The solution to the differential equation in this problem is given as follows:
y(t) = Ae^(3t) + Be^(2t).
How to solve the differential equation?The differential equation for this problem is given as follows:
y'' - 5y' + 6 = 0.
It is a simple linear and homogeneous second order differential equation, hence it can be solved with the characteristic equation method.
The characteristic equation for the differential equation is given as follows:
r² - 5r + 6 = 0.
The roots for the characteristic equation are obtained by finding the linear factors and using the factor theorem as follows:
(r - 3)(r - 2) = 0.
Hence:
r - 3 = 0 -> r = 3.r - 2 = 0 -> r = 2.These are real and non-repeated roots, hence the solution is given as follows:
y(t) = Ae^(3t) + Be^(2t).
In which A and B are constants depending on the initial conditions for the differential equation.
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4.) Fill in the table to show a proportional relationship and then identify the
constant of proportionality for the cost to the number of yoga classes. In
the answer box, please list the constant of proportionality.
Answer/Step-by-step explanation:
✔️Number of Yoga classes = x
Cost ($) = y
Constant of proportionality (k) = y/x
Using the pair form the table of values given, (4, 60), find the constant of proportionality:
✅k = 60/4 = 15
Equation that represents the relationship between x and y is:
y = 15x
✔️Let's complete the table.
✅When number of yoga classes (x) = 2:
Substitute x = 2 into y = 15x
Thus,
y = 15*2 = 30
That is, 2 Yoga classes will cost $30
✅When number of yoga classes (x) = 6:
Substitute x = 6 into y = 15x
Thus,
y = 15*6 = 90
That is, 6 Yoga classes will cost $90
✅When number of yoga classes (x) = 8:
Substitute x = 8 into y = 15x
Thus,
y = 15*8 = 30
That is, 8 Yoga classes will cost $120
SOMEONE PLEASE ANSWER 3 ITS DUE IN 3 MINUTES!! WHOEVER ANSWERS GETS BRAINLIEST
Answer:
9:10
Step-by-step explanation:
74 is the buccaneers, and 35+45=80
so the ratio is 74:80
simplify to 36:40
then to 18:20
then to 9:10
The price of a toy costing £50 is increased to £65
work out the percentage increase
Answer:
Percent increase = 30%
Step-by-step explanation:
Given that:
Old price of toy = £50
New price of toy = £65
Difference = New price - Old price
Difference = 65 - 50
Difference = £15
Percent increase = [tex]\frac{Difference}{Old\ price}*100[/tex]
Percent increase = [tex]\frac{15}{50}*100[/tex]
Percent increase = 0.3 * 100
Percent increase = 30%
Hence,
Percent increase = 30%
Workout the size of angle x 79 35
Answer:
66 degrees
Step-by-step explanation:
Add both of those angels. 79+35=114
And then every triangle equals 180 so subtract
180-114=66
2. A triangle has sides of lengths 15, 23, and 28. Is it a right triangle? Explain.
A. No; 152 + 232 = 282
C. Yes; 152 +232 +282
B. No; 152 +232 +282
D. Yes; 152 + 232 = 282
Answer:
A
Step-by-step explanation:
the sum of the square of the legs of a right triangle equal the square of the third side: a² + b² = c²
15² + 23² ≠ 28²
...................................................................................................................................................................
Answer:
stan stray kids periodt
The ratio of cars to trucks in a parking lot is 2:5. If there are 254 cars, how many trucks are in the lot? What is the answer plz
Answer:
635 trucks
Step-by-step explanation:
So first e know the ratio is 2:5
The amount of cars are 254
So the 2 in the ratio which represents cars is 254
So w can make that as A ratio
2:254
The 5 is known but the actual amount is unknown so we can make that x
5:x
Now we gotta make them equal to each other
2:254=5:x
Turn into fraction
2/254=5/x
Cross multiply (proportion)
2x=1270
Solve
x=635
So 635 trucks
Evaluate the algebraic expression 1.5t -7.2 for each given value 6 -5
Answer:
1.8 ; - 14.7
Step-by-step explanation:
Evaluate the algebraic expression 1.5t -7.2 for each given value 6 ; -5
For each of values 6 and - 5 ;
Substitute the values for t in the expression ; 1.5t - 7.2
Substituting 6 for t:
1.5(6) - 7.2
9 - 7.2
= 1.8
Substituting -5 for t:
1.5(-5) - 7.2
-7.5 - 7.2
= - 14.7
5) The probability that a typist makes 0, 1, 2, 3, 4, or 5 mistakes on a page are, respectively
0.09, 0.11, 0.24, 0.21, 0.17, 0.05. What is the probability that the typist makes three or more
mistakes mistakes on a page.
Answer:
0.43
Step-by-step explanation:
Formatting the Given data into a probability distribution table :
X : ____ 0 __ 1 ___ 2 ____ 3 _____ 4 ____ 5
P(x) : _0.09_0.11 _ 0.24 _0.21 ___ 0.17 __ 0.05
Probability of making 3 or more mistakes :
P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5)
P(x ≥ 3) = 0.21 + 0.17 + 0.05
P(x ≥ 3) = 0.43
How many different triangles can you make if you are given three lengths for sides?
Answer:
The lesson Triangle Construction discussed how to make a triangle given three side lengths. As you discovered, as long as two of the lengths added up to be greater than the third, they would form a unique triangle (only one triangle could be formed).
Step-by-step explanation:
Can you give a picture of what you're talking about so I can help? lol.
Please help me answer this question. There’s a picture attached.
this is isosceles triangle, so side AB and BC are the same !
9x-8 = 28
9x=36
x=4
Answer:
probably 4 since the sides are the same
Step-by-step explanation:
9x-8=28
28+8=36
9x=36
36÷9=4
x=4
Here is a list of ages (years) of children in a room: 2, 6, 5, 9, 6, 7, 2 State the median.
Amanda bill and Hong since a total of 80 text messages during the weekend bill sent eight more messages than Amanda Hong sent two times as many messages as Amanda how many messages did they each send
Answer:
amanda: 18
Hong: 36
Bill: 26
Step-by-step explanation:
a+b+h=80
b=8+a
H=2A
a+8+a+2a=80
4a+8=80
a=18
What is the y-intercept?
Answer:
the y intercept is where the line crosses the y axis
Please help I'm so confused
Answer:
the quotient is 805. the remainder is 5.
Step-by-step explanation:
when you multiply the 8 you put the number you multiplied on top. The first one is 80 and then 5. You have a 5 left over which makes that the remainder
Answer:
1. is 85.625
2. is .625
so you divide 685 and you know nothing multiplied by 8 will equal 685 so the remainder is 685
how are meiosis and mitosis different
Answer:
meiosis is the result of four cells dividing
mitosis is the result of 2 identical cells
Step-by-step explanation:
not 100% sure but i hope this helps <3
5x + y = 9
3x + 2y = 4
Solve with elimination method
Answer:
x=2 y=-1
Step-by-step explanation:
multiply the top equation by negative 2. then it is -7=-14
then you dive and find out that x=2 and plug it inot the equation and solve for x 10+?=9 which is -1
Answer:
x=2
y=-1
Step-by-step explanation:
make it so that you can cancel out the y
to do this multiply the top equation by 2
10x+2y=18
3x+2y=4
subtract to get rid of 2y
7x=14
x=2
substitute the x into one equation
3(2)+2y=4
6+2y=4
2y=-2
y=-1
\left(6x10^2\right)\div \left(3x10^{-5}\right)
Answer:
[tex]\frac{6\times 10^2}{3\times 10^{-5}}[/tex] = 2 x 10⁷
Step-by-step explanation:
Given expression is [tex]\frac{6\times 10^2}{3\times 10^{-5}}[/tex]
The given expression is simplified as follows;
[tex]\frac{6\times 10^2}{3\times 10^{-5}} = (\frac{6}{3} )\times 10^{2-(-5)}\\\\(\frac{6}{3} )\times 10^{2-(-5)} = (\frac{6}{3} )\times 10^{2+5}\\\\(\frac{6}{3} )\times 10^{2+5} = 2 \ \times \ 10^7[/tex]
Therefore, the result of the given expression is 2 x 10⁷
Write two equations, one with an x-intercept
but no y-intercept, and one with a y-intercept but no x-intercept. ( how do I do number 9 can sum1 give me the answer or help me pls)
Answer:
No X-intercept: √(x)+1
No Y-intercept: √(x-1)
Step-by-step explanation:
To solve this you need to have some knowledge about a bunch of parent graphs and so this question is kind of hard to explain
Can someone please help
You deliver flowers to an office building. You enter at ground level and go down 4 floors to make the first delivery! Then you go up 6 floors to make the second delivery. Write down integer that represent how you return to ground level.
Answer:
-2
Step-by-step explanation:
you went to floor -4 in the begining, then went up 6 floors to floor 2
-4+6=2
so now you have to go down 2 floors making it negative
no your answer is -2
A certain car can travel 28.45 miles with one gallon of gasoline. The gasoline tank can hold
11.5 gallons. How many miles can this car travel on a full tank of gas? SHOW YOUR WORK!
Answer:
Answer:
327.175 miles
Step-by-step explanation:
Step one:
given data
A car can travel 28.45 miles with one gallon of gasoline
We want to find how far the car can go with 11.5 gallons
Step two:
if 1 gallon can go 28.45 miles
then 11.5gallons will go x miles
cross multiply we have
1x= 28.45*11.5
x=327.175 miles
Write the exponent for the expression.
1/8 x 1/8
Answer:
[tex]8^{-2}[/tex]
Step-by-step explanation:
[tex]2^{-2} = 1/4[/tex]
So:
[tex]8^{-2} = 1/8*1/8[/tex]
How much does the nylon rope cost per meter?
Answer:
(a) $0.80
(b) 1.25 m
Step-by-step explanation:
(a) Put 1 where L is, and evaluate the equation.
... p = 0.8·1 = 0.8
The cost for 1 meter of rope is $0.80.
(b) Put 1 where p is and solve for L.
... 1 = 0.8L
... 1/0.8 = L = 1.25
The length of rope that costs $1 is 1.25 meters.
Answer:
Well that depends on where you buy it
Step-by-step explanation:
It could cost various things and you didn't add enough context for us to assume where you could have purchased the nylon rope
If the supplement of <1 is 32º less than the measure of <1, what is m<1? a 1060 b 74o c 61o d 29o
Answer:
a. 106 degrees
Step-by-step explanation:
m=measure of angle 1; m-32 degrees=measure of supplement
m+(m-32 degrees)=180 degrees Add 32 degrees to each side.
2m=212 degrees Divide each side by 2
m=106 degrees ANSWER: The measure of angle 1 is 106 degrees
CHECK:
106+(106-32)=180
106+74=180
180=180
In one day a store sold 3/4 as many DVDs as Blu-Ray discs. The total number of DVDs and Blu-Ray discs sold that was 406. How many DVDs were sold
Answer:
283.2
Step-by-step explanation:
The number of DVDs will be 304.5.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that In one day a store sold 3/4 as many DVDs as Blu-Ray discs. The total number of DVDs and Blu-Ray discs sold was 406.
The number of the DVDs will be calculated as below:-
Number = 406 x ( 3 / 4).
Number = 304.5
Therefore, the number of DVDs will be 304.5.
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how do you figure out what type of solution it is when their are 2 ordered pairs
Answer:
To figure out if an ordered pair is a solution to an equation, you could perform a test. Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.
Step-by-step explanation:
What type of number is this: 5 3/4?
Answer:
it’s mixed number
Step-by-step explanation:
Answer:
It is a Mixed number!
Step-by-step explanation:
Find three consecutive integers such that the sum of the first and twice the second is 68 minus three times the third.
Answer:
x=9.5
Step-by-step explanation:
x+2(x+1)=68-3(x+3)
x+2x+2=68-3x-9
3x+2=68=59-3x
6x=57
x=9.5
A 75 inch pipe is cut into two peices. One peice is two times the length of the other find the length of the shorter pipe