) consider the initial value problem y′−5y=15t+3et,y(0)=y0 y′−5y=15t+3et,y(0)=y0 (a) solve the initial value problem. (enter y0 for y0y0). y(t)y(t)= equation editorequation editor (b) determine the value of y0y0 that separates solutions that grow positively as t→[infinity]t→[infinity] from those that grow negatively.
Answers
Answer:
a)value attached below
b)Yo = [tex]\frac{-27}{20}[/tex]
Step-by-step explanation:
A) solving initial value problem
[tex]y' - 5y = 15t + 3e^t[/tex]
y(0) = yo
hence the solution of the initial value problem : y(t)
Y(t) =
Attached below is the detailed solution
B) Yo = [tex]\frac{-27}{20}[/tex] separates the solutions as
t →∞
this is because when y(t) < [tex]\frac{-27}{20} y(t) tends to inifiniy[/tex]
y(t) > [tex]\frac{-27}{20} y(t) tends to inifinity[/tex]
Related Questions
Use elimination to solve the system of equations. 2x+y=4 and -4x-2y=8
Answers
Answer: No solution
Step-by-step explanation:
To use elimination method, we need to choose a variable to eliminate. Let's eliminate x. To eliminate x, the x coefficient in both equations must be the same, regardless of the sign. To do so, let's multiply the first equation by 2.
(2x+y=4)2
-4x-2y=8
-------------------------------------------------------------------------------------------------------------
4x+2y=8
-4x-2y=8
Let's add both equations together.
0=8
-------------------------------------------------------------------------------------------------------------
Now that we got this far, we can see that something is wrong. This normally doesn't happen. If you notice, the second equation is the first equation but multiplied by 2. Instead, let's rewrite each equation.
2x+y=4 [subtract both sides by 2x]
y=-2x+4
-4x-2y=8 [add both sides by 4x]
-2y=4x+8 [divide both sides by -2]
y=-2x-4
-------------------------------------------------------------------------------------------------------------
If you analyze both equations, you will see that they are parallel lines. We know this because the slopes are the same, but different y-intercept. from our knowledge of parallel lines, they NEVER touch or cross. This means there would be no solution at all.
what would be equivalent to 32 ⋅ 35?
Answers
Step-by-step explanation:
35•32 or 1120 there you go
1.6.AP-9
A family is comparing different car seats. One car seat is designed for a child up to and including 25 lb. Another car seat is designed for a child between 16 lb and 35
Ib. A third car seat is designed for a child between 25 lb and 95 lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a
33-lb child?
The inequality for a child up to and including 25 lb is
(Simplify your answer. Type a compound inequality using x as the variable.)
Answers
Answer:
a. i. x ≤ 25 ii. 16 < x < 35 iii. 25 < x ≤ 95
b. The second and third car seats are appropriate for a 35 lb child.
Step-by-step explanation:
a. Model those ranges with compound inequalities
Let x represent the car seat.
i. A car seat designed for a child weighing up to and including 25 lb is described by the inequality.
x ≤ 25
ii. A car seat designed for a child weighing between 16 lb and 35 lb is described by the inequality.
16 < x < 35
iii. A car seat designed for a child weighing between 25 lb and 95 lb inclusive is described by the inequality.
25 < x ≤ 95
b. Which car seats are appropriate for a 33-lb child?
Since 35 lb is included in the range of the inequalities for the second and third card seats, the second and third car seats are appropriate for a 35 lb child.
Ratio of wins to losses in 42 games with 35 wins.
Answers
oh wait no nvm sorry i got t wrong im so sorry dont listen to me im trash
write two inequaltities to compare -5 and -3
Answers
-5 < -3 and the second inequality is -3 > -5
Can someone help please
Answers
Answer:
[tex]x > \frac{16}{3} [/tex]
Step-by-step explanation:
[tex]4x - 8 > 24 - 2x \\ 4x + 2x > 24 + 8 \\ 6x > 32 \\ x > \frac{16}{3} [/tex]
Solve for x. 20 points and I give brainliest
Pls provide work. Due in an hour
Answers
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
To solve for x, we can use the Exterior Angle Theorem.
The Exterior Angle Theorem states that the exterior angle is equivalent to the sum of the two opposite, interior angles.
So, we can write the following equation:
[tex](6+25x)=(44)+(18x-3)[/tex]
Now, we just have to solve for x.
On the right, let's subtract. So:
[tex]6+25x=18x+41[/tex]
Now, let's subtract 18x from both sides. This gives:
[tex]6+7x=41[/tex]
Now, let's subtract 6 from both sides. This will yield:
[tex]7x=35[/tex]
And, finally, let's divide both sides by 7, giving us:
[tex]x=5[/tex]
And we're done!
We can use the Exterior Angle Theorem.
6 + 25x = 44 + 18x - 3
6 + 25x = 18x + 41
25x = 18x + 35
7x = 35
x = 5
Best of Luck!
What is the value of m
Answers
Answer:
m = 10
Step-by-step explanation:
From the image given, we can tell that there are two sides for angle H for the segment IJ. From that we can see that angle H is a supplementary angle. A supplementary angle is an angle whose sum is 180°So: (2m+10)°+(5m+100)° = 180°(7m+110)° = 180°(7m)° = 70m = 10I want to pull all nighter and stay awake for 36 hours. If I woke up at 12 PM, and if it's currently 11:22 PM right now, then how long have I been awake?
( I actually need to know I'm pulling an all nighter to reset my sleep schedule)
Answers
Answer:
11 hours and 22 minutes
Why are there two solutions for the equation |6 + y| = 2? Explain.
(there should be a solution and an explanation onto why there is two answers)
Answers
|6+y| = 2
If you try -4 you get 2 in a positive form so -4 is one correct.
The second correct one is -8 because 6-8 is -2 but as I was saying before how the absolute value changes it into positive, that means -2 would be switched to 2 meaning that -8 is also a correct answer.
If you need more help just search up what absolute value is.
If you found my answer helpful pls mark has brainliest
Answer:
Sample response: The absolute value symbol in the equation indicates two solutions because absolute value is the distance from a number to zero on a number line. Two different directions, to the right and to the left, will determine the
Step-by-step explanation:
Sarah sold 12 boxes of girl scouts cookies. If Sarah sold three times as many boxes as Amiyah, how many boxes did Amiyah sell?
Answers
Answer:4
Step-by-step explanation:
you would set this up as 3x = 12.
to solve, just divide the 12 by 3, leaving you with X = 4.
A person becomes instagram famous when they have more that 5,000. Dmytryus currently has 2,000 followers. For every 500 likes a photo of his gets, he gains 20 followers. a.) what is the slope and what does it represent in this situation? b.) How many likes does Dmytryus need before he will become instagram famous? ANSWER THIS IS URGENT!!!!!
Answers
Answer:
a. 25/1, likes per follow b. 75,000 likes
Step-by-step explanation:
The slope is the likes per follow, which is 500/20 simplified to 25/1. To find how many he needs for answer b, you first need to find how many more followers he needs, which is 3000. You then multiply the number of likes per follow by the number of followers needed, 25x3000. Dmytryus needs 75000 likes to become Instagram famous.
Why is thinking about the problem before you work important?
Answers
Answer: It's good to think about things before doing them because it is more thought out and you have a better chance of getting things correct whereas without thinking your most likely going to get it wrong. Without thinking through your options you are basically guessing the answer. I hope this helped you have a great day and god bless you :D
a profit of 9$ integer
Answers
Answer:
+ or - $9
Step-by-step explanation:
[31pts and brainliest] What is the measurement of angle Z and why?
Answers
Answer:
the measure of angle Z is 104
Step-by-step explanation:
the angle z and 76 form a suplementary angle, which they add up to 180.
To find angle z, just subtract 76 from 180.
for which equations below is x = -3 a possible solution ?
lxl = 3
lxl = -3
l-xl = 3
l-xl = -3
-lxl = -3
Answers
Answer:
-/x/ = -3 (Sorry I couldn't put the lines)
Step-by-step explanation:
Negative and a negative = a positive
I hope this helps you :)
What equation can Janet use to calculate the principal amount? (and please don't just answer try to solve it someone ripped me off, the last time i asked by just typing)
Answers
Answer:
t = [tex]\frac{l}{pr}[/tex]
Step-by-step explanation:
Formula or literal equation used to calculate the simple interest is,
l = prt
where 'l' = Simple interest
p = principle amount invested
r = rate of interest
t = time or duration of the investment
If we have to calculate the time of investment form the given formula,
l = prt
By the division property of equality,
[tex]\frac{l}{pr}=\frac{prt}{pr}[/tex]
[tex]t=\frac{l}{pr}[/tex]
Therefore, formula to be used is, [tex]t=\frac{l}{pr}[/tex]
Please Help!!! 20 Points! Brainliest Answer! 2 questions
Answers
Answer:
Step-by-step explanation:
its D which is 7
make y the subject of the formula x=a-2by squared
Answers
Answer:
y = ± [tex]\sqrt{\frac{a-x}{2b} }[/tex]
Step-by-step explanation:
Given
x = a - 2by² ( subtract a from both sides )
x - a = - 2by² ( multiply through by - 1 to clear the leading negative )
a - x = 2by² ( divide both sides by 2b )
[tex]\frac{a-x}{2b}[/tex] = y² ( take the square root of both sides )
y = ± [tex]\sqrt{\frac{a-x}{2b} }[/tex]
Making y the subject of the formula, [tex]x = a - 2by^2[/tex] , the answer would be:
[tex]\mathbf{y = \sqrt{\frac{x - a}{-2b}} }[/tex]
Given the formula: [tex]x = a - 2by^2[/tex],
Required:
Making y the subject of the formula
This is done as shown below:
[tex]x = a - 2by^2[/tex]
Subtract a from both sides[tex]x - a = - 2by^2[/tex]
Divide both sides by -2b[tex]\frac{x - a}{-2b} = y^2[/tex]
Take the square root of both sides[tex]\sqrt{\frac{x - a}{-2b}} = y\\\\\\\mathbf{y = \sqrt{\frac{x - a}{-2b}} }[/tex]
Therefore, making y the subject of the formula, [tex]x = a - 2by^2[/tex] , the answer would be: [tex]\mathbf{y = \sqrt{\frac{x - a}{-2b}} }[/tex]
Learn more here:
https://brainly.com/question/19557491
AB=10,BC=6. What is AC
Answers
Answer:
16
Step-by-step explanation:
adding any two sides of a triangle is allways greater than the third side.
What’s the absolute value of -6.5
Answers
Answer:
6.5
Step-by-step explanation:
|-6.5| = 6.5
Answer:
6.5
Step-by-step explanation:
How do I solve this problem?
Answers
a^2 + b^2 = c^2
2^2 + 3^2 = c^2
4 + 9 = 13
square root of 13 = 3.6055...
round to the nearest hundredth..
The answer is 3.61 cm
The ratio of boys to girls in the lunch room was 4 to 3. If there were 84 students in the cafeteria, how many were girls?
Answers
Step-by-step explanation:
9868866858566586575765578
yes I am so certainly brainly right now
Answers
What is that supposed to mean
1. Give an example of the symmetric property
Answers
Answer:
if line segement XY is congruent to line segment MN, the line segemnt MN is congruent to line segment XY
Step-by-step explanation:
:)
A line segment has the endpoints P(-7, 6) and Q(-3, 9). Find the coordinates of its
midpoint M
Write the coordinates as decimals or integers.
Answers
Answer:
[tex]MP= (-5,7.5 )[/tex]
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )[/tex]
[tex]MP= (\frac{-7+-3}{2} )(\frac{6+9}{2} )[/tex] -7+-3= -10 6+9=15
[tex]MP= (\frac{-10}{2} )(\frac{15}{2} )[/tex] -10/2=-5 15/2=7.5
[tex]MP= (-5,7.5)[/tex]
x[8x + (-4)x]² - (4)-(-6)x
Answers
Use Similar triangles to calculate the height, h cm, of traingle ABE
Answers
Answer:
24 cm
Step-by-step explanation:
Since the triangles are similar, their dimensions are proportional. The base DC is half the base AE, so we know the ratio of triangle heights is 1 : 2.
Then the bottom height (h) ratio to the overall height is ...
h : 36 = 2 : (1+2) = 2 : 3 = 24 : 36
The height h is 24 cm.
What are polynomials? pls help, I don't understand!!!!!!
Answers
Answer:
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.
Answer:
They are expressions with variables. For example, 2x + 5 - 7x. That would be a polynomial.
Franklin deposited $75 in a no-interest bank account when he opened it. After that, he deposits $50 per month in the account. Assume he makes no other withdrawals or deposits. The equation below can be used to find m , the number of months it will take him to save a total of $175. 75 + ?m = 175
Answers
Answer:
2 months for $175
Step-by-step explanation:
2x5 is 10 so 2x50 = 100 and since 75 was already in the bank when he started doing deposits, it took him 2 month to deposit 100
Answer:
50
Step-by-step explanation:
i got this one wrong 175 isnt correct