Which expression is equivalent to y^3-2y^2+y

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.

Answer:

I think it's (-13,0)

Step-by-step explanation:

4x - 3y > 9

3y - 9 =x

y=-13

(-13,0)

Plz forgive me if i did that wrong I did try lol

Answer:

Equals means a person or thing considered to be the same as another in status or quality.

Or the mathmatic term is be the same as in number or amount.

Answer: 14

Step-by-step explanation: the area is found by base x height. the area is 1/2 and the base is 3/4.  so what we wanna do is 4/3 x 21/2 which gets us our answer, 14.

Answer:

I cant help u and I am sorry but thank you

Step-by-step explanation:

Answer:

Against the direction of the wind is [tex]x-10=35-10=25\ \text{mph}[/tex] and with the wind is [tex]x+10=35+10=45\ \text{mph}[/tex]

Step-by-step explanation:

Let x be the speed of the hawk in still air

The speed of the wind is 10 mph

So speed of the hawk when flying against the wind is [tex]x-10[/tex] and with the wind is [tex]x+10[/tex].

Distance the hawk travels when going against the wind is 50 miles and going with the wind is 90 miles

The hawk covers the above mentioned distances in the same amount of time.

[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\dfrac{50}{x-10}=\dfrac{90}{x+10}\\\Rightarrow \dfrac{50}{x-10}-\dfrac{90}{x+10}=0\\\Rightarrow \dfrac{50(x+10)-90(x-10)}{x^2-100}=0\\\Rightarrow 50x+500-90x+900=0\\\Rightarrow -40x+1400=0\\\Rightarrow x=\dfrac{1400}{40}\\\Rightarrow x=35\ \text{mph}[/tex]

The speed of the hawk in still air is 35 mph.

Speed of the hawk against the direction of the wind is [tex]x-10=35-10=25\ \text{mph}[/tex] and with the wind is [tex]x+10=35+10=45\ \text{mph}[/tex].

The first answer is messed up at the 3+9 part because they were supposed to multiply 9 and 2 first.

The second answer is messed up at the beginning because they didnt to the parenthesis first.

Follow PEMDAS

Answer:

Weren’t supposed to add until the end

It was supposed to be 81 not 27

Step-by-step explanation:

Answer:

i wish i could help so sorry

Step-by-step explanation:

Answer:

Answer is 74 square units

Step-by-step explanation:

I took the quiz.

Answer:

y= 1/2

Explanation:

Answer:

The probability is 2/5

Answer:

6/10

Step-by-step explanation:

as you said it easy.

Answer:

Rise/Run= 1/2

Step-by-step explanation:

Answer:

17xn

Step-by-step explanation:

Answer:

1  7 /25

Step-by-step explanation:

bc i did the math

Answer:

32/25

& Ig it's just cause math says so. I mean 24/25 then 3/4 then that divided by it

Step-by-step explanation:

0.0375 did you mean 80÷3 if so 26.6

Answer:

girlfriend

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

it is actually simple my guy chill

Answer:

it is 5/8 the second one

Step-by-step explanation:

Answer:

The first one is d: x=0 or x=6

the second one is the 3rd one

Step-by-step explanation:

The roots of the quadratic equation will be -

{x} = (1 ± i√29)/5

Given is the quadratic equation as -

5x² - 2x + 6 = 0

We can write the roots as -

{x} = {- b ± √(b² - 4ac)/2a}

{x} = (2 ± √-116)/10

{x} = (2 ± i 2√29)/10

{x} = 2(1 ± i√29)/10

{x} = (1 ± i√29)/5

Therefore, the roots of the quadratic equation will be -

{x} = (1 ± i√29)/5

To solve more questions on quadratic equations, visit the link below -

brainly.com/question/1041084

#SPJ6

Answer:

4 is your answer :) yayy

Answer: Your answer is 4

Step-by-step explanation: If you have 2 blocks, and someone gives you 2 more, you now have 4 blocks in total. Hoped this helped you. Have a wonderful day!!!

Answer:

4

Step-by-step explanation:

slope = dy/dx

We can see a dy (delta y) of 4 together with a dx of 1. In other words, when you step 1 to the right, you go up 4.

Answer:

the slope is-- 4/1 and the y intercept is where the line touches the vertical line. sorry the picture in not clear,so i could not see the number

Step-by-step explanation:

Answer:

The inequality will be: 1.25<t<5.99

Step-by-step explanation:

Inequalities are used to represent a range or less than or greater than quantities.

Compound inequalities are used to define ranges for a variable.

In the given statement,

t, in the store ranges between 1.25  and 5.99.

This means that t will be greater than 1.25 and less than 5.99

So,

The inequality will be: 1.25<t<5.99

Answer:

19

Step-by-step explanation:

20% of 95 is 19 :)

Answer:

h=-41/2

Step-by-step explanation:

Answer:

|7h+ 1| = |3h - 7|

Exact Form:

h  =  − 2 ,  3 /5

Decimal Form:

h  =  − 2 , 0.6

Answer:

30

Step-by-step explanation:

Those prime numbers are 2, 3 and 5

2 * 3 is 6 * 5 is 30

i hope this helped, please mark Brainliest, thank you!!

Answer:

30

Step-by-step explanation:

The three smaller primes are: 2, 3, and 5

So their product is: 2 * 3 * 5 =30

Answer:

10 dollars?

Step-by-step explanation:

Answer:

$10 dollars

Step-by-step explanation:

Answer:

x = 240 feet

Step-by-step explanation:

It is given that,

The angle of depression is 30 degrees from the bottom of the boat to a  deep sea diver at the depth of 120 ft.

We need to find the distance x the diver must  swim up to the boat. It can be calculate by applying trigonometry as follows :

[tex]\sin30=\dfrac{120}{x}\\\\x=\dfrac{120}{\sin30}\\\\x=240\ \text{feet}[/tex]

So, the distance the diver must swim up to the boat is 240 feet.

Answer:

+) m∠1 = m∠2 (vertical angles theorem)

+) m∠2 and ∠3 are supplementary (because a//b)

+)m∠3 = m∠4 (alternate interior angles theorem, c//d)

=> ∠1 and ∠4 are supplementary (substitution property of equality)

Step-by-step explanation:

Answer:

8

Step-by-step explanation:2 times 2 times 2

Answer:

1 gallon of gas is $2.75

Step-by-step explanation:

becuase 22 divided by 8 (since they put 8 gallons in) = 2.75

Answer:

2.75

Step-by-step explanation: