The general solution to the nonhomogeneous system is:
x(t) = c1e^(2t) + c2e^(-sqrt(3)t) + (3/8)t^2e^(2t) + (1/8)*
To solve the given nonhomogeneous system using variation of parameters, we first need to find the solution to the associated homogeneous system:
dx/dt = 2x − y
dy/dt = 3x − 2y
The characteristic equation is λ^2 - 4λ + 1 = 0, which has roots λ = 2 ± sqrt(3). Therefore, the general solution to the homogeneous system is:
x(t) = c1e^(2t) + c2e^(-sqrt(3)t)
y(t) = c1e^(2t) + c2e^(sqrt(3)t)
To find the particular solution using variation of parameters, we assume that the solutions have the form:
x(t) = u1(t)*e^(2t) + u2(t)*e^(-sqrt(3)t)
y(t) = v1(t)*e^(2t) + v2(t)*e^(sqrt(3)t)
We then differentiate these expressions and substitute them into the original system, yielding:
u1'(t)*e^(2t) + u2'(t)*e^(-sqrt(3)t) + 2u1(t)*e^(2t) - sqrt(3)*u2(t)*e^(-sqrt(3)t) = 6t
v1'(t)*e^(2t) + v2'(t)*e^(sqrt(3)t) + 3u1(t)*e^(2t) - 2sqrt(3)*v2(t)*e^(sqrt(3)t) = 0
We can solve for u1'(t), u2'(t), v1'(t), and v2'(t) using the method of undetermined coefficients, which yields:
u1'(t) = (6t + 2sqrt(3)te^(sqrt(3)t))/(4e^(2t) - sqrt(3)e^(-sqrt(3)t))
u2'(t) = (-6t + 2sqrt(3)te^(sqrt(3)t))/(4e^(2t) - sqrt(3)e^(-sqrt(3)t))
v1'(t) = (-3/4)(6t + 2sqrt(3)te^(sqrt(3)t))/(e^(2t) - 4e^(sqrt(3)t))
v2'(t) = (-3/4)(-6t + 2sqrt(3)te^(sqrt(3)t))/(e^(2t) - 4e^(-sqrt(3)t))
Integrating these expressions yields:
u1(t) = (3/8)t^2e^(2t) + (1/8)*sqrt(3)te^(-sqrt(3)t) - (1/8)*e^(2t)
u2(t) = -(3/8)t^2e^(2t) + (1/8)*sqrt(3)te^(-sqrt(3)t) + (1/8)*e^(2t)
v1(t) = (-3/16)te^(2t) + (3/16)*sqrt(3)*e^(sqrt(3)t)
v2(t) = (-3/16)te^(2t) - (3/16)*sqrt(3)*e^(-sqrt(3)t)
Therefore, the general solution to the nonhomogeneous system is:
x(t) = c1e^(2t) + c2e^(-sqrt(3)t) + (3/8)t^2e^(2t) + (1/8)*
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Suppose f(x) = x^3 + 1. Find the graph of
f(2x).
Step-by-step explanation:
I am sorry. I just typed the equation into my calculator app. Refer to the attached image above to make a deduction.
Answer:
Mga madlang pipol. The answer is graph 2
PLEASE HELP ASAP
Jonathan has a rectangular rug with whose length is 5 inches less than its width. The area of the rug is 36 square inches
This is a 2 part question! Use this information for the open-ended question that follows.
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
Valery increases her speed by 4% the next time she rides her bike. Her goal is to ride faster than Manuel.
Is the 4% increase enough to ride faster than Manuel? yes or no.
As part of your explanation, identify Valery's new speed. Then explain why or why not she met her goal.
Answer:
ok for the first part of the question This is a 2 part question! Use this information for the open-ended question that follows.
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
a) EXACTLY how many hours does it take Valery to ride her bike 40 miles?
ANSWER (A) 4.17
b) Use this graph below to identify what Manuels average speed is:
ANSWER (B) 10 mph
I don't know the open ended question
Please help
A school fundraiser sells holiday cards and wrapping paper. The school is trying to raise at least $400. It makes a profit of $2.50 on each box of holiday cards and 80% of the profit on each holiday box on each pack of wrapping paper. Write an inequality that represents the situation where x is the number of holiday boxes sold and y is the number of packs of wrapping paper sold.
x=
y=
Holiday Cards Profit:
Key word(s):
Linear Inequality:
Answer:
2.50x+80>4.00
Step-by-step explanation:
Determine the value of y, if x is-9.
Answer:
[tex]y=82[/tex]
Step-by-step explanation:
We know the value of x is -9 so we can plug it in as -9.
[tex]y=x^2+1\\y=(-9)^2+1\\y=81+1\\y=82[/tex]
Answer:
82=y
Step-by-step explanation:
-9 x -9 = 81
81 + 1 = 82
Rodeny rented a machine for $70.00 to make popcorn at a school event.In addition to the machine rental cost, the popcorn supplies cost him $0.15 per bag sold.Rodeny sold the popcorn for $1.00 per bag. How much profit did Rodeny make If he sold 200 bags of popcorn.
Answer:
100$
Step-by-step explanation:
he profit from 1 popcorn=0.85$
from 200=170$
170$-70$=100
13
Calculate a, b and m so that the
polynomials P and Q defined by :
P(x) = (m - 2)x2 + (2a + 3)x +b +6 and
Q(x) = 3x2 - (m - 2)x + 2a - 3 , are equal.
Answer:
m = 5
a = -3
b = -15
Step-by-step explanation:
(m - 2) = 3 for x^2
(2a + 3) = - (m - 2) = (2 - m) for x^1
(b + 6) = (2a - 3) for x^0
Question:
A soccer ball has a radius of 11 cm. What is the volume of the soccer ball in cubic centimeters? Use 3.14 for pi. Round your
answer to the nearest hundredth.
Answer:
V = 4/3 * pi * radius^3
= 4/3 * 22/7 * 11*11*11 = 117128/21 = 5577.5238092.....
Step-by-step explanation:
Sandra saves 7% of her salary for retirement. This year her salary was $2,000 more than her salary than in the previous year, and she saved $3,290. What was her salary in the previous year?
complete the equation 0.07( x+____) = 3,290
Sandras salary in the previous year was _____
9514 1404 393
Answer:
2,000$45,000Step-by-step explanation:
Where x represents the previous year's salary, its amount this year is said to be ...
x + 2000
The equation is trying to reflect the fact that 7% of that is $3,290. The missing number is 2000:
0.07(x +2000) = 3290
__
Solving for x, we find ...
x = (3290/0.07) -2000 = 45000
Sandra's salary the previous year was $45,000.
The ratio of the length to the width the official german flag is 5:3.Sanda is making 12 german flags for a cuiture show.Each flag she makes has a length of 20 centimeters . It takes her 4 hours to make all the flag. What is the width of each flag and the average amount of time it takes sandra to make each flag?
Answer: The width of each flag = 12 cm
The average amount of time it takes Sandra to make each flag = 20 minutes.
Step-by-step explanation:
Given: The ratio of the length to the width the official german flag is 5:3.
Let length = 5x, width = 3x
Length of each flag = 20 cm
i.e. [tex]5x=20\Rightarrow\ x=\dfrac{20}{5}=4\text{ cm}[/tex]
Then width of each flag = 3 x 4 = 12 cm
i.e. width of each flag = 12 cm
Total time to make 12 flags = 4 hours
Time taken to make 1 flag = [tex]\dfrac{4}{12}[/tex] hour
Time taken to make 1 flag = [tex]\dfrac{1}{3}[/tex] hour
1 hour = 60 minutes
Time taken to make 1 flag = [tex]\dfrac{1}{3}\times60[/tex] minutes = 20 minutes.
Hence, the average amount of time it takes Sandra to make each flag = 20 minutes.
please help! give the answer in simplified form
Answer:
5a. 8:21
6a. 26:1
What is the approximate area of the shaded region?
Answer:
196-49 pi
Step-by-step explanation:
diameter of circle is 14
radius-7
7^2=49
49 pi
14^2=area of square
196-49pi= area of shaded area.
Answer:
im pretty sure the area is 196
Step-by-step explanation:
because when finding the area of a rectangle/ square you use the formula Length * Width and as we can see the sides of the shaded are are equivalent and as we know the length of the shaded area is 14.
we would just plug in our information.
L*W
14*14= 196
The square root of y^3 simplified
Answer:
(√y)3
Step-by-step explanation:
What is the cross product of 1/4 = 5/20?
THhe cross product is found by multiplying the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction.
1/4 = 5/20
1 x 20 = 20
4 x 5 = 20
The cross product is 20
Answer:
20
Step-by-step explanation:
1 x 20 = 20
4 x 5 = 20
Hope that helps!
A lamp post with a height of 12 ft casts a shadow of 6 ft. A fire hydrant near it casts a shadow that is 1.5 ft long. How tall is the fire hydrant?
Answer:
3ft
Step-by-step explanation:
We are given that
Height of lamp, h=12ft
Height of shadow, l=6ft
Height of shadow of hydrant, l'=1.5ft
Let height of hydrant=h'
We have to find the height of fire hydrant.
All right triangles are similar
When two triangles are similar then, the ratio of their corresponding sides are equal.
Using the property
[tex]\frac{h}{h'}=\frac{l}{l'}[/tex]
[tex]\frac{12}{h'}=\frac{6}{1.5}[/tex]
[tex]h'=\frac{12\times 1.5}{6}[/tex]
[tex]h'=3[/tex]ft
Hence, the height of fire hydrant=3 ft
Need help ASAP please!!
Don’t know how to give brainliest sorry-
Answer:
32°
Step-by-step explanation:
All triangles must have a sum of 180°. Given the angle 58° and since this is a right triangle, we have 2 out of the 3 angles to work with.
90 + 58 + x = 180
x = 32
i'm really confused on this, anything will help
Answer:
I think its 1200 not sure though
Answer:
1,200
Step-by-step explanation:
first you would divide 480 copies by 4 minutes to see how many copies per minute (120) Then you would take 120 copies per minute and multiply it by the 10 and you would get 1200 copies per 10 minutes! lmk if that helps:)
I need help asap please
Step-by-step explanation:
5³×1/5⁵
5×5×5×1/5×1/5×1/5×1/5×1/5
=1/25
or
1/5²
Chose whether the fraction and percent are equivalent
Yes. No.
A.
40/1,000 and 40%
B.
6/5 and 120%
C.
50/33 and 117%
D.
1/8 and 12.5%
Step-by-step explanation:
A No because it's 4%
B Yes
C No
D Yes
If 9 x 7 = 3545 and 4 x 3 = 1520 then 6 x 8 = ?
Answer:
4030 or 3040 I think 4030 though
Step-by-step explanation:
I think this is it but 6*8 is 48....I used a little logic so hopefully this is right
Answer:
4030
Step-by-step explanation:
if 9× 7 = 3545 then it 7 × 5, 9× 5 which gives 3545
4x3 = 3× 5, 4×5 which gives 1520
so 6× 8 will give 8×5, 6×5 = 4030
Can anyone help me with this question...please i really need your help....
(Express the variable in the brackets as the subject of formula)
9514 1404 393
Answer:
p = q/(2 -3q)
Step-by-step explanation:
[tex]\dfrac{2p}{3p+1}=q \qquad\text{given}\\\\2p=q(3p+1) \qquad\text{multiply by the denominator}\\\\ 2p=3pq+q \qquad\text{eliminate parentheses}\\\\ 2p -3pq = q \qquad\text{subtract $3pq$}\\\\ p(2-3q)=q \qquad\text{factor out $p$}\\\\ \boxed{p=\dfrac{q}{2-3q}} \qquad\text{divide by the coefficient of p}[/tex]
Dora buys some T-shirts for $8.75 each and pairs of shoes for $27.50 each. If she buys 4 T-shirts, how much money would she have to spend in all
8.75*4=35 so $35 for shirts
and depending on how many shoes she buys but lets just say one pair
35+27.50= 62.50 so it would be a total of $62.50
Step-by-step explanation:
4 shirts with each price $8.75 = 4 × $ 8.75= $ 351 pair of shoes with price = $ 27.50so total price = $ 35 + $ 27.50 = $ 62.50MARK ME AS BRAINLISTPLZ FOLLOW MEJimmy's school is selling tickets to the annual dance
competition. On the first day of ticket sales
the school sold 6 adult tickets and 4 child tickets for a
total of $88. The school took in $186 on
the second day by selling 12 adult tickets and 9 child
tickets. Find the price of an adult ticket and
the price of a child ticket.
9° TERMINO DE 7.10.13
Answer:
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Answer:
Evaluate
18 ER TM×2,130
it’s sad when I help people because they don’t do the same for so pls... answer me once:((((((((((((((((((((((((((((((((((((((
16 model airplanes on his shelf
4 times as many model airplanes as model trains
let's denote the number of model trains as m
So,
m=16×4
m=64
Therefore,there are 64 model trains.
pleasemark me as brainliest answer
HELP.................................................................
Answer:
A. [tex]\frac{1}{6^{2} }[/tex]
Step-by-step explanation:
A. [tex]\frac{1}{6^{2} } = \frac{1}{36} = 0.02777[/tex]
B. [tex]6^{-3} = 0.004629[/tex]
C. [tex]\frac{1}{216} = 0.004629[/tex]
D. [tex]\frac{1}{6^{3} } = \frac{1}{216} = 0.004629[/tex]
Answer:
I think it is A because B or D is not it so I was left with A and C. So I am pretty sure that is A.
Find the area of the triangle.
Answer:
86.1yd
Step-by-step explanation:
area of a triangle= base*height/2
21*8.2=172.2
172.2/2=86.1
Answer:
86.1yd2
Step-by-step explanation:
area=1/2×b×h
a=1/2×21×8.2
a=86.1yd2
Write an exponential function for a graph that passes through the points (2,16) and (3,32).
Answer:
[tex]y = 4(2^{x} )[/tex]
Step-by-step explanation:
The general form for an exponential function is [tex]y = kb^{x}[/tex]
When x = 2, y = 16 So, [tex]16 = kb^{2}[/tex]
and when x = 3, y = 32 So, [tex]32 = kb^{3}[/tex]
Divide [tex]\frac{32}{16} = \frac{kb^{3} }{kb^{2} }[/tex]
2 = b
Now, [tex]16 = k2^{2}[/tex]
16 = 4k
k = 4
Therefore, the exponential function is [tex]y = 4(2^{x} )[/tex]
What is the length of one side of this regular pentagon if the area is 50 and apothem is 4?
Answer:
5
Step-by-step explanation:
i took the test
The required length of one side of the given regular pentagon is 5 units.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons, etc
Here,
We can use the formula for the area of a regular pentagon to solve for the length of one side,
Area = (1/2) * Perimeter * Apothem
Since the pentagon is regular, all sides are equal, so we can write:
Perimeter = 5 * Length of one side
Substitute in the first expression
50 = (1/2) * 5 * Length of one side * 4
50 = 10 * Length of one side
Length of one side = 5
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1. Use the distributive property to factor out the greatest common factor (GCF) and rewrite the
expression 36 minus 96.
a. 2(18-48)
B.6(6-16)
c 12 (3-8)
D. 12(6-2)