Answer:
The solution
[tex]Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}[/tex]
Step-by-step explanation:
Explanation:-
Consider the initial value problem y′+3 y=9 t,y(0)=7
Step(i):-
Given differential problem
y′+3 y=9 t
Take the Laplace transform of both sides of the differential equation
L( y′+3 y) = L(9 t)
Using Formula Transform of derivatives
L(y¹(t)) = s y⁻(s)-y(0)
By using Laplace transform formula
[tex]L(t) = \frac{1}{S^{2} }[/tex]
Step(ii):-
Given
L( y′(t)) + 3 L (y(t)) = 9 L( t)
[tex]s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }[/tex]
[tex]s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }[/tex]
Taking common y⁻(s) and simplification, we get
[tex]( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7[/tex]
[tex]y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}[/tex]
Step(iii):-
By using partial fractions , we get
[tex]\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}[/tex]
[tex]\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}[/tex]
On simplification we get
9 = A s(s+3) +B(s+3) +C(s²) ...(i)
Put s =0 in equation(i)
9 = B(0+3)
B = 9/3 = 3
Put s = -3 in equation(i)
9 = C(-3)²
C = 1
Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)
Comparing 'S²' coefficient on both sides, we get
9 = A s²+3 A s +B(s)+3 B +C(s²)
0 = A + C
put C=1 , becomes A = -1
[tex]\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}[/tex]
Step(iv):-
[tex]y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}[/tex]
[tex]y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}[/tex]
Applying inverse Laplace transform on both sides
[tex]L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})[/tex]
By using inverse Laplace transform
[tex]L^{-1} (\frac{1}{s} ) =1[/tex]
[tex]L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}[/tex]
[tex]L^{-1} (\frac{1}{s+a} ) =e^{-at}[/tex]
Final answer:-
Now the solution , we get
[tex]Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}[/tex]
Given: circle k(O), m AB = 120° m∠BCA = (x+60°) Find: x
Answer:
x=0
Step-by-step explanation:
<BCA is half of arc BA or half of 120 which is 60.
do the math, and then x has to be 0 degrees
What is the area of the triangle?
PLSSS help me
Answer:
The area of the triangle is [tex]A=6 \:units^2[/tex].
Step-by-step explanation:
The area A of a triangle is given by the formula [tex]A=\frac{1}{2} bh[/tex] where b is the base and h is the height of the triangle.
From the graph, we can see that the base is 3 units and the height is 4 units. Therefore, the area of the triangle is
[tex]A=\frac{1}{2} \cdot3\cdot 4=\frac{12}{2}=6 \:units^2[/tex]
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
Graph the circle (x-3)^2+(y-7)^2=4
Which statement is true?
Parallelograms are trapezoids.
A square is always a rhombus.
A rhombus is always a square.
A rectangle is a trapezoid.
Answer:
A square is always a rhombus.
Explanation:
A square has 4 sides of equal length.
Answer:
A square is always a rhombusStep-by-step explanation: trapezoids have 3 angles and 3 sides so in that case rectangles and parallelograms are not trapezoids.rhombuses aren't always squares.Find two numbers for which the sum is 101 and the difference is 47
Answer:
74 and 27
Step-by-step explanation:
let x and y be the numbers
x + y =101........eqn 1
x - y = 47.......eqn 2
solve simultaneously
from equation 2, make x the subject
x= 47 + y........eqn 3
put eqn 3 into eqn 1
(47+y) + y = 101
47 + 2y = 101
2y= 101 - 47
2y=54
y= 54/2
y= 27
put y=27 into eqn 3
x = 47 + 27
x = 74
A slot machine has 3 dials each dial has 30 positions one of which is jackpot. To win jackpot all three dials must be in jackpot position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot
Answer:
3/90
Step-by-step explanation:
1 slot is 1/30
2 slot is 1/30
3 slot is 1/30
this gives you that 3/90 when you had them
Answer:
D) 1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Step-by-step explanation:
which number when rounded to the nearest hundredth is 37.62
Answer:
Answer: B
Step-by-step explanation:
The number given is 37.62. So, by rounding to the nearest hundredths the number becomes 37.612 and this can be determined by using the rules of rounding off to the nearest hundredths.
Given :
Number - 37.62
The following steps can be used to round off any number to the nearest hundredth:
Step 1 - In the thousandths place value analyze that digit to round off a decimal.
Step 2 - If the value is 5 or more than 5 in the thousandth place then the digit is increased by 1 which is at the hundredth place and in the thousandth place digit and thereafter becomes zero.
Now, the number given is 37.62. So, by rounding to the nearest hundredths the number becomes 37.612.
Therefore, the correct option is B) 37.612.
For more information, refer to the link given below:
https://brainly.com/question/2096984
very simple why is it that math is the only subject that people seem to care about 50 points
Answer:
It's popular and hard
Step-by-step explanation:
what is the cube root of 1
Answer:
1.
Step-by-step explanation:
∛1= 1.
It can also be seen as:
1×1×1= 1.
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
B because first you need to read the problem and understand the information.
A self storage center is a storage room that is 8 feet long, 6 feet wide, and 10 feet high. What is the volume of the room? 24 cubic feet 48 cubic feet 140 cubic feet 480 cubic feet
Answer:
Step-by-step explanation: answer is 480 cubic feet. Just do 8 x 6 x 10.
Junior bought a bag of mixed fruit snacks. The flavors in the bag are 4 strawberry, 3 cherry, and 5 grape. If he chooses one fruit snack at random, what it the probability of the first one being grape?
Answer:I believe it would be 5/12
Step-by-step explanation:
You add all of them up then since it's 5 grapes and in total there is 12 fruit snacks. It should be 5 grapes of 12 fruit snacks in the bag.
100 POINTS
PLEASE PROVIDE STEPS.
THANK YOU!!!
Answer:
⅓ m/s
Step-by-step explanation:
Area of a square is:
A = s²
Take derivative of both sides with respect to time:
dA/dt = 2s ds/dt
Given that dA/dt = 6 m²/s and s = 9 m:
6 m²/s = 2 (9 m) ds/dt
ds/dt = ⅓ m/s
The Formula of the area of a square: A = bh or A = s^2
Solution:
~Take derivative of both sides
da/dt = 2s * ds/dt
~Use given values (6m^2/s and 9m)
6 = 2(9) * ds/dt
~Simplify
1/3m/s = ds/dt
Best of Luck!
If 3 13/44x = 2 7/11, then what is x?
Answer:
X equals 4
11 times 4 equals 44
Answer:
x = 4
Step-by-step explanation:
you multiply 11 by 4, and get 44
perform the following operations on matrices (1 8 0 7) (7 6 7 4) = ( )
Answer:
[tex]\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.
For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.
_____
Many calculators, spreadsheets, and web sites can do this tedious math for you.
Need help with this math problem
Answer:
[tex]f(x)=-5x-3[/tex].
Step-by-step explanation:
From the given machine diagram it is clear that:
[tex]f(x)=-8[/tex] at [tex]x=1[/tex]
[tex]f(x)=-13[/tex] at [tex]x=2[/tex]
[tex]f(x)=-18[/tex] at [tex]x=3[/tex]
It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.
Since the function changing at a constant rate, therefore it represents a linear function.
If a linear function passing through two points, then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is
[tex]y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)[/tex]
[tex]y+8=\dfrac{-5}{1}(x-1)[/tex]
[tex]y+8=-5(x-1)[/tex]
[tex]y=-5x+5-8[/tex]
[tex]y=-5x-3[/tex]
So, the required function is [tex]f(x)=-5x-3[/tex].
A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.
Answer:
D. Observational Study
Explanation:
An observational study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.
This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study is subject to bias because a positive or negative result might be because of other factors not related to the study.
Determine if the set of vectors shown to the right is a basis for IR3 If the set of vectors is not a basis, determine whether it is linearly independent and whether the set 311-4 spans R 12 Which of the following describe the set?
A. The set is a basis for R3
B. The set is linearly independent.
C The set spans R3
D. None of the above
Answer:
The problem is clearly solved in the attachment
The cost, in dollars, to produce 1 watt of solar energy is a function of the number of years
since 1977.t.
From 1977 to 1987, the cost could be modeled by an exponential function. Here is the
graph of the function.
80
60
dollars per Watt
40
20
4
8
10
6
years since 1977
1. What is the statement f (9) 36 saying about this situation?
2. What is f(4)? What about f (3.5)? What do these values represent in this context?
3. When f(t) = 45, what is t? What does that value of t represent in this context?
4. By what factor did the cost of solar cells change each year? (If you get stuck consider
creating a table.)
Answer:
In the figure attached, the graph of the function is shown.
1. f(9) ≈ 6 means that at t = 9 (year 1977 + 9 = 1986) the cost to produce 1 watt of solar energy was $6
2. f(4) ≈ 25, which means at year 1981 (=1977 + 4) the cost was $25 per watt
f(3.5) ≈ 28, which means at half of year 1980 (=1977 + 3.5) the cost was $28 per watt
3. When f(t) = 45, t is equal to 2, which means that the year wass 1979 (= 1977 + 2)
4. From the graph we can compute the following table:
x | y
0 | 80
1 | 60
The general exponential decay formula is:
f(x) = a*b^x
where a is the initial value and b si the decay factor. Replacing with data from the table:
f(0) = a*b^0
80 = a
f(1) = a*b^1
60/80 = b
0.75 = b
Apply the distributive property to factor out the greatest common factor of all three terms. Explanation: 9-12x+6y what is the answer??
Answer: [tex]3(3-4x+2y)[/tex]
Step-by-step explanation:
[tex]9-12x+6y[/tex]
[tex]3(3-4x+2y)[/tex]
Employees that work at a fish store must measure the level of nitrites in the water each day. Nitrite levels should remain lower than 5 ppm as to not harm the fish. The nitrite level varies according to a distribution that is approximately normal with a mean of 3 ppm. The probability that the nitrite level is less than 2 ppm is 0.0918.
1. Which of the following is closest to the probability that on a randomly selected day the nitrite level will be at least 5 ppm?
(A) 0.0039
(B) 0.0266
(C) 0.0918
(D) 0.7519
(E) 0.9961
Answer: .0039
Step-by-step explanation:
Drag each tile to the correct box. Not all tiles will be used.
Arrange the equations in the correct sequence to find the inverse of f(x) = y = 3x / 8 + x
Answer:
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the function
[tex]f(x) = \frac{3 x}{8+x}[/tex]
Given function is one-one and onto function
Hence f(x) is bijection function
[tex]y = f(x) = \frac{3 x}{8+x}[/tex]
now cross multiplication, we get
( 8+x)y = 3 x
8 y + x y = 3 x
8 y = 3 x - x y
taking Common 'x' we get
x (3 - y) = 8 y
[tex]x = \frac{8 y}{3-y}[/tex]
Step(ii):-
The inverse function
[tex]x = \frac{8 y}{3-y} = f^{l}(y)[/tex]
The inverse function of x
[tex]f^{l}(x) = \frac{8 x}{3-x}[/tex]
Final answer:-
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Which fraction is in simplest form 4/20 6/9 5/13 14/21
Answer: 5/13
Step-by-step explanation:
Answer:
5/13 is in simplest form, because it cannot be reduced any further.
Step-by-step explanation: 4/20 can be reduced to 1/5, 6/9 to 1/3, and 14/21 can be reduced to 2/3
PLZ HELP WILL RATE BRAINLIEST REMEMBER IT HAS 5 DIGITS
Answer:
The number: 13,226
Step-by-step explanation:
1. The smallest 5-digit number possibile is: 10,000
2. The smallest 5-digit number being odd should be: 10,001
3. All factors of 6 are {1, 2, 3, 6} so that the smallest possible way to arrange these numbers would be: 11,236
4. Now this number contains 3 prime numbers, 2 being {2 and 3}. If we were to consider another prime number, still being a factor of 6, that would be: 2. That would mean instead of the 1 being the second digit of the value 11,236 it could be 2: 12,236.
5. The digit in the thousands place (2) should be greater than the digit in the tens place (3). Let's swap these digits for now so that condition is satisfied: 13,226. 2 is the only number that has a number greater than it, besides 1, but 1 can't be a digit in the tenth place as it would make a greater 5 digit-number. Thus, provided the conditions are still satisfied, the number 13,226 is the smallest number possible.
10 X 5/11=
just multiplication get it right and get brainlyest
60pts or whatever it narrows it down to
The answer is 4.55
When you divide 5 by 11 you will get 0.45454545454 than when you multiply these numbers by 10 you will get 4.54545454545 and then the rounded answer is 4.55.
Answer: 4.54
Step-by-step explanation:
will mark the branliest to first one who answers
Answer:
3 1/4
Step-by-step explanation:
3/4 + (1/3 ÷1/6) - (-1/2)
Subtracting a negative is adding
3/4 + (1/3 ÷1/6) +1/2
Parentheses first
Copy dot flip
3/4 + (1/3 * 6/1) +1/2
3/4 + 2 + 1/2
Get a common denominator
3/4 + 2 + 2/4
2 + 5/4
2 + 4/4 +1/4
2+1 + 1/4
3 1/4
e is 5 more than d.
fis 7 less than d.
a) Write an expression for e in terms of d.
Answer:
C
Step-by-step explanation:
Answer:
e = d + 5
Step-by-step explanation:
e = d + 5
f = d - 7
Solve for e means write as e = ...d
and this is already there...
You can not write it more compact then this.
If you try, you will notice you finally end with the initial equation which you started with, or you endup with something which is obviously very true like
e = e or d = d.
What is the volume of this cube with a side length of 6 centimeters
6 cm
Answer:
V = 216 cm^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = (6)^3
V = 216 cm^3
Answer:216 cm^3
Step-by-step explanation:
In cube, the length of all sides are equal
length of side=6cm
Volume of cube=length x length x length
Volume of cube=6 x 6 x 6
Volume of cube=216
Volume of cube=216 cm^3
Which value has an absolute deviation of 5 from the mean of this data set?
26, 12, 35, 28, 14
A 28
B. 35
C. 26
D. 14
Answer: 28
Step-by-step explanation: see prev. explanation
The absolute deviation of 5 from the mean of this data set is 28.
What is absolute deviation?
Absolute deviation is "the distance between each data point to the mean".
According to the question,
The data set is 26, 12, 35, 28, 14
Average of the data set = [tex]\frac{sum of the data value }{Total number of observation}[/tex]
= [tex]\frac{26+12+35+28+14}{5}[/tex]
= [tex]\frac{115}{5}[/tex]
= 23.
Thus, the average of the data set is 23.
In order to find absolute deviation of 5 subtract each data point from the mean.
26 - 23 = |3| = 3
12 - 23 = |-11| = 11
35 - 23 = |12| = 12
28 - 23 = |5| = 5
14 - 23 = |-9| = 9.
Hence, the absolute deviation of 5 is from the mean of the data set is 28.
Learn more about absolute deviation here
https://brainly.com/question/4364130
#SPJ2
