Find the solution of the differential equation that satisfies the given initial condition.
Answers
The first equation is separable:
dy/dx = x/y ⇒ y dy = x dx
(provided that y ≠ 0)
Integrating both sides yields
1/2 y² = 1/2 x² + C
Given that y(0) = -8, we find
1/2 • (-8)² = 1/2 • 0² + C ⇒ C = 32
so that the particular solution is
1/2 y² = 1/2 x² + 32
Solving for y explicitly, we have
y² = x² + 64
y = ± √(x² + 64)
but since y(0) is negative, we take the negative solution:
y = - √(x² + 64)
The second equation is also separable:
du/dt = (2t + sec²(t)) / (2u) ⇒ 2u du = (2t + sec²(t)) dt
Integrate both sides:
u² = t² + tan(t) + C
Given u(0) = -6, we have
(-6)² = 0² + tan(0) + C ⇒ C = 36
and so
u² = t² + tan(t) + 36
u = ± √(t² + tan(t) + 36)
but again we take the negative root here to agree with the initial condition, so
u = - √(t² + tan(t) + 36)
Related Questions
what is the surface area of a polyhedron with measurements 4cm x 4cm x 7cm?
Answers
Check the picture below.
so let's add all sides and that'd be the area of the rectangular prism.
[tex]\stackrel{\textit{top and bottom}}{2(4\cdot 7)}+\stackrel{\textit{left and right}}{2(4\cdot 4)}+\stackrel{\textit{front and back}}{2(4\cdot 7)}\implies 56+32+56\implies 144[/tex]
Solve for x in the triangle. Round your answer to the nearest tenth.
Answers
Answer:
x = 13.9
Step-by-step explanation:
15cos(22) = 13.9
Answer:
x = 13.9
Step-by-step explanation:
For the 22° angle, x is the adjacent leg. The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
cos 22° = adj/hyp
cos 22° = x/15
x = 15 × cos 22°
x = 13.9
Answer: x = 13.9
NEED HELP! GIVING OUT BRAINLIEST! (Need long answer)
The diagram below shows a proportional relationship between the number of cans of soup and the price.
Explain what this value means in terms of the soup.
Answers
Step-by-step explanation:
The diagram below shows a proportional relationship between the number of cans of soup and the price.
1st:
$3.75 for 3 cans
per can
2nd:
$6.25 for 5 cans
per can
If x is the number of cans and y is the price of x cans, then
This means the constant of proportionality is 1.25 and its meaning is the soup price per can
A. The graph shows how much money Farrah has in her savings account after weeks of saving on a regular basis. How much money does Farrah have in her savings account after 10 weeks of saving?
Answers
Answer:
Step-by-step explanation:
wheres the graph
Answer:
How much money does priya have after 10 weeks? 320
How long did it take her to save 200? 5
How much did priya have in her savings account when she started to save regularly? 80
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE <3
Answers
Answer:
It's Micrograms. The rest are from the imperial system, which is the system that is commonly used in the United States. The metric system is an international system for scientists and mathematicians to use so that sharing and giving information is a lot easier when conveying to other people around the world.
Can anyone find all for me please ?
Answers
Answer:
It's a good question I seen thank you so much for your help and support me in the morning and have a talk
if g(x) = |2x-9|, find g(2)+g(3)
Answers
What happens to the median of the data set
{10, 2, 8, 9, 5, 2, 6} if the number 12 is added to the data set?
A. The median increases by 2.
B. The median decreases by 1.
C. The median does not change.
D. The median increases by 1.
Answers
Answer:
D
Step-by-step explanation:
Median- The average
The average can be found by adding the numbers together and dividing by the amount of numbers, in this case that would be 7. 10+2+8+9+5+2+6=42. 42÷7= 6. So the average before 12 is 6. 42+12 is the total adding that 12 and would equal 54. 54÷8=6.75, averaging out to 7. The average increased by about 1. So, the answer is D.
Answer: D. The median increases by 1.
Step-by-step explanation: This is correct.
what is the slope of -y=-x+6
Answers
Answer:
m = 1b = -6Step-by-step explanation:
We know that:
-y = -x + 6y = mx + bFirst, we need to change the 'y' sign.
=> -y = -x + 6=> y = x - 6Now, let's compare both of the equations to find slope.
=> (y = x - 6) = (y = mx + b)We can see that the slope is 1 and the y-intercept is -6.
Conclusion:
Therefore:
m = 1b = -6Hoped this helped.
Last year, a gardening store ordered 8,910 potted plants. This year, they ordered 9,801 potted plants. What is the percent of increase in the number of potted plants ordered annually?
Answers
Answer:
Step-by-step explanation:
100(9801 - 8910)/8910 = 10%
A jet can carry up to 200,000 liters of fuel.it used 130,000 liters of fuel during a flight. What percentage of the fuel capacity did it use on this flight
Answers
=(130000/200000)*100%
=65%
Which Graph is (x—5)^2/25 - (y+3)^2=1
Answers
Answer:
One that looks like this.
Step-by-step explanation:
Graph the solution set to this inequality. -2x+9_> 5x-12
Answers
x ≤ 3 (closed dot going to the left)
Each of the 14 students in the art club needs 4 1/4 ounces of paint for a project. The art store sells paint only in 8 ounce bottles. How many bottles of paint does the art club president need to buy for the project?
A - 3
B - 4
C - 7
D - 8
Answers
Answer:
C-7
Step-by-step explanation:
Answer: The art club president need to buy 14 bottles of paint for the project.
Step-by-step explanation: Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.
We are to find the number of bottles of paint that the art club president need to buy for the project.
We will be using the unitary method to solve the given problem.
Number of bottles filled by 8 ounces of paint = 1.
So, the number of bottles filled by 1 ounce of paint is
So, the number of bottles filled by 4 ounces of paint will be
Now, number of bottles of paint needed by 1 student
Therefore, the number of bottles of paint needed by 14 students will be
Thus, the art club president need to buy 14 bottles of paint for the project.
The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle
Answers
Then l = 3w-4
Perimeter = 2(w+l)
p = 2(w+3w-4) = 2w+6w-8 = 8w-8
Perimeter is 32…
8w-8 = 32
8w = 32+8
8w = 40
w = 5
l = (3×5)-4 = 11
Check… p = 2(5+11) = 2 × 16 = 32
Ans = length is 11
Hope it helps!
Answer:
11
Step-by-step explanation:
Create your own example for each cases of multiplying
polynomials
Case 1: Distributive Property
Case 2: FOIL Method
Case 3: Binomial to Polynomial
Pls needed badly
If you have nothing to answer dont answer
Answers
Step-by-step explanation:
CASE 1:2x(3x+7) = 6x^2+14x.CASE 2:(2x + 3)(3x – 1)CASE 3:x2 + 4xevaluate the expression when b=3/10 and x= -2/15
3x-b
Answers
Answer:
3x - b
3 (-2/15) - 3/10
-6/15 -3/10
-60/150 - 45/150
- 105/150
if you dont wear a retainer after braces can your teeth still be straight without wearing one cause mine still are and its been 6 months?
Answers
what is c3 - 1 when c = 4
Answers
4x3=12-1=11
c3-1
4*3-1
12-1
=11
area of a triangle b-2s^2+3t^2 h-4s^2-3t^2
Answers
Answer:
1 flmpysc - ax + x - y - 2
this could help
The chart shows the sizes and prices of different sized boxes of Alex's favorite cereal.
Answers
Step-by-step explanation:
Compare the rates
Whichever has the smaller rate is the best deal.
remember, to be able to compare both cereal boxes they must have the same unit of measure (grams with grams, ounces with ounces, etc.)
Answer:
Price of box of cereal #1
---------------------------- = $ per ounce(or other unit)
Size of box #1 (in ounces,
or some other unit)
The penalty box on a soccer field extends
54 ft from the goal line. The line where a
player gets to take a penalty kick is 12 yards
from the goal line. What is the ratio of the
distance from the goal line and where a
player takes a penalty kick?
Answers
Answer:
I dont know sorry
next time
I need help with this question
Answers
Answer:
check online for more information
Pls help I’ll brainlest help I’m failing do it on a paper and put it in the answer box
Answers
A dairy needs 364 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 364 gallons?
Answers
Answer:
Step-by-step explanation:
Let x be gallons of 7%
Let y be gallons of 3%
364 = x + y
y = 364 - x
364(0.06) = x(0.07) + y(0.03)
364(6) = x(7) + y(3)
364(6) = 7x + 3y
364(6) = 7x + 3(364 - x)
364(6 - 3) = 7x - 3x
364(3) = 4x
x = 273
y = 364 - 273 = 91
273 gallons of 7%
91 gallons of 3%
Which table of values represents possible solutions to
the equation y = 0.7x - 4.3?
х
49
у
30
X y
49 40
19 19
-11-12
-31-16
19 19
-11-12
-31 -26
B
Х
у
30
49
19 9
-11-12
-31 -26
Х
у
49 40
19 19
-11 -2.
-31 -16
D
Answers
Step-by-step explanation:
it will be c as shown in the photo
Please help, I will give good rating and brainliest of possible!!
Thank you!!!!!!!!
Answers
Answer:
[tex]g(x)=x+8[/tex]
Step-by-step explanation:
Translating a function up is very simple, all you need to do here is add 8.
If you want to think of it logically,
[tex]f(x)=x[/tex]
the whole right side of the function here can be our output. If x is 8, then the output, or height, is also 8. if you wanted to translate that up to 10, you'd simply need to add 2 to it, meaning [tex]x+2[/tex]. Then, at any given point on the function, it'd be 2 higher than it would be otherwise.
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6600 and his stock in Company B was worth $3500. The stock in Company A has increased 7% since last year and the stock in Company B has increased 1%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary). pls asap
Answers
Answer:
4.9%
Step-by-step explanation:
6600 * 107/100 = 66*107 = 7062.
3500 * 101/100 = 35x101 = 3535
7062+3535=10597. Original worth: 10100
10597-10100 = 497
497/10100 = 0.0492079208, or 4.92%, rounds to 4.9%
Help help help help help help help math
Answers
Answer:
Angle 6
Step-by-step explanation:
They are both the same angle size
Answer:
Angle 1
Step-by-step explanation:
Refer to the attached picture
Find the derivative of y=a^x
Answers
If y = aˣ, then y = exp(ln(aˣ)) = exp(x ln(a)). (Here I use exp(x) = eˣ.)
Then using the chain rule, the derivative of y is
dy/dx = exp(x ln(a)) • ln(a)
and undoing the rewriting, we end up with
dy/dx = ln(a) aˣ