The homogeneous linear ODE
[tex]y^{(4)} + y''' + y'' = 0[/tex]
has characteristic equation
[tex]r^4 + r^3 + r^2 = r^2 (r^2 + r + 1) = 0[/tex]
with a double root at [tex]r=0[/tex] and two complex roots
[tex]r^2 + r + 1 = 0 \implies r = -\dfrac{1 \pm i\,\sqrt3}2[/tex]
Hence the characteristic solution is
[tex]y = C_1 e^{0x} + C_2x e^{0x} + C_3 e^{((-1/2)-i(\sqrt3/2))x} + C_4 e^{((-1/2)+i(\sqrt3/2))x}[/tex]
[tex]y = C_1 + C_2x \\\\ ~~~~~~~~~~ + C_3 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) - i\, \sin\left(\dfrac{\sqrt3}2x\right)\right) \\\\ ~~~~~~~~~~ + C_4 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) + i\,\sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]
[tex]y = C_1 + C_2x + C_3 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_4 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right)[/tex]
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 70 yd whats the length and width
Answer:
length is 20 width is 5
Step-by-step explanation:
35
5 20
According to descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=−4x6−3x5 2x2−4x 1?
There are three possible positive and one negative root for the equation.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
We have been given the equation as
⇒ -4x⁶ - 3x⁵ + 2x² - 4x + 1 = 0
Check the polynomial "as is" for positive zeros, the symbol changes three times. This means that you might either have one or three positive zeros. If they are imagined, they will depart in pairs.
So changes signs 3 times: possible positive roots 3 or 3-2=1
The polynomial must be rewritten as [tex]f(-x)[/tex] for negative zeroes, or
⇒ -4x⁶ + 3x⁵ + 2x² + 4x + 1
This polynomial changes signs just once, So There will have 1 negative zero.
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The question seems to be incomplete the correct question would be
According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation
-4x⁶ - 3x⁵ + 2x² - 4x + 1 = 0
square root 147 simplified
Answer:
7√3
Step-by-step explanation:
79 tens X 27 tens with rounding
3
43. Be Precise To amend the U.S. Constitution, 4
of the 50 states must approve the amendment.
If 35 states approve an amendment, will the
Constitution be amended?
45, In the voting for City Council Precinct 5, only of all e
To amend the U.S. Constitution, 4 of the 50 states must approve the amendment. The Constitution cannot be amended if 35 states approve an amendment.
What do you mean by the Constitution?Constitution is the basic principles and the laws of a nation, state, or social group that determine the powers and duties of the government and guarantee certain rights to the people in it.
We need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be amended, & that is represented like this:
35/50 >= 3/4
that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify fractions to compare easily:
35/50 >= 3/4
7/10 >= 3/4
now we need to find the least common multiplier of 10 and 4 to take fractions to a common denominator and compare easy.
Lets multiply the numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:
7/10 >= 3/4
(2/2)(7/10) >= (5/5)(3/4)
2*7/2*10 >= 5*3/5*4
14/20 >= 15/20
we can see that inequality does not hold, so,
35/50 >= 3/4
does not hold either.
Therefore, the Constitution cannot be amended.
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The total number of data items with a value less than the upper limit for the class is given by the _____ distribution.
The cumulative frequency distribution indicates the total number of data items with values below the class's upper limit.
By cumulative frequency, what do you mean?Cumulative frequency analysis examines how frequently values of a phenomena occur that are less frequent than a reference value. The phenomenon could depend on time or place. Another name for cumulative frequency is frequency of non-exceedance. Each frequency from a frequency distribution table is added to the total of its predecessors to determine the cumulative frequency. Since all frequencies will have previously been added to the prior total, the final result will always be equal to the sum of all observations. The quantity of an element in a set is referred to as the element's frequency. The accumulation of all earlier frequencies up to the present time is another definition for cumulative frequency.
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The Transitive Property states that if a=b and b=c, then a=c. Explain how you can use the Transitive Property to show that the expressions 0 + x + 13 and 13 + x are equivalent.
According to transitive property, 0 + x + 13 = x + 13 and also x + 13 is equal to 13 + x. Thus, we can equally say that; 0 + x + 13 is equal to 13 + x
How to Interpret Transitive Property?
We are told that the Transitive Property states that if a = b and b = c, then a = c.
Now, if a = 3 for example, then by the transitive property, it means that b and c must both also be 5.
Now, we want to apply the the transitive property to show that the expressions 0 + x + 13 and 13 + x are equivalent.
Now, the expression 0 + x + 13 is equal to x + 13.
Now, according to transitive property, 0 + x + 13 = x + 13 and also x + 13 is equal to 13 + x. Thus, we can equally say that;
0 + x + 13 is equal to 13 + x
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If the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5
The 10th score should be 9.5 for the mean to be 5.
What is mean value ?The mean value is the average value of the given data.
According to the given question the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5.
The total average score for 9 games is
= ( 9 × 4.5 )
= 40.5.
The total average score for the mean to be 5 in 10 games is
= ( 10 × 5 )
= 50.
∴ The 10th score must be ( 50 - 40.5 ) which is
= 9.5.
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You rent an apartment that costs \$1100$1100 per month during the first year, but the rent is set to go up 9.5% per year. What would be the rent of the apartment during the 12th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 12th year of living in the apartment is $2076.30
Geometric order is a geometric series or sequence. By multiplying the terms of a geometric series, we arrive to conclusions. A geometric sequence, to put it simply, progresses from one term to the next by multiplying (or dividing) each phrase by the same constant value or number.
A mathematics series is a sum of an infinite number of terms with the objective of maintaining a constant ratio between the progressing terms.
Given:
In the n-th year, the rent will be ...
an = a1·r^(n-1) . . . . . . . . . r is the year on year ratio: 1+rate of increase
an = 1100·(1.095^(n-1))
Then the rent in the 8th year is ...
a8 = 1100·(1.095^(8-1)) ≈ 2076.30
The rent in the 8th year would be $2076.30.
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Which equation is true when c = 3?
2c + 8 = 31
35 − 5c = 32
9 − 6c = 0
4c + 8 = 20
Answer:
4c + 8 = 20
Step-by-step explanation:
To find which equation is true, we have to plug 3 into x in each equation.
2c + 8 = 31
Plug in 3 into c
2(3) + 8 = 31
6 + 8 = 31
14 = 31
Since 14 doesn't equal 31, this equation isn't true.
35 − 5c = 32
Plug in 3 into c
35 − 5(3) = 32
35 - 15 = 32
20 = 32
Since 20 doesn't equal 32, this equation isn't true.
9 − 6c = 0
Plug in 3 into c
9 − 6(3) = 0
9 − 18 = 0
-9 = 0
Since -9 doesn't equal 0, this equation isn't true.
4c + 8 = 20
Plug in 3 into c
4(3) + 8 = 20
12 + 8 = 20
20 = 20
Since 20 equals 20, this equation is true.
Have a lovely rest of your day! :)
It rained a total of 10 inches in a week. the first day it rained 6 inches, then it rained 2/3 every day after that. how many more days did it rain for?
Solving the given fraction, we get that It will rain for 1 day more, that means a total of 2 days.
According to the question, first day it rained 6 inches. Then it rained 2/3 every day after that. Solving the fractions, we get that second day it will rain,
(6 × 2/3) = 4 inches as it rained 2/3 every day after that .
So, it rained a total of, 6 + 4 inches = 10 inches in a week.
We have been given that it rained a total of 10 inches in a week. While solving the fraction, we found that it rained for 10 inches in just days, 6 inches in a day and 4 inches the other day. This tells us that it will not rain for the remaining 5 ( 7 - 2 ) days.
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A rectangular bathroom mirror has a perimeter of 24 feet and an area of 20 square feet. What are the dimensions of the mirror?
A rectangular bathroom mirror having a perimeter of 24 feet and an area of 20 square feet, The length and breadth of rectangle are 10 feet and 2 feet respectively.
Given,
perimeter of the rectangle = 24 feet
area of rectangle = 20 sq. feet
Formula of perimeter of rectangle = 2(L + B)
where L = length of the rectangle , Breadth of the rectangle.
⇒ 24 = 2(L + b)
⇒ 12 = L + B
⇒ L = 12 - B ........(1)
Formula of area of rectangle = L × B
⇒ 20 = L × B
⇒ L = 20 / B .......(2)
From (1) and (2)
equating two equations,
12 - B = 20 / B
⇒ 12B = 20 + B²
⇒ B² - 12B + 20
On solving,
⇒ B = 10, 2
So, the Length and breadth of rectangle are 10 feet and 2 feet
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On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was:______.
On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was Left skewed.
The meaning of grade point averages?
You can determine your grade point average (GPA) by dividing the total number of high school credits you have earned by the total of all of your course grades. The majority of secondary and universities record grades on a 4.0 scale.What exactly does a 4.0 GPA mean?
High schools commonly report grade point averages (GPAs) on a 4.0 scale. A 4.0, or the highest grade, is awarded. You can get your total GPA by averaging your grades from all of your classes. This scale is regularly used in the majority of institutions and many secondary schools.Learn more about grade point averages
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Which is the order from least to greatest of the following: four thirds, 0.8, one fifth, thirty percent?
four thirds, 0.8, one fifth, thirty percent
thirty percent, four thirds, 0.8, one fifth
one fifth, four thirds, thirty percent, 0.8
one fifth, thirty percent, 0.8, four thirds
The order from least to greatest of the numbers will be D. one fifth, thirty percent, 0.8, four thirds.
How to calculate the value?It should be noted that 1/5 = 0.2
It should be noted that 30% = 0.3
It should be noted that 4/3 = 1.33
Therefore the order from least to greatest of the numbers will be one fifth, thirty percent, 0.8, four thirds
In conclusion, the correct option is D.
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A firm has sales of $4690, costs of $2490, interest paid of $164, and depreciation of $463. the tax rate is 30 percent. what is the cash coverage ratio?
13.41% is the cash coverage ratio.
What do we mean by cash coverage ratio?The cash coverage ratio is a calculation that assesses a company's ability to pay off its liabilities with cash that it already has. It is a method of determining a company's liquidity. Only cash and cash equivalents are included in the cash coverage ratio. It excludes things like accounts receivable and inventory.To find the cash coverage ratio:
The cash coverage ratio is calculated as follows:
But first, the EBIDTA Is:
EBIDTA = Revenue - Cost= 4,690 - 2,490= 2,200The Cash Coverage Ratio is now:
= (EBIDTA) ÷ Interest= 2,200 ÷ 164= 13.41Therefore, 13.41% is the cash coverage ratio.
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solve tis question pls
Identify the domain for the following function.
Answer:
( -∞, ∞ )
Step-by-step explanation:
Because the given function has arrows and reaches both up and out in both directions, this means that the domain of the function is All Real Numbers, or ( -∞, ∞ ). When the x-values of a function have no maximums and minimums, then the domain is All Real Numbers.
MP Reason Inductively A student said you
can add the same number to both terms of
a ratio to find an equivalent ratio. Is the
student correct? Explain why or why not.
The student said you.can add the same number to both terms of a ratio to find an equivalent ratio. This is wrong.
How to explain the ratio?It should be noted that equivalent ratios are the ratios that are the same.
In this case, the student said you.can add the same number to both terms of a ratio to find an equivalent ratio. It should be noted that this is incorrect.
The proper thing is to multiply.
For example, 3/4 will be 3 × 2 / 4 × 2 = 6/8. This is the equivalent fraction.
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Answer:
yeah
Step-by-step explanation:
yup
FIND THE TERMS AND SUM OF TERMS:
Answer:
The terms are 2, 6 and 12
The sum is 20
Step-by-step explanation:
n n + 1 n(n+1)
-- ------- ---------
1 2 1 x 2 = 2
2 3 2 x 3 = 6
3 4 3 x 4 = 12
The terms are 2, 6 and 12
The sum is 2 + 6 + 12 = 20
the price for 15 boxes of pencils is $67. The price for 34 boxes is $143. by how much does the cost increase for each additonal box of pencils purchased?
Answer:
$0.3
Step-by-step explanation:
Cost of one box in a set,
→ 67/15
→ 4.47 = $4.5
Cost of one box in another set,
→ 143/34
→ 4.205 = $4.2
The cost increase for each extra box,
→ 4.5 - 4.2
→ $0.3
Hence, the answer is $0.3.
Substitute the given values into the formula, and solve for the unknown variable. A=bh
b=10 A=70
Answer:
h = 7
Step-by-step explanation:
We are given the equation A=bh , and need to work out the unknown variable .
So we substitute the values of A and b given :
70 = (10)(h)
70 = 10 × h
Divide both sides by 10 :
70 ÷ 10 = h
h = 7
Hope this helped and have a good day
Baton Twirling
Jill is a drum major for the Altadena High School marching band.For the finale of the halftime performance, Jill tosses her baton in the air so that it reaches a maximum height of 22 feet. This gives her 2 seconds to twirl around twice and catch the baton when it comes back down.
•independent quantity:
•Dependent quantity:
The independent quantity is the height of the baton and the dependent quantity is the seconds she has to twirl.
What is an independent and dependent variable?The independent variable is the variable that the person carrying out an activity can change or manipulate. It is the independent quantity that determines the dependent quantity.
The dependent variable is the variable that is being measured in an experiment. The dependent quantity is usually affected by the independent quantity.
In this question, the height of the baton determines the time she has to twirl. The higher the baton goes, the longer the time she has to twirl. This makes the height of the baton the independent quantity and the time she has to twirl the dependent quantity.
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find a proposition with three variable p, q and r that is true when at most one of the three variables is true, and false otherwise
The proposition with three variable p, q and r are as -
C = (p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)
What is compound proposition?A proposition is defined as a statement that expresses an idea, suggestion, or plan. A proposition is the notion that death penalty is an effective way to reduce crime.
Now, as per the given question-
This compound proposition C employs the outer disjunction (∨), and it is true if and only if any one of finally three propositions is true, (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.First, it is impossible for two or three of these propositions to be true at the same time. As an example, suppose (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjunction) & r is true (from the second), resulting in a contradiction. All other possible options can be ruled out using the same logic.Because these propositions have become mutually exclusive, C is true if and only if one of the three is true (and false otherwise).
This is only possible if two of p,q, & r are true while the third is false.For instance, (p∧q∧¬r) is true once p and q are true but r is false.
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I need someone to fill in the blanks and and answer the other questions.
1) This is an arithmetic sequence and the complete sequence is;
5, 10, 15, 0, 25, 30, 35,....
2)This is a geometric sequence and the complete sequence is given as;
20, 10, 5, 2.5, 1.25, .....
3) This is an arithmetic sequence and the complete sequence is given as; 2, 5, 8, 11, 14, 17, .....
4) This is an arithmetic sequence and the complete sequence is given as; 30, 24, 18, 12, 6,.....
How to find the sequence terms?1) The sequence is given as;
5, 10, 15, ___, 25, 30, _____
This is an arithmetic sequence with the formula;
a_n = 5 + (n - 1)d
In this case, the common difference is;
d = 10 - 5 = 5
The complete sequence is;
5, 10, 15, 0, 25, 30, 35,....
2)The sequence is given as;
20, 10, ___, 2.5, _____, .....
This is an geometric sequence with the formula;
a_n = 20r^(n - 1)
In this case, the common ratio is;
r = 10/20 = 1/2
The complete sequence is given as;
20, 10, 5, 2.5, 1.25, .....
3)The sequence is given as;
2, 5, 8, ___, 14, _____, .....
This is an arithmetic sequence with the formula;
a_n = 2(n - 1)d
In this case, the common difference is;
d = 5 - 2 = 3
The complete sequence is given as;
2, 5, 8, 11, 14, 17, .....
4) The sequence is given as;
30, 24, ___, 12, 6,.....
This is an arithmetic sequence with the formula;
a_n = 30(n - 1)d
In this case, the common difference is;
d = 24 - 30 = -6
The complete sequence is given as;
30, 24, 18, 12, 6,.....
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The volume, in cubic centimeters, of a fish tank is represented by the polynomial model V(x)=36x^2-3.75x^3. What is the maximum volume of the fish tank?
A. 384.00 cubic centimeters
B. 333.83 cubic centimeters
C. 472.85 cubic centimeters
D. 491.52 cubic centimeters
Answer:
D. 491.52
Step-by-step explanation:
round 1344 to two decimal places
A huge 52-foot subway sandwich is cut into 7 pieces. There are five pieces one length, and the other two pieces are five feet longer. What is the length of the larger pieces?
Based on the length of the subway sandwich, the length of the larger pieces is 11 feet.
How long are the larger pieces?Assume that the length of the shorter pieces is x.
The length of the larger pieces is therefore 5 + x.
The relevant equation to find the length is:
52 = x + x + x + x +x + 5 + x + 5 + x
52 = 7x + 10
x = (52 - 10) / 7
= 6 foot
The length of the larger pieces is:
= 5 + x
= 5 + 6
= 11 foot
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Please help me I’m very confused!!
first off let's keep in mind that an absolute value is really a ± equation in disguise, so |5x -4| can pretty much be rewritten as ±(5x - 4), so is a dual equation, let's solve both for "x".
[tex]|5x-4|\leqslant 3x\implies \pm(5x-4)\leqslant 3x \\\\[-0.35em] ~\dotfill\\\\ +(5x-4)\leqslant 3x\implies 5x-4\leqslant 3x\implies 2x-4\leqslant 0\implies 2x\leqslant 4 \\\\\\ x\leqslant \cfrac{4}{2}\implies {\LARGE \begin{array}{llll} x\leqslant 2 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-(5x-4)\leqslant 3x\implies (5x-4)\stackrel{\stackrel{notice}{\downarrow }}{\geqslant} -3x\implies 8x-4\geqslant 0 \\\\\\ 8x\geqslant 4\implies x\geqslant \cfrac{4}{8}\implies {\LARGE \begin{array}{llll} x\geqslant \cfrac{1}{2} \end{array}}[/tex]
Check the picture below.
Write 7 1/2 as a decimal number.
Answer:
First, We convert it to an improper fraction
which in this case, is 15/2
Found by Multiplying the whole number (7) with the denominator (2) and adding it with the numerator (1)
After that Use the same denominator to get 15/2
and then we divide the new numerator (15) by the denominator (2_ to get our answer.
which is, 7.5.
All Done!
Answer:
7.5
Step-by-step explanation:
Turn into an improper fraction.
2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 1/2 = 15/2
Divide 15 by two.
7.5
Solve the equation −108 = 6x for x.
Answer:
[tex] \sf \large \: x = −18[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
−108 = 6x
Step 1: Flip the equation.
6x = −108
Step 2: Divide both sides by 6.
6x/6 = −108/6
x = −18