Answer:
x=-1
Step-by-step explanation:
5c. Solve the differential equations using Laplace transforms
y"+y' - 2y = e-³x, y(0) = 0 and y'(0) = 0
Answer:
[tex]y(x)=\frac{1}{2}e^{-3x}-\frac{2}{3}e^{-2x}+\frac{1}{6}e^{x}[/tex]
Step-by-step explanation:
[tex]y''+y'-2y=e^{-3x},\: y(0)=0,\: y'(0)=0\\\\\mathcal{L}\{y''\}+\mathcal{L}\{y'\}-2\mathcal{L}\{y\}=\mathcal{L}\{e^{-3x}\}\\\\s^2Y(s)-sy(0)-y'(0)+sY(s)-y(0)-2Y(s)=\frac{1}{s+3} \\ \\s^2Y(s)+sY(s)-2Y(s)=\frac{1}{s+3}\\ \\(s^2+s-2)Y(s)=\frac{1}{s+3}\\ \\Y(s)=\frac{2}{(s+3)(s^2+s-2)}\\ \\Y(s)=\frac{2}{(s+3)(s+2)(s-1)}[/tex]
Perform the partial fraction decomposition
[tex]\frac{2}{(s+3)(s+2)(s-1)}=\frac{A}{s+3}+\frac{B}{s+2}+\frac{C}{s-1}\\ \\2=(s+2)(s-1)A+(s+3)(s-1)B+(s+2)(s+3)C[/tex]
Solve for each constant
[tex]2=((-2)+2)((-2)-1)A+((-2)+3)((-2)-1)B+((-2)+2)((-2)+3)C\\\\2=-3B\\\\-\frac{2}{3}=B[/tex]
[tex]2=(1+2)(1-1)A+(1+3)(1-1)B+(1+2)(1+3)C\\ \\2=12C\\\\\frac{2}{12}=C\\ \\\frac{1}{6}=C[/tex]
[tex]2=((-3)+2)((-3)-1)A+((-3)+3)((-3)-1)B+((-3)+2)((-3)+3)C\\ \\2=4A\\\\\frac{2}{4}=A\\ \\\frac{1}{2}=A[/tex]
Take the inverse transform and solve for the IVP
[tex]Y(s)=\frac{\frac{1}{2}}{s+3}+\frac{-\frac{2}{3}}{s+2}+\frac{\frac{1}{6}}{s-1}\\\\y(x)=\frac{1}{2}e^{-3x}-\frac{2}{3}e^{-2x}+\frac{1}{6}e^{x}[/tex]
Solve 3x^3 - 12x = 0 by factoring
Please help me I can’t solve it. Please!!
Answer:
x = 0, 2, -2
Step-by-step explanation:
3x^3 - 12x = 0
3x ( x^2 - 4 ) = 0
3x = 0
x = 0
x^2 - 4 = 0
( x -2 ) ( x + 2 ) = 0
x -2 = 0
x = 2 , x + 2 = 0
x = -2
simplificar cada expresion numerica. -24+(-65)÷5
Answer:
-37
Step-by-step explanation:
-24+(-65) /5
-24 + (-13)
-37
Answer:
-37
Step-by-step explanation:
-24+(-65)/5
-24+(-65/5)
-24 - 13
-37
Mathematics pls help 4 questions will give brain to best answer
Answer:
There probably isn't a mode.
Step-by-step explanation:
Because the numbers in this set of data are continuous, it is impossible to have a mode, the number that occurs most frequently in a set of data.
Answer:
[1] Not enough information to draw valid conclusion
[2] The mean will be 12.
[3] 14
[4] 5 and 7
Step-by-step explanation:
[1] if the range for a set of data is 24, from 2 to 26 and the mean is 17, what can you conclude about the data
17 is the typical data value.
Not enough information to draw valid conclusion.
The median will be 17 also.
There probably isn't a mode.
Answer: Not enough information to draw valid conclusion.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[2] The extreme values in a set of data are 5 and 19. What is true about the data set?
The mean will be 12.
There is not enough data.
The range is 14.
There will be more than one mode.
Answer = The mean will be 12.
Explanation : Mean = add all values and divide by the number of values. 5+19=24, 24/2=12
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[3] What is the mean for the following set of data, to the nearest whole number?
5,9,15,18,22
Answer = 14
Explanation:
5 + 9 + 15 + 18 + 22 = 69
69 / 5 = 13.8
Round 13.8 = 14
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[4] What is the mode for the following set of data?
4,5,5,6,7,7,8,12.
Mode = Most Often Seen
Answer = 5 and 7
Explanation:
Base on given you can see that the most is two number. There is two five and there is two seven.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~Lenvy~
hello help me with this question thanks in advance
[tex]\bold{\huge{\underline{ Solution \: 1 }}}[/tex]
Basic theorems on similarity of trianglesTheorem 1 :- SSS Similarity
When all the three sides of one triangle are in proportion to the other three sides of the another triangle then those 2 triangles are similar by SSS similarity .Theorem 2 :- AA similarity
When the two corresponding angles of one triangle are congruent to other two corresponding angles of another triangle then both the triangles are similar by AA Similarity .Theorem 3 :- SAS similarity
When the two sides of one triangle are in proportion to the other two sides of another triangle and the one of the angles of both the triangles that lie between two corresponding sides are equal then both the triangles are similar by SAS similarity.Theorem 4 :- AAA similarity
When all the three angles of one triangle are equal to other three angles of another triangle then both the triangles are similar by AAA similarity. Let's Begin :-Here, We have given statement that
" If an angle of one triangle is congruent to an angle of another triangle and the corresponding sides including those angles are in proportion, then the two triangles are similar . "From above theorem, we can conclude that
Both the triangles are similar by SAS similarityHence, Option C is correct
[tex]\bold{\huge{\underline{ Solution \: 2 }}}[/tex]
The given statement is proved by using Pythagorean theorem.
Pythagorean theorem states that the square of hypotenuse that is longest side is equal to the sum of the squares of base and perpendicular height that is the smallest sides of the given triangle.That is,
[tex]\sf{\red{ (Hypotenuse)^{2} = ( Perpendicular)^{2} + ( Base) ^{2}}}[/tex]
Hence, Option D is correct that is Pythagorean theorem.
The y-intercept of the line whose equation is 5+y=2x
Answer:
(0, -5)
Step-by-step explanation:
We need to isolate y.
5+y=2x -- Subtract 5 from 5+y
y = 2x - 5
The image connected is what the graph would look like.
Answer:
y-int = (0,-5)
Step-by-step explanation:
Substitute 0 for x and solve to find the y-intercept.
[tex]5+y=2(0)\\ 5+y=0\\y=0-5\\y=-5[/tex]
Rectangle with l = 4f ft, w = 1 ft (show work)
Answer:
if it's 41 and 1 then the answer is 41 but if it's 4 and 1 then the answer is 4
Step-by-step explanation:
you take length times with and so 4 times 1 which is 4 or 41 times 1 which is 41
How many bags can you purchase with 20$
Answer:
The answer is 3/5=x/20
If you can buy 3 bags for $5 then you can buy 12 bags with $20
Step-by-step explanation:
Basically divide 20 by 5
Then you multiply the answer to 20/5 which is 4 by 3 to get x
Which would be 12
Can someone please answer this it would mean the world to me cause im failing right now
Answer:
Alright, for question 7, the angle pair relationship is that they are corresponding angles.
So, 17x - 34 = 13x - 14. This means that 4x = 20, and x = 5 :)
For question 8, the angles are a linear pair. They are supplementary (adding to 180) :)
So, 37x - 17 + 33x - 13 = 180
This means taht 4x = 210, and x = 52.5? (I'm not sure if I screwed up on the arithmetic on this one, please correct if you find any mistakes!)
The number of chairs Amal can paint varies directly with the amount of time she spends painting. Amal can paint 7 chairs in 3 hours. How many chairs can Amul paint in 15 hours? Enter your answer in the box.
Answer:
35
Explaination:
This problem can be represented by the equation: (7/3)=(x/15) Then solve for x, which is 35.
Amul can paint 35 chairs in 15 hours
Let the number of chairs Amal can paint be represented as N
And amount of time she spends painting be represented as t
such that
The number of chairs Amal can paint varies directly with the amount of time she spends painting will be expressed as
N∝t
Introducing the constant of proportionality,K becomes
N=Kt
Amal can paint 7 chairs in 3 hours.K becomes
N=Kt
7=K3
K=7/3
Now if Amul paint in 15 hours, she would paint
N=Kt
N=7/3 X 15
N=35 Chairs
See related answer here:https://brainly.com/question/14073678
social media influence communication
Answer:
what whats the question so I can answer
PLS HELP AGIAN if u guess just for points ill report you question in the picture
Answer:
[tex]\sf y = \dfrac{17}{2}[/tex]
explanation:
[tex]\sf 7y-4=9y+13-4y[/tex]
collect variables in one side
[tex]\sf 7y -9y +4y = 13 +4[/tex]
simplify by addition and subtraction
[tex]\sf 2y = 17[/tex]
divide both sides by 2
Hence, ,final answer:
[tex]\sf y = \dfrac{17}{2}[/tex]
Answer:
A. y = 17/2
Step-by-step explanation:
Given equation:
7y - 4 = 9y + 13 - 4y
Collect like terms:
7y - 4 = 9y - 4y + 13
Combine like terms:
7y - 4 = 5y + 13
Subtract 5y from both sides:
2y - 4 = 13
Add 4 to both sides:
2y = 17
Divide both sides by 2:
y = 17/2
which of the following statements is not true about reflections?
a. The image faces the same direction as the pre-image
b. The image is the same shape as the pre-image
c. The image is the same size as the pre-image
d. Points on the pre-image are the same distance from the line of reflection as the corresponding points on the image
Answer:I’m pretty sure it would be A!
Step-by-step explanation:
Answer:
Should be A
Step-by-step explanation:
But it all depends on the mirror
1 Solve for the variable. 3x + 8 = 44
Answer:
x=12
Step-by-step explanation:
3x12=36
36+8=44
Answer:
x = 12
Step-by-step explanation:
3x + 8 - 8 = 44 - 8
3x = 36
simplify to get 12
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 vears and making monthly payments. What would their monthly payment be?
Answer:
a) payment: $1082.84
b) interest: $194,822.40
Step-by-step explanation:
The monthly payment on the mortgage can be found using the given formula with the given values of principal (P=195000), interest rate (r=0.053), and time period (t=30). The value of n is 12, corresponding to the number of months in a year.
a)The monthly payment is ...
[tex]k=\left(1+\dfrac{r}{n}\right)^{nt}=\left(1+\dfrac{0.053}{12}\right)^{12\cdot30}\approx 4.88661119\\\\\text{monthly payment}=\dfrac{P\cdot\dfrac{r}{n}\cdot k}{k-1}=\dfrac{195000\cdot0.0044166667\cdot4.88661119}{4.88661119-1}\\\\\boxed{\text{monthly payment}=\$1082.84}[/tex]
__
b)The interest owed is the difference between the total of monthly payments and the principal of the loan:
interest owed = (360)(1082.84) -195000 = 194,822.40
The interest owed over 30 years is $194,822.40.
sin
[tex] \sin( \binom{ - 11\pi}{3} ) \times \tan( \frac{35\pi}{6} ) \times \sec( - ) [/tex]
Answer:
solve it :)
Step-by-step explanation:
Jabari owns 100 shares of Stock A and 45 shares of Stock B. For the past month, his stocks have been
fluctuating inversely. Stock A decreased by m cents per share and Stock B increased by n cents per share.
Which equation can be used to find the total change in value of Jabari's shares per month?
A V = (100.-m)+(45.n)
B V = (100-m)+(45.-n)
V = 100(4.-m)+45(4.n)
D V=145(-mºn)
Answer:
Answer is A
(100*-m)+(45*n)
Step-by-step explanation: because stock a decreases per sock so your going to multiply 100 times -m because it is decreasing so it will be negative
Then it will be 45*n because it increase per number of stocks so you multiply 45 which is the number of stocks times n
Step-by-step explanation:
Two of my digits are odd, but my ones digit is even.
The sum of my digits is 16.
I am between 520 and 570, and I am NOT 556.
What am I?
Answer:
the correct answer is 565
Find the total surface area of the following cone. Leave your answer in terms of a. 2V3 cm 2 cm SA = [ ? ] cm Hint: Surface Area of a Cone = tre + B Where e = slant height, and B = area of the base
Answer: the answer is
90
Answer:
12
Step-by-step explanation:
What is the slope of the line on the graph
Answer:
slope = -3
Step-by-step explanation:
slope = -3
Answer:
-1/3
Step-by-step explanation:
we know ,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}- x_{1} }[/tex]Here , m= slope
(x1,y1) , (x2,y2) are point of the slope
[tex]m=\frac{6-2}{-6-6 }[/tex]
or, [tex]m=\frac{4}{-12 }[/tex]
so , m= -1/3
Find the LCM of 4 and 42
Answer:
84
Step-by-step explanation:
Morgan needs 3 gallons of paint to paint the walls in his bedroom.
If the paint he uses costs $24 per gallon, how much will he spend
on paint to paint his room?
A. $24
B. $ 48
C. $60
D. $72
7.RP.A.1
Answer:
72
Step-by-step explanation:
You multiply 3 by 24 to get 72
Find the value of x that will make A||B
Answer:
x = 20
Step-by-step explanation:
When two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.
5x + 20 = 3x + 60
Now subtract 3x form both sides
5x - 3x + 20 = 3x - 3x + 60
2x + 20 = 60
Subtract 20 from both sides
2x + 20 -20 = 60 - 20
2x = 40
Divide both sides by 2
x = 40/2
x = 20
A pair of jeans originally cost $48, but its price decreased by 25%. What is the new price?
Answer:
$36
Step-by-step explanation:
$48 × (100 - 25)% = $36
Round 47,250 to nearest thousand
Answer:
your answer will be 47000
Answer:
The correct answer is 47,000.
4. Write an equation that represents the line graphed below.
CCP
Answer:
(2,-6)
Hey my answer could be wrong but i checked so i hope you think this is helpful!
Find the weight of pure gold in 10 grams of 20 carat. It is given that 24 carat gold is cent-percent pure gold.
Answer:
The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold is 83.33 grams
hope this is helpful
Answer:
The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold is 83.33 grams.
Step-by-step explanation:
To find : The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold ?
Solution :
The percentage of pure gold in 10 grams can be measured of 24 carat gold.
In fact, this is equal to 100 percentage of pure gold in 10 grams of 1 carat.
The pure gold in 10 grams of 24 carat gold is
\frac{10}{24}\times 100=4.16
24
10
×100=4.16
The pure gold in 10 grams of 20 carat gold is
4.16\times 20=83.334.16×20=83.33
Therefore, The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold is 83.33 grams.
solve the equation..
Answer:
y=252/5=50.4
Step-by-step explanation:
[tex](A)\ 9y-252=4y\\(B)\ 5y=252\\(C)\ y= \frac{252}5 = 50.4[/tex]
In step A we multiplied both sides by the least common multiple of the denominators, in order to deal with only integers for as long as possible.
In step B you subtract 4y and add 252 to both sides ("moving them on the other end of the equal sign").
In step C you finally divide by 5 to isolate y.
How to solve 18 - 1 and 7/16 - 7/12
Answer:
- 7/48, decimal form 0.145 and 17
Step-by-step explanation:
(5x7) + (5x9) = 5x (7+?
Answer:
9
Step-by-step explanation:
this is because it is 9 and it could be 9
Answer:
First let's find what (5x7) + (5x9) equals;
(5x7) + (5x9)
35 + 45
= 80
Now 80 has to equal to;
5 x (7 + y) ( where 'y' is our unknown number)
So we set up the equation:-
80 = 5 x (7 + y)
80 = 35 + 5y
-35 -35
45 = 5y
/5 /5
9 = y
Let's double check:
80 = 5 x (7 + y)
80 = 5 x (7 + 9)
80 = 35 + 45
80 = 80, we are correct.