Answer:
5/9, 9/12, 6/7, 6/9 are the ones I believe so far
Step-by-step explanation:
3. For each differential equation, find the Laplace transform of the solution y:
3y' + 5y = x^2 , y(0) = 2.
y'' − y = 5e^−4x + 2x, y(0) = y'(0) = 0.
y'' + 3y' + 2y = 5 sin(πx), y(0) = y'(0) = 0.
Answer:
See below for answer
Step-by-step explanation:
First problem
[tex]3y'+5y=x^2,\: y(0)=2\\\\3\mathcal{L}\{y'\}+5\mathcal{L}\{y\}=\mathcal{L}\{x^2\}\\\\3[sY(s)-y(0)]+5Y(s)=\frac{2}{s^{3}}\\ \\3[sY(s)-2]+5Y(s)=\frac{2}{s^{3}}\\\\3sY(s)-6+5Y(s)=\frac{2}{s^{3}}\\\\(3s+5)Y(s)-6=\frac{2}{s^3}\\ \\(3s+5)Y(s)=\frac{2}{s^3}+6\\\\Y(s)=\frac{2}{s^3(3s+5)}+\frac{6}{3s+5}\\ \\Y(s)=\frac{2+6s^3}{s^3(3s+5)}[/tex]
Perform the partial fraction decomposition
[tex]\frac{2+6s^3}{s^3(3s+5)}=\frac{A}{s}+\frac{B}{s^2}+\frac{C}{s^3}+\frac{D}{3s+5}\\ \\2+6s^3=s^2(3s+5)A+s(3s+5)B+(3s+5)C+s^3D\\\\2+6s^3=3s^3A+5s^2A+3s^2B+5sB+3sC+5C+s^3D\\\\2+6s^3=3s^3A+s^3D+5s^2A+3s^2B+5sB+3sC+5C\\\\2+6s^3=s^3(3A+D)+s^2(5A+3B)+s(5B+3C)+5C[/tex]
Solve for each constant
[tex]\begin{cases} 3 A + D = 6\\5 A + 3 B = 0\\5 B + 3 C = 0\\5 C = 2 \end{cases}[/tex]
[tex]5C=2\\C=\frac{2}{5}[/tex]
[tex]5B+3C=0\\5B+3(\frac{2}{5})=0\\5B+\frac{6}{5}=0\\5B=-\frac{6}{5}\\B=-\frac{6}{25}[/tex]
[tex]5A+3B=0\\5A+3(-\frac{6}{25})=0\\5A-\frac{18}{25}=0\\5A=\frac{18}{25}\\A=\frac{18}{125}[/tex]
[tex]3A+D=6\\3(\frac{18}{125})+D=6\\\frac{54}{125}+D=6\\D=\frac{696}{125}[/tex]
Take the inverse transform and solve for the IVP
[tex]Y(s)=\frac{\frac{18}{125}}{s}+\frac{- \frac{6}{25}}{s^{2}}+\frac{\frac{2}{5}}{s^{3}}+\frac{\frac{696}{125}}{3 s + 5}\\\\y(x)=\frac{18}{125}-\frac{6}{25}x+\frac{1}{5}x^2+\frac{232}{125}e^{-\frac{5}{3}x}[/tex]
a class has 28 students 13 boys and 15 girls what is rstio girls to boys
Answer:
15 : 13
Step-by-step explanation:
Girls : Boys
15 : 13
A scientist mixes water (containing no salt) with a solution that contains 20% salt. She wants to obtain 140 ounces of a mixture that is 5% salt. How many ounces of water and how many ounces of the 20% salt solution should she use?
Hi please help me really need it!
Answer:
C
Step-by-step explanation:
To Solve, just cube the terms on the right side to see if they go back to the number on the left.
The first part is true because multiplying 11 * 11 * 11 = 1331.
The second part is true because multiplying 5 * 5* 5 = 125.
The third part is false because multiplying 8 * 8 * 8 = 512.
The fourth part is true because multiplying 1 * 1* 1 = 1.
24
,
Factor:
x²-9
A
(x + 3XX-3)
B
(x+3)2
с
(x-3)
(x+3)(x+3)
Answer:
(x-3)(x+3)
Step-by-step explanation:
We are given the expression [tex]\displaystyle \large{x^2-9}[/tex]:—
To factor this expression, we have a formula for it which is difference of two squares:—
[tex]\displaystyle \large{a^2-b^2=(a+b)(a-b)}[/tex]
You can also swap from [tex]\displaystyle \large{(a+b)(a-b)}[/tex] to [tex]\displaystyle \large{(a-b)(a+b)}[/tex] via multiplication property.
From the expression, factor using the formula above:—
[tex]\displaystyle \large{x^2-9=(x^2)-(3)^2}\\\displaystyle \large{x^2-9=(x-3)(x+3)}[/tex]
Therefore, the factored expression is:—
[tex]\displaystyle \large{\boxed{(x-3)(x+3)}}[/tex]
__________________________________________________________
If you have any questions regarding the problem or need clarification of my answer/explanation, do not hesitate to ask in comment!
please help with math
Graphing an interger function and finding its range for a given domain
For the function and given domain, the range is {-9,-1,5,7}.
Linear FunctionA linear function can be represented by a line. The standard form for this equation is: [tex]y=ax+b[/tex], for example, y=2x+7.
Domain and RangeThe domain of a function is the set of input values for which the function is real and defined. On the other words, when you define the domain, you are indicating for which values x the function is real and defined.
While the domain is related to the values of x, the range is related to the possible values of y that the function can have.
The equation of this exercise, 2x+1, is a linear equation because it presents the form: ax+b. Thus, you already know that your graph will be a line.
Find values of y for given domain:For this, you should replace -5,-1, 2,3 for x in the equation 2x+1.
For x=-5, [tex]y=2*(-5)+1=-10+1=-9[/tex]
For x=-1, [tex]y=2*(-1)+1=-2+1=-1[/tex]
For x=2, [tex]y=2*(2)+1=4+1=5[/tex]
For x=3, [tex]y=2*(3)+1=6+1=7[/tex]
Therefore, the range is {-9,-1,5,7}
Plot the graphFrom the values x of domain and the values of y calculated previously, plot the points and draw the line. See the image attached.
Learn more about the range and the domain here:
brainly.com/question/10197594
A school hires an entertainment company to host a party. The company charges
a setup fee of $75, plus $500 per hour. The same company pays 7 employees $20
per hour. Write a function that models the amount of money the company will
receive for hosting the party and another function that shows how much it will
cost the company to host the party. Combine the two functions to show the
amount of revenue the company will make for hosting the party. How much
money will the company make if the party lasts 5 hours?
Answer:
Money received = $(75 + 500.t)
A college basketball stadium has 4 sections of seats. Each section has 24 rows, with 15 seats in each row. During a basketball game, one of the sections was entirely filled with fans. How many fans were sitting in this section?
Answer:
360 fans were sitting in that section.
Step-by-step explanation:
multiply 24 by 15
please help me with this escape room !
Answer:
16. L
17. I
18. H
Step-by-step explanation:
Answer:
LIH
16. L
17. I
18. H
Step-by-step explanation:
[tex]16. \sqrt{45a^{2}b } =\sqrt{(9)(5)a^{2} b} =3a\sqrt{5b}[/tex]
[tex]17. \sqrt{54a^{2}b^{3} } =\sqrt{(9)(6)a^{2}b^{2}b } =3ab\sqrt{6b}[/tex]
[tex]18. \sqrt{45ab^{4} } =\sqrt{(9)(5)ab^{2}b^{2} } =3b^{2} \sqrt{5a}[/tex]
Hope this helps
Find the number of subsets of the set {1, 2, 3, ..., 9}
Answer:
512
Step-by-step explanation:
the number of subsets of the set {1, 2, 3, ..., 9} is : 2^9 = 512
Solving Multi-step Equations
Solve the equation 9x+2=3x+4 algebraically.
Answer:
x=1/3
Step-by-step explanation:
9x+2=3x+4
Minus 2 from both sides: 9x=3x+2
Minus 3x from both sides: 6x=2
Divide by 6: 2/6=1/3
x=1/3
Answer:
x=1/3 or x=0.3
Step-by-step explanation:
If it is a fraction it will be the first one if not I will be the second one
A rectangular swimming pool has a base of 200 square feet. The pool has a depth of 5 feet. What is the volume of the pool? 25 ft³ 100 ft³ 500 ft³ 1,000 ft³
please answers soon i'll give you 50 points!!
Answer:
D. 1000 ft³Step-by-step explanation:
The volume is the product of base area and the height:
V = BhFind the volume:
V = 200 *5 = 1000 ft³Correct choice is D
why is the answer to this question?
Answer:
what question ⁉️
Step-by-step explanation:
bye IG
bye have a great day
I have a math problem that i need help with.
Answer:
Total cost = $1,481.9
Solving steps:
Step 1: And all the total requirements for each person
=> $52.95 + $18.95 + $33.95
Add all the values
=> $105.85
Step 2: Multiply it by 14
=> 105.85 × 14
multiply 105.85 by 14
=> $1,481.9
The question is in the picture please help me
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!
[tex]Answer: y =\dfrac{1}{2}(x +2)^{2}+[/tex]Answer:
Step-by-step explanation:
Vertex form of quadratic function: y =a(x -h)² + k
Where (h,k) is the vertex
vertex (-2 , 6)
y = a(x -[-2])² + 6
y = a(x + 2)² + 6
This is passing through (-4,8)
8 = a(-4 + 2)² + 6
8 = a(-2)²+ 6
8 = 4a +6
8 - 6 = 4a
4a = 2
a = 2/4
a = 1/2
[tex]Answer: y =\dfrac{1}{2}(x +2)^{2}+6[/tex]
What is the circumference of a chips ahoy cookie?
In this problem, p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if its demand function is p = 121 − [tex]x^{2}[/tex] and its supply function is p = [tex]x^{2}[/tex] + 6x + 65. (Round your answer to the nearest cent.)
The market equilibrium is the point where the demand and supply functions are equal
The producer's surplus at market equilibrium for a product is #105
How to determine the producer's surplusThe functions are given as:
[tex]p = 121 - x^2[/tex]
[tex]p = x^2 + 6x + 65[/tex]
Equate both functions
[tex]x^2 + 6x + 65 = 121 - x^2[/tex]
Collect like terms
[tex]x^2 + x^2 + 6x + 65 - 121 = 0[/tex]
Evaluate the like terms
[tex]2x^2 + 6x -56 = 0[/tex]
Divide through by 2
[tex]x^2 + 3x -28 = 0[/tex]
Expand
[tex]x^2 + 7x - 4x - 28 = 0[/tex]
Factorize
[tex]x(x + 7) - 4(x +7)= 0[/tex]
Factor out x + 7
[tex](x - 4)(x +7)= 0[/tex]
Solve for x
x = 4 or x = -7
The number of units cannot be negative,
So, we have:
x = 4
Substitute 4 for x in [tex]p = 121 - x^2[/tex]
[tex]p = 121 - 4^2[/tex]
p = 105
Hence, the producer's surplus at market equilibrium for a product is #105
Read more about equilibrium at:
https://brainly.com/question/110832
ASpoon is sold at a loss of 47%. If it was sold at 200
Calculate the Cost Price
Answer:
377.36(2decimal places)
Step-by-step explanation:
Solution
First write down all known info about problem
Loss(L) percent:47%
Selling price(SP):200
Cost Price is unknown but CP percent equals 100%(basic percent b'cos it represents the basic cost of the item)
When at a loss, the CP is higher than the SP so subtract the L% from the CP% to get the SP percent...
∴SP% equals CP%-L%
100%-47%:53% ∴SP%:53%
We can simply cross multiply now by saying,
If 53% equals 200
∴100% equals a variable(x)
Cross multiplying,we get:
53x equals (200×100) so dividing both sides by 53,
x equals 377.36(2 decimal places)
Therefore, the CP is 377.36
Gabriel invested $77,000in an account paying an interest rate of
3 1/2
% compounded continuously. Isabella invested $77,000in an account paying an interest rate of
4 1/8
% compounded quarterly . After 6 years, how much more money would Isabella have in her account than Gabriel, to the nearest dollar?
Answer:
3592
Step-by-step explanation:
interest
Step-by-step explanation:
I dont no because I cannot try 2 counting like that money
Counting Generation as the (first-counted) generation, how many generations occur until the pattern of cells
stabilizes? In other words, how many total iterations occur until the pattern isn't different between generations? You
may use any resources or additional graph paper to determine this number. Type the number of your answer in the
space provided. Example: (Generation 0 + Generation 1 + Generation 2 + Generation 3 + Generation 4) = 5 generations
Answer: ↓↓↓
Step-by-step explanation: Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.
Determine if true:
9x0^1x9=9
Answer:
False
Step-by-step explanation:
9x0=0
0^1=0
0x9=0
0=9
The numbers don't match.
Hence, the equation is false.
Answer:
False
Step-by-step explanation:
9*0=0
0^1 =0
0*9 = 0
0≠9
Question 1
Which best describes the error in solving the equation?
Both sides of the equation should have been multiplied by 28.
Both sides of the equation should have been multiplied by 28.
Both sides of the equation should have been divided by 28.
Both sides of the equation should have been divided by 28.
Both sides of the equation should have been multiplied by 4.
Both sides of the equation should have been multiplied by 4.
From both sides of the equation, 4 should have been subtracted.
From both sides of the equation, 4 should have been , subtracted.
Question 2
Find the correct solution.
The correct solution is x=
.
Answer:
x=112
Step-by-step explanation:
(1-1/10)(1-1/11)(1-1/12)...(1-1/99)(1-1/100)
Answer:
actually it's 0
Step-by-step explanation:
all of them have 1-1 and that is 0 and no matter what number you divide it by you will get 0
pls give me brainlest
The system of equations above is graphed below. Find the solution to the system.
Group of answer choices
(0,-6)
(-1,-5)
(1,-5)
(-5,1)
Solution:
The solution to the given system of equation is the intersection point created with the 2 lines. The solution must satisfy all equations. We can see the intersection. To identify the solution, plot the solution on the graph.
=> Solution of two lines: (x = 1, y = -5)=> Solution of two lines in (x,y) form: (1, -5)Option C is correct.
~Refer to image for plotted solution~
Given that NQ||PR find NP
Answer:
NP = 1.25
Step-by-step explanation:
ΔQMN similar to ΔRMP
[tex]\frac{QM}{RM}=\frac{MN}{MP}[/tex]
[tex]\frac{8}{10}=\frac{5}{MP}[/tex]
[tex]MP=\frac{5*10}{8} =6.25[/tex]
[tex]MP = MN + PN\\6.25 = 5 + PN\\PN = 6.25-5 =1.25[/tex]
A state university locks in costs for a student once a student starts attending the university. The total cost is $22,500. A student has the following help in covering the costs of school.
An academic scholarship of $10,000.
Other scholarships and grants of $4,400.
Parents pay $1,800.
What is the amount that the student will need to save every month in order to pay off the remaining costs in 10 months?
a. $525
b.$630
c.$1,200
d. $1,440
Answer:B $630 Per Month So B
Step-by-step explanation: $22,500-$10,000=$12,500-$4,400=$8,100-$1,800=$6,300/10Months=$630
Answer:
$690
Step-by-step explanation:
If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690
Amount and interest
Given the following information from the question
The total cost of fee = $23,500
Amount got as help;
An academic scholarship of $8,200.
Other scholarships and grants of $7.400.
Grandparents pay $1,000
Amount she had = 8200 + 7400 + 1000
Amount she had = $16600
Amount remaining = 23500 - 16600
Amount remaining = $6900
If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690
https://brainly.com/question/22112075
What is the answer to this question? (100 points pls answer!)
Answer : 14 Meters
Explanation : 2 * 3 * 14 Is = To 84
◊ YusuCr ◊
Answer:
14 m
Step-by-step explanation:
The formula to find the volume of a rectangular prism is [tex]l * w * h = V[/tex]. We are given the volume as 84, height as 3, and width as 2.
[tex]84 = l * 2*3[/tex] [tex]84=6l[/tex] [tex]84/6 = 6l/6[/tex] [tex]l = 14[/tex]Therefore, the length of the prism is 14 meters.
A square with side of k cm has perimeter of 36 cm. find the value of k.
Answer: 9
Step-by-step explanation:
36/4 = 9
also if you want me to explain I can just ask…
but also I dunno if my answer is correct tho
What is 7/8 expressed as a percent? Enter your answer as a decimal.
Answer:
87.5% because calculator
Step-by-step explanation:
;)
Answer:
The Answer Is: D..! ) 0.875
Step-by-step explanation:
I Hope This Helped! Have a Great Day!