Answer:
0.066666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
Step-by-step explanation:
4 divided by 60=that
Find the solution of the differential equation that satisfies the given initial condition. xy' + y = y2, y(1) = −5
Answer: [tex]y=\dfrac{5}{5-6x}[/tex]
Step-by-step explanation:
The given differential equation: [tex]xy' + y = y^2[/tex]
[tex]\Rightarrow\ xy'=y^2-y[/tex]
[tex]\Rightarrow\ \frac{1}{y^2-y}y'\:=\frac{1}{x}\\\\\Rightarrow\ \dfrac{1}{y(y-1)}\dfrac{dy}{dx}=\frac{1}{x}\\\\\Rightarrow\dfrac{y-(y-1)}{y(y-1)}dy=\dfrac{1}{x}dx\\\\\Rightarrow\dfrac{1}{(y-1)}dy+\dfrac{1}{y}dy=\dfrac{1}{x}dx[/tex]
Integrate both sides , we get
[tex]\int\dfrac{1}{(y-1)}dy+\int\dfrac{1}{y}dy=\dfrac{1}{x}dx\\\\\Rightarrow\ \ln(y-1)-\ln y=\ln x+c\ \ \ \ (i)[/tex]
At x=1 , y=-5 (given)
[tex]\ln(-5-1)-\ln -5=\ln 1+c\\\\\Rightarrow\ \ln (-6)-\ln(-5)=0+c\\\\\Rightarrow\ \ln(\dfrac{-6}{-5})=c\\\\\Rightarrow\ \ln(\dfrac{6}{5})=c[/tex]
[tex][\ \ln a+\ln b=\ln ab ,\ \ \ \ \ \ln a-\ln b=\ln\dfrac{a}{b}\ ][/tex]
Put value of x in (i), we get
[tex]\ln(y-1)-\ln y=\ln x+\ln (\dfrac65)\\\\\Rigtarrow\ \ln (\dfrac{y-1}{y})=\ln(\dfrac{6}{5}x)[/tex]
[tex]\Rightarrow\ 1-\dfrac{1}{y}=\dfrac{6}{5}x\Rightarrow\ \dfrac{1}{y}=1-\dfrac{6}{5}x\\\\\Rightarrow\ \dfrac{1}{y}=\dfrac{5-6x}{5}\\\\\Rightarrow\ y=\dfrac{5}{5-6x}[/tex]
hence, the required solution: [tex]y=\dfrac{5}{5-6x}[/tex]
The solution to the differential equation
[tex]xy'+y=y^2[/tex]
given the initial condition [tex]y(1)=-5[/tex] is [tex]y=\frac{5}{5-6x}[/tex]
Given the differential equation
[tex]xy'+y=y^2[/tex]
We can rearrange it as follows:
[tex]x\frac{dy}{dx}+y=y^2\\\\x\frac{dy}{dx}=y^2-y\\\\\frac{1}{y^2-y}\frac{dy}{dx}=\frac{1}{x}\\\\\frac{1}{y^2-y}dy=\frac{1}{x}dx[/tex]
Factoring the denominators of the LHS, and decomposing into partial fractions, we get
[tex]\frac{1}{y(y-1)}dy \implies \frac{1}{(y-1)}dy+\frac{1}{y}dy[/tex]
The final rearranged equation is
[tex]\frac{1}{(y-1)}dy+\frac{1}{y}dy=\frac{1}{x}dx[/tex]
Integrating both sides;
[tex]\int\frac{1}{y-1} dy +\int\frac{1}{y}dy=\int\frac{1}{x}dx\\\\ln(y-1)-ln(y)=ln(x)+c\\\\ln(\frac{y-1}{y})=ln(x)+c[/tex]
(We made of a law of logarithms on the last line to simplify the equation)
The initial condition [tex]y(1)=-5\implies y=-5 \text{ when }x=1[/tex]
Substituting into the general solution we got earlier
[tex]ln(\frac{y-1}{y})=ln(x)+c\\\\ln(\frac{-5-1}{-5})=ln(1)+c\\\\ln(\frac{-6}{-5})=ln(1)+c \\\\(\text{since }ln(1)=0)\\\\ln(\frac{-6}{-5})=c\\\\ln(\frac{6}{5})=c[/tex]
Substituting the value of [tex]c[/tex] back into the general solution
[tex]ln(\frac{y-1}{y})=ln(x)+c\\\\ln(\frac{y-1}{y})=ln(x)+ln(\frac{6}{5})\\\\ln(\frac{y-1}{y})=ln(\frac{6x}{5})\\\\\frac{y-1}{y}=\frac{6x}{5}[/tex]
When [tex]y[/tex] is made the subject of the formula
[tex]y=\frac{5}{5-6x}[/tex]
Therefore, the solution that satisfies the initial condition [tex]y(1)=-5[/tex] is [tex]y=\frac{5}{5-6x}[/tex]
Learn more about solving differential equations here: https://brainly.com/question/4537000
What was the golfers total score for the tournament ?
Answer:
-11
Step-by-step explanation:
-3+(-1)+(-5)+(-2)
-3+(-1)=(-4)
-4+(-5)=(-9)
-9+(-2)=(-11)
(-11)
HOPE THIS HELPS!!
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
Based on the table, which function models this situation?
Answer:
f(n) = -3n + 24
Step-by-step explanation:
Let the function representing Number of meals and amount of Pet Food remaining is,
f(n) = an + b
Where a = number of meals dispensed
n = amount of Pet food per meal
b = Initial amount of Pet food
From the table attached,
For n = 1 and f(n) = 21,
21 = a(1) + b
a + b = 21 -----------(1)
For n = 3 and f(n) = 15,
15 = a(3) + b
3a + b = 15 -----------(2)
Equation (2) - equation (1),
(3a + b) - (a + b) = 15 - 21
a = -3
From equation (1),
-3 + b = 21
b = 24
Therefore, function will be,
f(n) = -3n + 24
Answer:f(n)=-3+24
Explanation
Unit rate of the table is three therefore taking away 3 cups each time food is dispensed aka -3n. 24 represents the starting point. 21+3=24
2.4 x 0.87 help help help
Answer:
2.088
Step-by-step explanation:
Trust me I am in high school honors algebra with almost an average of 100.
The product of 2.4 x 0.87 is 2.088.
What is a decimal ?A decimal is represented by a dot which separates the whole part and the fractional part of a number.
According to the given question we have to multiply two decimals numbers 2.4 and 0.87.
Multiplication of decimals numbers can be easily done just by removing the decimas and multiplying them in form of integers and after obtained result we'll put the decimal as many digits before from the rightmost side as the sum of the digits which those two numbers have after the decimal.
So, (24×87) = 2088 now the sum if the digits is 3 so we'll put the decimal 3 places before which is 2.088.
learn more about decimals here :
https://brainly.com/question/548650
#SPJ2
uch Nancy earned? Please my daughter
Answer:
Number 2
Step-by-step explanation:
Each player at a paintball park pays an entrance fee to use the course. The paintball park also charges each player for the number of paintballs used. When a player uses LaTeX: nn paintballs, the total cost in dollars to play is given by the expression LaTeX: 0.60n+150.60 n + 15.
Complete the statements below with the appropriate values.
The entrance fee to the paintball park is $
.
Each purchase of 15 paintballs costs $
.
Answer:
The entrance fee to the paintball park is $15
Each purchase of 15 paintballs costs $9
Step-by-step explanation:
We are given the expression [tex] 0.60n + 15 [/tex] as the total cost in dollars that a player pays when he plays paintball in the course.
Where,
n = number of paintballs a player uses
$0.60 = cost per paintball
$15 = entrance fee charged to for using the course
Completing the statement given in the question becomes now easy and clear.
We already know that the entrance fee is $15, which is the starting cost.
The cost for our each purchase of 15 paintballs is expressed as = cost per paintball × number of paintballs
= 0.60n
= 0.60 × 15 = $9
Answer:
Entrance Fee = $15
15 point balls cost = $9
Step-by-step explanation:
Two cars are 180 mi apart and travel toward each other along the same road. They meet in 4 hr. One car travels 5 mph slower than the other car. What is the
average speed of each car?
Answer:
The speed of the slower car = 20 mph
The speed of the faster car = 25 mph
Step-by-step explanation:
Let the speed of the slower car be s - 5
Let the speed of the other car be s
Two cars are 180 mi apart and travel toward each other along the same road. They meet in 4 hr.
Hence, the total speed = Distance/Time
= 180 miles/4hr
= 45 miles/hr or 45mph
Therefore:
s + s - 5 = 45 mph
2s - 5 = 45 mph
2s = 45 + 5
2s = 50
s = 50/2
s = 25 mph
The speed of the other car = s = 25mph
The speed of the slower car be s - 5
s - 5
= 25 - 5 = 20mph
Therefore,
The speed of the slower car = 20 mph
The speed of the faster car = 25 mph
Simplify.
9a +4b+4+4a +5b+7
Answer:
13a + 9b + 11
Step-by-step explanation:
9a + 4a = 13a4b + 5b = 9b4 + 7 = 11Put them together: 13a + 9b + 11I hope this helps!
Answer:
13a+ 9b+ 11
Step-by-step explanation:
9a+4a= 13a
4b+ 5b= 9b
4+7=11
The 5 members of the
Jackson family went
to a hockey game.
They paid $20 for
snacks. In all, the
tickets cost 4 times
the cost of the snacks.
How much did a
single ticket cost?
Answer:
16
Step-by-step explanation:
80 divide by 5 is 16
HELP PLEASE I WILL MARK BRAINLIEST AND GIVE YOU THANKS AND % STARS
Which expression is equivalent to (3x-5)+(x+2y)
Answer:
4x-3y
Step-by-step explanation:
Answer:
(3x-5y) + (x+2y)
Let just go ahead and open brackets and simplify
3x - 5y + x + 2y
3x + x + 2y - 5y
4x - 3y
Brainliest??
GIVING 30 POINTS
need it RN
Which equation represents a line which is perpendicular to the line
5x + 4y = -24?
Please Answer! Brainliest! 25 points!
Answer:
x= 18
y= 54
Step-by-step explanation:
(Sorry if i'm too late)
Okay lets do this!
We will start with X:
If AOD is equal to COB, then we can do 90-72 to find AON
18 +2x= 3x
18 = x (wow that was simple :))
x= 18
Lets try Y now
If AB is a straight line, then 72 +y +3x is 180
so 72 + y + 3( 18) = 180
72 + y + 54 = 180
y = 54
We should check our work now:
2(18)+ 18 + 72 + 54 + 3 (18) + 126 = 360 !!!
Yayyyyy
So this should be correct
Please tell me if this is wrong :)))
(7p² + 4p+3)-(4p²- 3p+1)
Answer:
Step-by-step explanation:
(7p² + 4p+3)-(4p²- 3p+1)
opening the brackets
7p² + 4p + 3 - 4p²+ 3p - 1
By grouping the like terms,
7p² - 4p² + 4p + 3p + 3 - 1
3p² + 7p + 2
Hope this helps
plz mark as brainlest!!!!!!!
Solve 1/2 + (- 3/4) =
Please answer this as fast as you and it needs to be common denominators before you can add the fractions.
Answer:
-0.25 or 1/4
Step-by-step explanation:
Eh just know
Use the distributive property to write an equivalent expression.
9(8w + 4)
Answer:
72w+36
Step-by-step explanation:
The sum of three consecutive integers equals 39 more than the least of the integers. Find the integers
Answer: 12, 13, 14
Explanation: This was on my test last week and this is the correct answer.
Answer:
18, 19, 20
Step-by-step explanation:
We can have the lowest number be [tex]x[/tex], and the second and third numbers be [tex]x+1[/tex] and [tex]x+2[/tex]. Now we have the equation [tex]x+x+1+x+2=x+39.[/tex]
[tex]3x+3=x+39\\\\2x=36.[/tex]
x=18, so the numbers are 18, 19, and 20.
T is the midpoint of KL. K has coordinates (2,−6), and T has coordinates (−4,2). Identify the coordinates of L.
Answer:
[tex]L = (-10,10)[/tex]
Step-by-step explanation:
Given
[tex]K = (2,-6)[/tex]
[tex]T = (-4,2)[/tex]
Required
Determine the coordinates of L
Since T is the midpoint of K and L, we make use of:
[tex]T_x = \frac{K_x + L_x}{2}[/tex]
and
[tex]T_y = \frac{K_y + L_y}{2}[/tex]
Solving for [tex]L_x[/tex]
[tex]T_x = \frac{K_x + L_x}{2}[/tex]
[tex]-4 = \frac{2 + L_x}{2}[/tex]
Multiply through by 2
[tex]-8 = 2 + L_x[/tex]
[tex]L_x = -8 - 2[/tex]
[tex]L_x = -10[/tex]
Solving for [tex]L_y[/tex]
[tex]T_y = \frac{K_y + L_y}{2}[/tex]
[tex]2 = \frac{-6+L_y}{2}[/tex]
Multiply through by 2
[tex]4 = -6 + L_y[/tex]
[tex]L_y = 4 + 6[/tex]
[tex]L_y = 10[/tex]
Hence: The coordinates of L is:
[tex]L = (-10,10)[/tex]
The lines below are parallel if the slope of the solid line is 2, what is the slope of the gas line?
Answer:
2
Step-by-step explanation:
Parallel lines have the same slope. Hope this helps!
Simplify.
Remove all perfect squares from inside the square root.
450
Answer:
[tex]15 \sqrt{2 } [/tex]
that the answer
John gets to play a total of 96 songs at his school dance. He wants twice as many fast songs, y, as slow dance songs, x. Write a pair of equations to represent this situation and use those equations to find the number of fast and slow songs John can play. Then solve for x and y.
Answer:
The number of fast songs is 64 and the number of slow songs is 32
Step-by-step explanation:
∵ Y represents the number of fast songs
∵ x represents the number of slow dance songs
∵ John gets to play a total of 96 songs at his school dance
→ That means the sum of x and y is 96
∴ x + y = 96 ⇒ (1)
∵ He wants twice as many fast songs, y, as slow dance songs, x
→ That means y is twice x
∴ y = 2x ⇒ (2)
→ Substitute y in equation (1) by equation (2)
∵ x + 2x = 96
∴ 3x = 96
→ Divide both sides by 3 to find x
∴ [tex]\frac{3x}{3}=\frac{96}{3}[/tex]
∴ x = 32
→ Substitute the value of x in equation (2) to find the value of y
∵ y = 2(32)
∴ y = 64
∴ The number of fast songs is 64 and the number of slow songs is 32
Which statistic indicates the strength of the relationship between the length of the auction and final price?
Answer:
Percentage of bid.
Step-by-step explanation:
The auction price is the initial start of bidding. This price is set for the thing which are placed under auction and below that auction price the trade cannot take place. This is usually considered as a starting point and then bidders start to quote their bid for the auctioned. The final price is determined when the bidders quotes the highest possible price after which no one else quotes any other bid. The auction is then closed and the bidders gains the auctioned things.
ILL GIVE BRAINLIEST PLZ HURRY
Answer:
Mode = 86Median = 86Mean = 86Range = 15Step-by-step explanation:
Hope this helps! <3
is -4 greater,less than or equal to +4 ?
The sum
of a negative
and positive
integer is
negative?
Complete question is;
State whether true or false
The sum of a negative integer and a positive integer is always a negative integer.
Answer:
False
Step-by-step explanation:
The statement is false. This is because it's not in every case that sum of negative integer and a positive integers is equal to zero.
For example let's consider the integers -5 and 8.
The sum is; -5 + 8 = 3
The result is not negative
Whereas if we consider -8 and 5,the sum is; -8 + 5 = -3
This result is negative
So sometimes the sum can yield a positive or negative results.
Thus, the statement in the question is false.
Kathryn is getting ready for Halloween and is headed to the store to pick up a costume. At the Halloween store,
she sees that there are 20 green wigs, 15 blue wigs, and 30 black wigs. Write the ratio of blue wigs to total
wigs in the Halloween store.
Answer:
15;30
Step-by-step explanation:
Question 5 (1 point)
In 2001, the Guinness Book of World Records recognized a breakfast which served 18,941 people
as the largest ever cooked. Which number below shows 18,941 rounded to 3 significant digits?
18,900
18,940
10,000
19,000
Review Answers
Saved at 7:09 pm
to search
Answer: 18900
Step-by-step explanation:
Given the question:
In 2001, the Guinness Book of World Records recognized a breakfast which served 18,941 people as the largest ever cooked. Which number below shows 18,941 rounded to 3 significant digits?
18,941 rounded to 3 significant figures
To round to 3 significant figures, the first 3 numbers are kept intact, then the subsequent number is rounded up to 1 if up to or greater than 5 and added to the third figure. If less than 5, all subsequent numbers are rounded down to 0
Hence,
18,941 = 18900 (because 4 is less than 5, 4 and all subsequent numbers are rounded down to 0).
Which relation is a function?
(8,-4), (8,2), (3, -3), (3, 1), (-1,-1)
(2.0), (4,0), (2, 1), (4, 1), (2, 3)
(2, 1), (4,2), (6,4), (7,5), (8, 6)
(3, 8), (7, 6), (5,5), (4,4), (3, 2)
PLEASEEEEEEEEEEEEEEE HELPPPPPPPPP i'll give you brainliest
The dosage for a medication is increased from 20 mg (milligrams) to 30 mg. What is the percent increase in the dosage?
Step-by-step explanation:
10%
In the figure, <6 and <2 are
Answer:
d
Step-by-step explanation:
consecutive angles aren't a thing and the others there would have to be an angle on the other side.
if andre rides his bike for 8 miles, how long will this take?
Answer:
25 minutes
Step-by-step explanation:
it kinda depends on how fast hes going but most likely 25 minutes
