need help really bad​

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

Answer: 66ft

Step-by-step explanation:

A=1/2bh

462=1/2(14)(h)

462=7h

66=h

Answer:

A, D and F are the answers because for the 1st question, 64.7 is the bigger number, for the second 65 is the biggest and for the last 65 is the largest number.

Answer:

0.769296

Step-by-step explanation:

The desired probability can be calculated from binomial probability distribution because there are 21 independent trials and probability of success(saving nothing for retirement) 0.2 remains same for each trial. Here, n=21 and p=0.20. We want to compute P(X>5).

The pdf of binomial distribution is

P(X=x)=nCx(p)^x(1-p)^(n-x)

P(X>5)=1-P(X≤5)

P(X≤5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X=0)=21C0*(0.2)^0*(1-0.2)^(21-0)=0.009223

P(X=1)=21C1*(0.2)^1*(1-0.2)^(21-1)=0.048423

P(X=2)=21C2*(0.2)^2*(1-0.2)^(21-2)=0.121057

P(X=3)=21C3*(0.2)^3*(1-0.2)^(21-3)=0.191673

P(X=4)=21C4*(0.2)^4*(1-0.2)^(21-4)=0.215632

P(X=5)=21C5*(0.2)^5*(1-0.2)^(21-5)=0.183287

P(X≤5)=0.009223+0.048423+0.121057+0.191673+0.215632+0.183287

P(X≤5)=0.769296

P(X≤5) can also be computed by using excel function BINOM.DIST(5,21,0.2,TRUE) which results in

P(X≤5)=0.769296.

The probability that more than five of the selected adults save nothing for retirement is; P(X > 5) = 0.239928

We are told that 20% of adults in the US save nothing for retirement. Thus;

p = 20% = 0.2

21 adults are selected randomly. Thus;

n = 21

Probability that more than five of the selected adults save for retirement is gotten from formula for binomial probability distribution which is;

P(X = x) = nCx × p^(x) × (1 - p)^(n - x)

Thus;

P(X > 5) = 1 - P(X ≤ 5)

Where;

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X = 0) = 21C0 × 0.2^(0) × (1 - 0.2)^(21 - 0) =

0.009223

Using online binomial probability calculator, we can find the remaining as;

P(X = 1) = 0.048423

P(X = 2) = 0.121057

P(X = 3) = 0.191673

P(X = 4) = 0.215632

P(X = 5) = 0.183287

Thus;

P(X ≤ 5) = 0.048423 + 0.121057 + 0.191673 + 0.215632 + 0.183287

P(X ≤ 5) = 0.760072

Thus;

P(X > 5) = 1 - 0.760072

P(X > 5) = 0.239928

Read more about binomial probability distribution at; https://brainly.com/question/24239758

false false false false false

Answer:

no the first on is true and the last one is false

Step-by-step explanation:

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (Eq. 1)

Where:

[tex]A[/tex] - Area of the triangle, measured in square centimeters.

[tex]b[/tex] - Base of the triangle, measured in centimeters.

[tex]h[/tex] - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

[tex]\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}[/tex] (Eq. 2)

Where:

[tex]\frac{dA}{dt}[/tex] - Rate of change of area in time, measured in square centimeters per minute.

[tex]\frac{db}{dt}[/tex] - Rate of change of base in time, measured in centimeters per minute.

[tex]\frac{dh}{dt}[/tex] - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

[tex]\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}[/tex]

[tex]\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}[/tex] (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

[tex]b = \frac{2\cdot A}{h}[/tex]

If we know that [tex]A = 130\,cm^{2}[/tex], [tex]h = 15\,cm[/tex], [tex]\frac{dh}{dt} = 2.5\,\frac{cm}{min}[/tex] and [tex]\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}[/tex], the rate of change of the base of the triangle in time is:

[tex]b = \frac{2\cdot (130\,cm^{2})}{15\,cm}[/tex]

[tex]b = 17.333\,cm[/tex]

[tex]\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)[/tex]

[tex]\frac{db}{dt} = -2.262\,\frac{cm}{min}[/tex]

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Answer: Its remainder is 1 when you divide 17 by 2.

In other words, 17/2 = 8 remainder 1.

The 8 is the quotient.

The reason why we know we get a remainder 1 is because the condition of "if n is an odd number" and here n = 17 is odd. So the first condition is met allowing us to use the full "if, then" statement given to us.

Answer:

100

Step-by-step explanation:

Answer:

4 in one set

Step-by-step explanation:

So if 24%6= 4

Answer:

11 words

Step-by-step explanation:

The question is poorly formatted.

The right relationship between M and t is given as:

M = −0.001t³ + 0.1t²

Required

Solve for M when t = 10

To do this, substitute 10 for t

So,we have:

M = −0.001t³ + 0.1t²

M = -0.001 * 10³ + 0.1 * 10²

M = -0.001 * 1000 + 0.1 *100

M = 1 + 10

M = 11

11 words in 10 minutes

Answer:

16

Step-by-step explanation:

192/12=16

hope this helps :3

if it did pls mark brainliest

Answer:16

192/12 equals 16

Answer:

same side interior for 2 and 6 i think

Answer:

m= -90 is your answer

Step-by-step explanation:

For future reference, you should try using Symbolab, it works really well and I use it ALL the time!

Answer: $50, The account will have $50 in interest after 2 years.

Step-by-step explanation:

2.5% / 100 = 0.025

$1,000 * .025 = 25

25 * 2 = 50

Answer:

d

Step-by-step explanation:

i looked it up

Answer:

a. is 2/21 hours to complete one task

b. is 10 1/2 tasks in one hour

Robot takes 2/21 hour to complete the task.

In one hour, robot complete 21/2 task.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Time taken to complete 7 tasks = 2/3 hours.

To find the time taken to complete one task and tasks that completed in one hour,

Use ratio method,

7 tasks take = 2/3 hours

1 task takes = 2/(3 x 7) = 2 / 21 hours.

In 2/3 hours = 7 tasks completed,

1 hour = 21/2 tasks.

In one hour, 21/2 tasks can be completed.

To know more about Ratio on:

https://brainly.com/question/23724140

#SPJ5

Answer:

D.) x²-10x+25 sq. units

Step-by-step explanation:

The question is not properly written. The question should have been:

If each side of a square is (x-5) units, which expression can be used to represent the area of the square.

Area of a square = L² where:

L is the length of the square

Given

L = x-5

Required

Area of the square

Substitute the given function into the formula to get the required as shown:

Area of the square = (x-5)²

Expand

A(x) = (x-5)(x-5)

A(x) = x(x)-5x-5x-5(-5)

A(x) = x²-10x-25

Hence the area of the square is (x²-10x+25)sq. units. Option D is correct.

Answer:

1) graph b

2)appears to decrease more

Step-by-step explanation:

Answer:

D: A rhombus is always a parallelogram

Step-by-step explanation:

A rhombus is a quadrilateral, and it is also a parallelogram. However, a parallelogram is not always a rhombus.

Answer:

A rhombus is always a parallelogram

Step-by-step explanation:

it's lines parallel to the other side

Answer:

x=2

Step-by-step explanation:

Answer:

-157

Step-by-step explanation:

Answer:  -162

Hope this helps you

Step-by-step explanation:

subtract and add

Answer:

x=19

Step-by-step explanation:

8(3x-2)-8x=9(2x-6) Distribute.

24x-16-8x=18x-54   Combine like terms.

16x-16=18x-54         Subtract 16x from both sides (getting rid of a variable first  

-16x     -16x               is easier).

-16=2x-54                 Add 54 to both sides.

+54    +54

38=2x                       Divide both sides by 2.

/2   /2

19=x

Hope this helps!! Have a great day ^^

Answer:

AB, BC, AC

Step-by-step explanation:

Hopefully I helped!! :)

Answer: -4 x 16, -48

Step-by-step explanation:

word phrase: -4 x 16

symplified = -48

product means multiply

Answer:

Vertices A B y C

A ( 2 , 3 )    B ( -1 , 1 )  C ( 3, 1 )

Step-by-step explanation:

We have to solve a two-equation system, by pair of equations as follows

equation (1)   2x - 3y + 5 = 0

equation (2)  2x + y -7    = 0

Solving this system we find let´s say vertex A

0x - 4y +12 = 0      y = 3

Then x ?

2x - 3y + 5 = 0

2x - 9 + 5 = 0     ⇒ 2x = 4     x = 2

Then vertex A ( 2 , 3 )

From equation (1) and (3)

2x - 3y + 5 = 0

2x + 5y - 3 = 0

Agan subtracting (1) - (2)

0x -8y + 8 = 0

y = 1    and      

2x + 5y = 3

2x + 5 = 3

2x = -2

x = -1

Vertex B ( -1 , 1 )

Finally from equation (2) and (3) we get the third vertex C

2x + y - 7 = 0

2x + 5y - 3 = 0

0x -4y -4 = 0

y = 1

2x + y = 7

2x + 1 = 7

2x = 6

x = 3

C ( 3 , 1 )

Answer: 0.2254

Step-by-step explanation:

Let E= Event of getting of female lives in a dorm.

F = Event of getting of female lives in a 'Other'.

From the table , n(E) = 276  and n(F) = 99

and n(E∩F) = 0  [E and F are Mutually exclusive]

Now, n(E∪F)=  n(E) + n(F) - n(E∩F)

= 276+99-0

= 375

also, n(S) =1664       (Sample size)

Required probability : [tex]P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}[/tex]

[tex]=\dfrac{375}{1664}\approx0.2254[/tex]

Hence, the  probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254

Answer:

-2.4 meters

Step-by-step explanation:

-86 + 83.6 = -2.4

You need 6 cups red and 10 cups yellow.

Answer:

0.6 + 0.08

Step-by-step explanation: