Answer:
The solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
Step-by-step explanation:
This second-order differential equation is homogeneous and linear of the form:
[tex]y'' + p\cdot y' +q\cdot y = 0[/tex] (1)
Where:
[tex]p[/tex] - First-order constant coefficient, dimensionless.
[tex]q[/tex] - Zero-order constant coefficient, dimensionless.
Whose characteristic polynomial is:
[tex]\lambda^{2}+p\cdot \lambda + q = 0[/tex] (2)
Where [tex]\lambda[/tex] contains the roots associated with the solution of the differential equation.
If we know that [tex]p = 6[/tex] and [tex]q = 9[/tex], the roots of the characteristic equation are, respectively:
[tex]\lambda^{2}+6\cdot \lambda + 9 = 0[/tex]
[tex](\lambda +3)\cdot (\lambda + 3) = 0[/tex]
Which means that [tex]\lambda_{1} = \lambda_{2} = 3[/tex] and the solution of the differential equation is of the form:
[tex]y(x) = e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)[/tex] (3)
Where [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are integration constants.
The first derivative of the equation above is:
[tex]y'(x) = 3\cdot e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)+c_{2}\cdot e^{3\cdot x}[/tex] (4)
Now, if we get that [tex]y(0) = 0[/tex] and [tex]y'(0) = 1[/tex], then the system of equations to the solved is:
[tex]c_{1} = 0[/tex] (3b)
[tex]c_{1}+c_{2} = 1[/tex] (4b)
The solution of this system is: [tex]c_{1} = 0[/tex], [tex]c_{2} = 1[/tex]. Therefore, the solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
Pls help ASAP WILL GIVE BRAINEST :/
Step-by-step explanation:
b=1 the person above or below me has the explanation
can u pls help me with this question
Answer:
The correct answer is D, 6/8.
Step-by-step explanation:
For ratios or fractions an equivalent fraction has the same value but just more pieces. Think of it like a pizza. But to make sure they are equivalent you have to multiply or divide them by a fraction equal to 1. In other words the numerator and the denominator have to be the same number. So, when we multiply 3/4 by 2/2 you get 6/8 because 3 x 2 = 6 (numerators) and 4 x 2 = 8 (denominators).
If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. Stay safe and please mark brainliest! :)
A triangle has angles of 30° 60° and 90° It is dilated by a scale factor of three give the angle measures of the dilation of the triangle
The scale factor will create a similar triangle and thus there will be no change in angles so angles will still be 30° 60° and 90°.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Scale factor gives either a small or big similar image of a triangle, for example, if we have a triangle with vertices 2,4,6 and it is scaled by 1/2 then the resultant dimension will 1,2,3 but angles still remain the same.
Hence "The scale factor will create a similar triangle and thus there will be no change in angles so angles will still be 30° 60° and 90°".
To learn more about scale factors,
brainly.com/question/22312172
#SPJ1
which term of the series 2187,729,243...is 1/9
Answer:
Step-by-step explanation:
Givens
a = 2187
r = 1/3
L = 1/9
what is n
Formula
L = a*r^(n-1)
1/9 = 2187 * (1/3)^(n-1)
1/(9 * 2187) = (1/3)^(n - 1)
1/19683 = (1/3)^(n - 1)
=================
You need to break 19683 down into its prime factors.
19683 = 3* 729
19683 = 3 * 3 * 243
19683 = 3 * 3 * 3 * 81
81 = 3^4 so there are 4 more threes in the breakdown.
19683 = 3 * 3 * 3 * 3 * 3 * 3 * 3
1/19683 = 1/(3)^(7-1)
1/9 is the 6th term in the series.
Make w the subject of the formula y - aw = 2w - 1
Answer:
[tex]w=\frac{y+1}{a-2} (a\neq 2)[/tex]
Step-by-step explanation:
[tex]y - aw=2w-1\\y-aw-2w=-1\\-aw-2w=-1-y\\-w(a-2)=-(y+1)\\w(a-2)=y+1\\w=\frac{y+1}{a-2} (a\neq 2)[/tex]
Hope this helps!
Two-thirds of the fruit in a basket are apples. One-fourth of the apples are green apples. What fraction of the fruit in the basket are green apples?
Answer:
1/6
Step-by-step explanation:
2/3*1/4
=2/12
=1/6
PLS GIVE BRAINLIEST
4n-(7-6n)
Helppp plz
I need help plz!!!!!! Will give 100 points.
Point-Slope Form: y - 5 = 3(x - 1)
Standard Form: ???? HELP
What is an equation for the line that passes through the points (-2, 3) and (2, 1)
Help plzzzz will give brainliest
Answer:
It's positive.
Step-by-step explanation:
There are many reasons.... but one of the obvious ones is that it would've shown negative, correct?
increase 120 by 5% (answer)
Answer:
what is question is this the question
Answer:
126
Step-by-step explanation:
[tex]\frac{5}{100}[/tex] × 120 = 6
120+6= 126
Help me with this please
Answer:
101.5m left to use after the big top goes up.
Step-by-step explanation:
18*10=180 [tex]\pi[/tex]r[tex]x^{2}[/tex]= 3.14*5^{2}=3.14*25=78.5
180-78.5= 101.5m
The proportion of observations from a standard Normal distribution that take values larger than -0.75 is about A) 0.2266 B) 0.7704 C) 0.7734 D) 0.7764 E) 0.8023
Answer:
Option C: 0.7734
Step-by-step explanation:
From z-distribution table attached,
P(Z ≤ -0.75) = 0.2266
However, we are looking for proportion of observations from a standard Normal distribution that take values larger than -0.75.
Thus;
P(Z > -0.75) = P(Z ≤ 0.75) = 1 - 0.2266
P(Z > -0.75) = 0.7734
Option C is the correct answer.
Help me out please I beg you
Answer:
tesrdxtcfygvoubucewh cwcs wuehcbwch w
Step-by-step explanation:
w edch dwjbsxchwej chwxc
can someone answer these?
Answer:
1. SSS
2.SSA
3.ASA
Step-by-step explanation:
For number one there is three congruent sides with the on in the middle
For number two there is two sides and one angle congruent
And number three has an embedded side between the two angles
Helllppppppp. A wheelbarrow has a wheel with a diameter of 10 in. What is the distance, in
inches, that the wheelbarrow moves after 16 full rotations of the wheel?
Answer:
160 in.
Step-by-step explanation:
10 * 16 = 160
hellpppppp please I will give brainliest
Answer:
I think the answer is y=2x-2
Hope it is correct! The x is positive because the angle is pointing to the right, and the -2 came from the position of the line.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
WHATS A FUTURE FUNKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
500,325+6,773,500,135
Answer: future the time or a period of time following the moment of speaking or writing; time regarded as still to come.
Step-by-step explanation:
Quick answer please!!!! Brodie hires a technician to fix his air conditioning unit. The total cost includes $26.50 for parts and $50.00 per hour the technician works on the job. Which equation can be used to find y, the total cost Brodie pays, given x represents the number of hours the technician works on the job? y=26.50x−50 y = 26.50x + 50 y = 50x + 26.50 y=26.50(x+50)
Answer:
y = 50x + 26.50
Step-by-step explanation:
we put the x after 50 be cause we don't know how many hours he worked
then add 26.50 the cost of the parts.
Hoped this helped.
Answer:
C: y=50x+26.50
Step-by-step explanation:
I just took the test and i got it right!!! 100%
do i get brainlest
If $2,500 is invested at 12% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
Answer: 3,583.32
Step-by-step explanation:
Use money chimp calculator
Solve each equation. y + 20 = 7
Answer:
I Meant y = -13
Step-by-step explanation:
Answer:
y= -13
Step-by-step explanation:
-13 plus 20 is 7
plug the -13 in where the y is and do the equation
-13+20=7
Missy wants to find the surface area of a snack box in her pantry her work is shown below
Answer:
Step 2: Missy did not multiply the area of each face by 2 before adding.
Step-by-step explanation:
I took the test :)
what function best models the data and what wil be the chicken breast after 50 miutes
Answer:
Students use linear, quadratic, and exponential functions to model data from tables and choose the regression
most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a
regression model and then interpret the function in context. They then make predictions based on their model
and use an appropriate level of precision for reporting results and solutions.
Lesson 7 focuses on data sets that cannot be modeled accurately, and students are asked
to articulate why. Students use skills learned in Lesson 14 of Module 2 (where they used
calculators to write linear regressions) and apply similar techniques for data sets that are
better suited to modeling with quadratic or exponential regressions. Students use that
same technique to find linear regressions and use their graphing calculators to examine
the correlation coefficient and to find quadratic and exponential regressions. They
compare correlation coefficients to determine which model is best for the data.
Ultimately, students choose the regression model (linear, quadratic, or exponential) most
appropriate to a given data set and then write, verify, and interpret these models in
context. Students need a graphing calculator to complete this lesson. Graphing calculator
instructions are provided, but steps may vary slightly depending on the model of the
graphing calculator.
Refer to the following full modeling cycle during this lesson (Found on page 61 of the CCLS
and page 72 of the CCSSM).
Scaffolding:
Students are more
engaged when working
with relevant and real data
that interests them.
Websites that provide
data sets are a good
resource for classroom
investigations.
This lesson might need to
be divided into two days if
students need more time
to master the technology.
Step-by-step explanation:
In a group of 20 students, there are 7 boys. What is the ratio of girls to boys?
Answer: percent is 0.53%
The ratio is 7 to 13 so you just divide 7/13
Step-by-step explanation:
HELP ME ASAP!
What is the result when the number 44 is decreased by 75%?
Answer:
11
Step-by-step explanation:
Earl runs 60 meters in 40 seconds. How many meters per second does Earl run?
Earl runs 1.5 meters per second.................
During the winter months, heating bills can be expensive. A contractor claims that installing a new brand of insulation will considerably lower your heating bill (which was $205 last month). After conducting the test (assuming the data were provided). you find that the results are significant at the 5% level. You may also conclude: __________.a. the test would also be significant at the 10% level. b. the test would also be significant at the 1% level. c. both of the above. d. none of the above.
Answer:
The correct option is a
Step-by-step explanation:
Generally the null hypothesis is rejected (that the result is significant ) when the p-value is less that the the level of significance
Now from the question when the the level of significance was 5% the p-value was less than the level of significance so also when the level of significance is 10% the p-value will be less than the level of significance hence null hypothesis will also be rejected at this level(that is the result will also be significant at the level of significance )
Which best describes the error in solving the system of linear equations?
Only the x-value is given.
The wrong value for x is given.
The blue line is graphed incorrectly.
The red line is graphed incorrectly.
Answer:
a. Only the x-value is given.
Step-by-step explanation:
Taking a look at the graph of both equations, both equations are graphed correctly, because the slope (m) and y-intercept (b) values corresponds of each equation corresponds with what we have on the graph representing each equation.
The solution of two linear equations ought to be in a coordinate pair, (x, y). This means the x-value and it's correaponding y-value of the solution needs to be stated, not just the x-value.
Thus, the correct solution. Of the two linear equations are x = 4, when y = 3.
Solution in coordinate pair form is (4, 3).
Therefore, the statement that describes the error is:
a. Only the x-value is given.
which two triangles are congruent? complete the congruence statement.
This graph shows linear
y = f(x) and y = g(x).
Find the solution to the equation f(x) - g(x) = 0
Step-by-step explanation:
This graph shows linear
y = f(x) and y = g(x).
Find the solution to the equation f(x) - g(x) = 0