, what is the average speed that a plane flies on this trip? Include the appropriate units.
Answer:
450 miles / hour or 201.17 meters/second
Step-by-step explanation:
Speed = distance / time
Distance = 2475 miles
Time = 5 hours and 30 minutes
I will solve this in both miles per hour and meters per second and I am unaware of the appropriate units for your class.
Since 30 minutes = 1/2 an hour, 5 hours and 30 minutes = 5.5 hours
2475 miles / 5.5 hours = 450 miles / hour
1609.34 meters = 1 mile
3600 seconds = 1 hour
450 miles / hour * 1609.34 meters/1 mile * 1 hour/3600 seconds = 201.1675 meters/second (can round to 201.17)
Note that when multiplying, I am simply multiplying the result by 1. Since
1609.34 meters = 1 mile , 1609.34 meters/1 mile = 1 if I divide both sides by 1. Because I multiply by 1, the number is still the same. In terms of the numerator and denominator, I choose which is which by analyzing which units should cancel out. For example, I multiply by 1 hour/3600 seconds because in miles/hour, hour is on the bottom, and hour is on the top in hours/seconds.
Solve for x (13x + 2) (5x - 7) (3x - 4)
Thank you
[tex]\huge \bf༆ Answer ༄[/tex]
As we know, sum of interior angles of a triangle is 180°
that is ~
[tex] \sf13x + 2 + 5x - 7 + 3x - 4 = 180[/tex][tex] \sf21x - 9 = 180 [/tex][tex] \sf21x = 180 + 9[/tex][tex] \sf x = \dfrac{189}{21} [/tex][tex] \sf x = 9 \degree[/tex]
Hence, value of x is 9°
Answer:
x = 9Step-by-step explanation:
Sum of interior angles is 180:
(13x + 2) + (5x - 7) + (3x - 4) = 18021x - 9 = 18021x = 189x = 189/21x = 9What's the missing addend 634 + =644
Answer:
10
Step-by-step explanation:
it is 10 cause 634+10=644
Answer:
10
Step-by-step explanation:
What is the missing addend?
We can fill in the blank with x
634+x=644
Now we need to get x to the other side
The rule to do this is what we do on one side we have to do the same thing to the other side
so if we subtract 634 on one side we also have to do that on the other side as well:
634-634+x=644-634
634-634 is 0
So it is
x=644-634
644-634 is 10
x=10
So the missing addend is 10
Hope this helps!
Larry wishes to invest $1500. he can invest in an investment club which pays simple interest of 8% for 3 years. what is the amount in his account after three years?
A. $1830
B. $1860
C. $5024
D. $1524
Victoria wants to purchase a skateboard. She has $125 to spend. She finds one that regularly sells for $140 and is on sale for 15% off. Sales tax is 7%.
Victoria says that she has enough money to buy the skateboard. Is she correct?
Round 743,214 to nearest ten thousand
Kendall tracked the amount of water his windowsill plant needed each week over ten weeks. Her data is shown below.
Which of the following is true?
A.
There is a negative association between the number of weeks and the ounces of water the plant needed.
B.
There is a positive association between the number of weeks and the ounces of water the plant needed.
C.
There is no association between the number of weeks and the ounces of water the plant needed.
D.
There is both a positive and negative association between the number of weeks and the ounces of water the plant needed.
Answer:
Perfort the indicated operation Show your solution in
the gevin below
During a visit to the tide pools, Brent observed 16 sea stars, 4 sea urchins, and 52 sea anemones. What is the ratio of sea anemones to sea stars?
Answer:
16 to 52
Step-by-step explanation:
expand the function f(x)=(x+5)^3
The function f(x) = (x + 5)³ when expanded is f(x) = x³ + 15x² + 75x + 125
How to expand the function?The function in the equation is given as
f(x) = (x+5)^3
Rewrite this function properly
So, we have the following representation
f(x) = (x + 5)³
Solving further, we need to expand the expression into factors
So, we have the following representation
f(x) = (x + 5)(x + 5)(x + 5)
Next, we expand the first two brackets in the equation
This gives
f(x) = (x² + 5x + 5x + 25)(x + 5)
Evaluate the like terms
This gives
f(x) = (x² + 10x + 25)(x + 5)
Solving further, we need to expand the last two brackets
So, we have the following representation
f(x) = (x³ + 5x² + 10x² + 50x + 25x + 125)
Evaluate the like terms
This gives
f(x) = (x³ + 15x² + 75x + 125)
Remove the brackets
So, we have
f(x) = x³ + 15x² + 75x + 125
Hence, the function is f(x) = x³ + 15x² + 75x + 125
Read more about functions at
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6. Expand the brackets: a) 3(x - y) )
Answer:
3x-3y
Step-by-step explanation:
3(x-y)
open the brackets:
(3×x)-(3×y)
= 3x-3y
Need help please and thank you.
Answer:
[tex]log_4(\frac{1}{64})=-3[/tex]
Step-by-step explanation:
[tex]log_b(b^x)=x[/tex]
Let b = base and x = the exponentLooking at the equation given, we know the base (the number with the exponent) is 4, the exponent itself is -3, and the value is 1/64. Based on this information, fill in the formula and simplify any values.
[tex]log_4(4^{-3})=-3\\log_4(\frac{1}{64})=-3[/tex]
Therefore, the logarithmic form is [tex]log_4(\frac{1}{64})=-3[/tex].
Rebecca can swim 90 meters in 2 minutes. If you graph this with minutes on the x-axis and meters on the y-axis, what will be the slope of the line?
May I please have some help with this problem?
The slope of a line is the average rate of change of the line.
The slope of the line would be 45
From the question, we understand that she can swim 90 meters in 2 minutes.
So, the slope (m) of the line of the graph would be
[tex]m=\frac{90 - 0}{2 - 0}[/tex]
Simplify the numerator, and the denominator
[tex]m=\frac{90}{2}[/tex]
Divide 90 by 2
[tex]m=45[/tex]
Hence, the slope of the line would be 45
Read more about slopes at:
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Circle A was dilated with the origin as the center of dilation to creat circle b
Answer: The answer is B.)
Have a great Day/Night!
A student is told to work any 8 out of 10 questions on an exam. In how many different ways can he complete the exam
Answer:
Step-by-step explanation:
Assuming the order in which he answers the questions matter the answer is the number of permutations of 8 in 10.
This is 10! / (10-8)!
= 1,814.400.
If the order does not matter then the answer is the number of combinations of 8 from 10:
This is 10!/8!*2!
= 45.
Simply:
3 (2x - 2) -2 (x - 2)
A: 3x -3
B: 3x -4
C: 4x -2
D: 4x -4
Answer:
4x-2
Step-by-step explanation:
6x-6-2x+4
=4x-2
