Answer: y(x) = (2/3)*(x + 1)^(3/2) + 1/3.
Step-by-step explanation:
We have the differential equation:
2*y'(x)*y''(x) = 1.
y(0) = 2
y'(0) = 1.
I will use the change:
u = y'
u'= y''
Then we must solve:
2*u*u' = 1.
The product does not depend on x:
u*u' = 1/2.
By looking at the problem, i know that the functions must be something like:
u = a*(x + b)^n
Where a and b are real numbers.
u' = n*a*(x + b)^(n - 1)
such that:
(x + b)^n*(x + b)^(n - 1) does not depend on x
This means that:
(x + b)^n*(x + b)^(n - 1) = (x + b)^(n + n - 1) = 0
n + n - 1 = 0
2n = 1
n = 1/2
Then:
u = a*(x + b)^(1/2)
u' = (a/2)*(x + b)^(-1/2)
The differential equation becomes:
u*u' = 1/2
a*(x + b)^(1/2)* (a/2)*(x + b)^(-1/2) = 1/2
(1/2)*a^2 = 1/2
a^2 = 1.
And by the initial conditions, we have:
y'(0) = u(0) = 1
then:
u(0) = a*(0 + b)^(1/2) = a*b^(1/2) = 1
now, if a = -1, then b^(1/2) must be negative, this can not really be then we must have:
a = 1
u(0) = 1*b^(1/2) = 1
then b = 1.
u(x) = (x + 1)^(1/2).
And remember that y'(x) = u(x).
Then we need to integrate u(x) over x.
let's use the change of variables:
w = x + 1
dw = dx
Then the integration of u(x) is:
y(w) = ∫(w)^(1/2)dw = (2/3)*w^(3/2) + c
where c is a constant of integration.
now we can go back to x:
y(x) = (2/3)*(x + 1)^(3/2) + c
And we know that:
y(0) = 1 = (2/3)*(0 + 1)^(3/2) + c
1 = (2/3)*1 + c
1 - 2/3 = c
1/3 = c
Then:
y(x) = (2/3)*(x + 1)^(3/2) + 1/3.
calculate pqrst in the diagram above showing your solutions
Answer:
a. p = 6
b. q = 4
c. r = 8
d. s = 10; t = 8.3
Step-by-step explanation:
1. a. The side length of two similar triangles are proportional, therefore:
[tex] \frac{9}{p} = \frac{15}{10} [/tex]
Cross multiply
[tex] 15*p = 10*9 [/tex]
[tex] 15*p = 90 [/tex]
Divide both sides by 15
p = 6
b. Based on the midsegment theorem,
[tex] q = \frac{1}{2}(8) [/tex]
[tex] q = 4 [/tex]
c. The side length of two similar triangles are proportional, therefore:
[tex] \frac{4}{10} = \frac{r}{20} [/tex]
Multiply both sides by 20
[tex] \frac{4}{10} \times 20 = \frac{r}{20} \times 20 [/tex]
[tex] \frac{80}{10} = r [/tex]
r = 8
d. The side length of two similar triangles are proportional, therefore:
[tex] \frac{9 + 6}{9} = \frac{s}{6} [/tex]
[tex] \frac{15}{9} = \frac{s}{6} [/tex]
Multiply both sides by 6
[tex] \frac{15}{9} \times 6 = \frac{s}{6} \times 6 [/tex]
[tex] \frac{15 \times 6}{9} = s [/tex]
s = 10
[tex] \frac{9 + 6}{9} = \frac{t}{5} [/tex]
[tex] \frac{15}{9} = \frac{t}{5} [/tex]
Multiply both sides by 5
[tex] \frac{15}{9} \times 5 = \frac{t}{5} \times 5 [/tex]
[tex] \frac{15 \times 5}{9} = t [/tex]
t = 8.3 (nearest tenth)
Helppp?
Modelling exponential growth and decay
1. The population of a town is currently 4000 and it is increasing at a rate of 3% per year.
(a). What is the growth rate
(b). Express the growth rate in months
(c). What is the population of the town after 5 years?
2. A bank pays 0.8% interest per month. What is the interest rate for one year(months-years)
3. Determine the monthly interest rate given the following annual interest rate(years-months)
36%
Answer:
c) 1000. 10'00 that the answer is there anything else please cantact me
Find the value of the expression below. Show your work. 10 + 9(- 6) - (- 1 + 8)
please answer this as quick as possible
Answer:
-18
Step-by-step explanation:
Hope This Helps :)
PLEASE HELP ME I'LL GIVE BRAINLIEST
Answer:
the answer is A buddy
Step-by-step explanation:
Rick has 1/4 of a footlong sub left from yesterday. He ate 2/3 of the leftover sandwich as a snack. What fraction of the entire sandwich did he eat as a snack?
Group of answer choices: 1/6 1/3 3/7 11/12
Answer:
1/6
Step-by-step explanation:
1/4 = .25
2/3 = .6666...
.25(.6666...) = 1.6665...
1/6 = 1.666666
1/6 is the close enough answer bc the others would def not be it
1/3 = .3333....
3/7 = .428571428571
11/12 = 9.16666...
Hope this helps dude ! ^-^
14. Mr. White is renting an oversized truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 535 + 170d to find how much he will pay for a 10-day rental.
The amount paid for the 10-day rental will be equal to $2235.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Mr White is renting an oversized truck for one week and a few additional days d. He does not have to pay a per-mile fee. The expression is 535 + 170d.
The total amount will be calculated as,
A = 535 + 170d
A = 535 + ( 170 x 10 )
A = 535 + 1700
A = $2235
To know more about an expression follow
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Question attached just look at the picture
Name 2 alternate exterior angles do not copy of internet
Answer:
Transversal
Parallel Lines
Vertical Angles
Step-by-step explanation:To help you remember: the angle pairs are on Alternate sides of the Transversal, and they are on the Exterior of the two crossed lines.
Parallel Lines
When the two lines being crossed are Parallel Lines the Alternate Exterior Angles are equal. When two lines are crossed by another line (called the Transversal): Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Exterior Angles: a and h.
3) reflection across y=1
Answer:
The line y=-1 is a horizontal line and thus is a line that is parallel to the x-axis. If we reflect about a line that is parallel to the x-axis, then the x-coordinate of the point (that is reflected) will remain the same, thus the image of (2,-4) has x-coordinate 2 and thus the point is of the form (2,b).
Step-by-step explanation:
can i get Brainliest qwq
PLEASE HELP. DUE IN 10 MINUTES. 20 POINTS!!
Answer:
y=2+3x
Step-by-step explanation:
what is 15/27 in a decimal?
Answer:
0.55555
Step-by-step explanation:
the 5 keeps repeating
A number decreased by half of the number is four find the number
Help please!
Answer:
8
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
Write equation:
x=the unknown number
x-x/2=4x
Next: Solve equation
Isolate the variable on one side. The answer is:
x=0 The number is 0.
Help please thanks so much
Answer:
d
Step-by-step explanation:
A food scientist determines that a new type of orange has 15.38 mg of vitamin C/oz. How much vitamin C is in an orange that weighs 6 3/5 oz? Enter your answer, as a decimal to the nearest tenth, in the box.
Answer:
(Sorry this is a late response) 15.38=101.508 or 101.5
Step-by-step explanation:
You would divide 3 and 5 or 5 and 3 because 3 and 5 equals the fraction 3/5. The dividend is 3 and the 5 is the divisor. The quotient of this is 0.6. So the next step would be to add the 6 from 6 3/5 so this is the whole number so add it in front of 0.6 so it would turn into 6.6. The last step is to multiply the weight of the orange by the mg of vitamin C/oz that is 15.38 so multiply 6.6 by 15.38 this would equal 101.508 so you would just round this to a better answer and that would make it 101.5.
Tell me if I am wrong.. thanks
C personalities are organized and controlled. They take their time completing tasks accurately, like to research things thoroughly, and are always prepared. Because they put so much time and effort into everything they do, they hate to be criticized. They are perfectionists at heart and take even the smallest complaint personally. This makes them extremely difficult to confront. The best way to approach it is to focus on parts of the problem largely out of the C personality’s control or aspects of the problem they might not have considered. Make it clear that you appreciate all of their efforts and that you’re bringing something to their attention because it’s a variable that they need to have in the equation in the future. No matter what, don’t frame the conflict as a personal attack. If you do, the C personality will likely become resentful and go out of their way to avoid future interactions with you.
(1, 4); slope = -2 write the linear equation in slope intercept form given
Answer:
y=-2x+2
Step-by-step explanation:
The slope is -2x, meaning that the y-intercept can be found by working backwards from the given point. If the y value of the point is 4, subtracting 2 to get you to the point (0, 2) would provide the y-intercept.
Slope Intercept form is y=mx+b (m is the slope, x is the entered value, b is the y intercept)
Question 2
Measure and record the slopes of these line segments in the original logo. Then set n = 0.5, n = 2, and n = 3, and note the slopes of the
corresponding line segments in the resulting image.
Answer: LK= 2 for all (original, n=0.5, n=2, n=3)
GB= 0 for all
AH= undefined for all
Step-by-step explanation: my answer and PLATO answer
Answer:
LK = 2 for all in that column
GB = 0 for all in that column
AH = undefined
Step-by-step explanation:
Really hope this helps !!!
a nonagon is a nine-sided polygon, if a regular nonagon was rotated about its center point, which of the following angels of rotation would not map the figure onto itself
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Shape: Nonagon[/tex]
Required
Angles of rotation that would not map the shape on itself
Side of a nonagon is:
[tex]Sides = 9[/tex]
and a complete rotation is:
[tex]Complete\ Rotation = 360\°[/tex]
To start with, we calculate a possible angle of each rotation:
This is calculated by dividing the complete rotation by number of sides
[tex]Each\ Rotation = \frac{360}{9}[/tex]
[tex]Each\ Rotation = 40[/tex]
The question lacks option; so, it's difficult to give a specific answer.
However, I'll give a generalized answer
For the nonagon to map on itself, the angle must be a multiple of the calculated angle of rotation (40)
i.e.
[tex]Possible\ Angles = 40,80,120,160,200,240,280,320,360......[/tex]
Any angle different from the above listed angles (or any other multiple of 40 not listed above) answers the question.
The angles of rotation that would not map the figure onto itself will not be the multiple of 40 and this can be determined by evaluating the possible angle of each rotation.
Given :
A nonagon is a nine-sided polygon.A regular nonagon was rotated about its center point.To determine angels of rotation that would not map the figure onto itself, first, evaluate the possible angle of each rotation.
To determine the possible angle of each rotation the following calculation can be used:
The possible angle of each rotation is the ratio of the complete rotation to the number of sides.
[tex]\rm Each \;Rotation = \dfrac{360^\circ}{9}[/tex]
Each Rotation = [tex]40^\circ[/tex]
So, the angles of rotation that would not map the figure onto itself will not be the multiple of 40.
For more information, refer to the link given below:
https://brainly.com/question/22051318
What equations are equal to 6x+9=12
Answer:
x= 1/2 OR x= 0.5
Use the Distributive Property to simplify the expression. 2w+4+13w+1=
Answer:
15w+5
How I did it:
add 2 and 13 and put the "w" after the answer which is 15. Then add 4 and 1. That is 5 so then it is 15w+5.
The simplified Expression of 2w+4+13w+1 is 5 ( 3w+ 1).
What is Distributive Property?The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.
i.e., A ( B+ C) = AB + AC.
Given:
2w+4+13w+1
Now, solving
= (2w+ 13w) + ( 4+ 1)
= 15 w+ 5
Using Distributive Property
a x ( b+ c) = (a x b) + (a x c)
= 15 w+ 5
= 5 x 3w + 5
=5 ( 3w+ 1)
Hence, the expression is 5 (3w+1 ).
Learn more about Distributive Property here:
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Using the knowledge that 3 feet is equivalent to 1 yard, how many yards is equivalent to 885 feet?
Answer:
295
Step-by-step explanation:
The measure of EOD. Please help
Answer:
20 or 35
Step-by-step explanation:
Answer:
the measure of EOD is 60degrees
Please answer this quetion and get thanks if ur right the picture is right up
Answer:
C and D
Step-by-step explanation:
Additions have distributive property so the parentheses will not change the answer
Martin plays on a basketball team. In two games he scored 2/5 of the total points his team scored. His team scored 50 points the first game and 30 points in the second game. What was the number of points Martin scored in these two games?
Answer:
He scored 20 points in the first game and 12 points in the second game
Step-by-step explanation:
2/5 of 50 is 20 and 2/5 of 30 is 12. In total, he scored 32 points
Hope this helps!
(9x+5) - (4x+ 3)=? Qrite it out step by step
Answer: 13x+8
Step-by-step explanation: You add all of the like terms. so 9x+4x. You get 13x. Then you should do 5+3 which is 8. You’re left with 13x+8, and you can’t combine them so that’s your simplified equation.
Step-by-step explanation:
1Remove parentheses.
9x+5-4x-3
2 Collect like terms.
(9x-4x)+(5-3)
3 Simplify.
5x+2
(Sorry if its wrong, but I hope I helped ^-^)
Can someone make a free brainliest post so i can get too 5 crowns ?
Answer:
hi I'm Anna achooooooo
Answer:
How many crowns do you need to get to your next rank?
Step-by-step explanation:
I'm willing to help.
If these two trapezoids are similar, what is the measure of the missing angle?
Answer:
The answer is 900
Step-by-step explanation:
What is the Volume?
Answer:volume is what makes up the space
Step-by-step explanation:lenth times width times height
Answer:
2092.8
Step-by-step explanation:
Assuming that one of the sides is a square
Volume= l*w*h
32.7*8*8=32.7*64
=2092.8
Simplify your answer as much as possible. 3/x-4/7
Answer:
That is ur answer. I was unable to type that so I use took a screenshooton my phone .
Step-by-step explanation:
F(-7) =6x^3+6x
Help me ASAP
Answer:
-2100
Step-by-step explanation:
F(-7)=6(-7)^3+6(-7) = -2100
