Find two consecutive integers whose product is 12 more than the square of the smaller
number.

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]

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Answer: I think it’s J, because the picture is also holding the smallest finger up (the pinky) and the rest of the fingers are folded inside the palm of the hand and the thumb is folded over them, I hope this helps!!

Step-by-step explanation:

The letter J is a counter example. Option a is correct.

Letters of alphabet to be determine.

Alphabets are the sets of letters from A to Z.

Here, the little finger is up and all the finger is folded and the thumb folded over the three finger implies its 'J'.

Thus, the letter J is a counter example.

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Answer: -4 x 16, -48

Step-by-step explanation:

word phrase: -4 x 16

symplified = -48

product means multiply

Answer/Step-by-step explanation:

Given:

m<3 = 54°

m<2 = right angle

a. m<1 + m<2 + m<3 = 180° (angles in a straight line)

m<1 + 90° + 54° = 180° (substitution)

m<1 + 144° = 180°

m<1 = 180° - 144°

m<1 = 36°

b. m<2 = 90° (right angle)

c. m<4 = m<1 (vertical angles)

m<4 = 36° (substitution)

d. m<5 = m<2 (vertical angles)

m<5 = 90°

e. m<6 = m<3 (vertical angles)

m<6 = 54°

f. m<7 + m<6 = 180° (same side interior angles)

m<7 + 54° = 180° (substitution)

m<7 = 180 - 54

m<7 = 126°

g. m<8 = m<6 (alternate interior angles are congruent)

m<8 = 54°

h. m<9 = m<7 (vertical angles)

m<9 = 126°

i. m<10 = m<8 (vertical angles)

m<10 = 54°

j. m<11 = m<4 (alternate interior angles are congruent)

m<11 = 36° (substitution)

k. m<12 + m<11 = 180° (linear pair)

m<12 + 36° = 180° (substitution)

m<12 = 180° - 36°

m<12 = 144°

l. m<13 = m<11 (vertical angles)

m<13 = 36°

m. m<14 = m<12 (vertical angles)

m<14 = 144° (substitution)

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the smaller number. Then the sum of squares is ...

  x² +(x+2)² = 14

  2x² +4x +4 = 14 . . . eliminate parentheses

  2x² +4x -10 = 0 . . . put in standard form

  x² +2x -5 = 0 . . . . . divide by 2 (because we can)

  (x +1)² -6 = 0 . . . . . complete the square

  x +1 = √6  . . .   we want the positive root

  x = -1 +√6

  x+2 = 1 +√6

The numbers are √6±1.

Answer:

Yes: Ramya's grade increased by two points

No: the difference between Escher's highest score and two

Yes: the number of chapters Wally read plus two more

No: O two fewer than the maximum number of absences Ellie is allowed

Yes: two added to Allison's age.

Yes: the sum of Mikel's height and two

Step-by-step explanation:

If it says yes, it is because it was adding 2. If it says no, it was either subtracting 2 or any other form of math other than adding 2.

Answer:

A,C,E,F

Step-by-step explanation:

Just shortening it up! The person above me is correct, though. Don't forget to make them brainliest (if you want to of course)! Major Big brain moment... lol!

Answer answered by Jordan

Stay Safe <3

↖(^ω^)↗

Answer:

1) graph b

2)appears to decrease more

Step-by-step explanation:

Answer: 66ft

Step-by-step explanation:

A=1/2bh

462=1/2(14)(h)

462=7h

66=h

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:

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.

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Answer:

100

Step-by-step explanation:

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:

k = K^2

Step-by-step explanation:

Subtract  K^2 from both sides of the equation.

Answer:

no they share the same y value for two different x values

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:

I need these answers and the ones he put in in the comments are all wrong

Answer:

1 5 10 10 5 1

Step-by-step explanation:

The complete question has been attached as an image.

Looking at the triangle, we see a pattern. The first level we have 1, in the next level we have 1 1, the next evel we have 1 2 1, the next level we have 1 3 3 1 and so on. From here, we see that to get the numbers of the next level, we have to write 1 as the first number, then add 1 to the next number after it in the previous level to get the second number in the next level then add the second number of the previous level to the next number beside it to get the third number in the next level and so on until you get to the last number before 1 in the previous level, add that number to 1 to get the second to the last number in the next level and finally put 1 as the last number in the next level. Now, we have

1 4 6 4 1

1 5 10 10 5 1

And that is the required set of numbers.

Answer:

y=5

x=10 and

z=2

Step-by-step explanation:

since they are equivalance then,

for

triangle ABC and triangle DFE

AB=DF,BC=FE and AC= DE

So, AB=DF

8y-20= 4y

or, y=5

Then, BC= FE

2x+5=x+15

or, x=10

and

AC=DE

3z+9=10z-5

or, z= 2

hope u got ut.

The triangles are parallel thus their sides are equal to each other peer to peer.

So ;

[tex]x + 15 = 2x + 5[/tex]

Subtract sides -5

[tex]x + 15 - 5 = 2x + 5 - 5[/tex]

[tex]x + 10 = 2x[/tex]

Subtract sides -x

[tex]x - x + 10 = 2x - x[/tex]

[tex]x = 10[/tex]

_________________________________

[tex]4y = 8y - 20[/tex]

Subtract sides -8y

[tex]4y - 8y = 8y - 8y - 20[/tex]

[tex] - 4y = - 20[/tex]

Negatives simplifies

[tex]4y = 20[/tex]

Divided sides by 4

[tex] \frac{4}{4}y = \frac{20}{4} \\ [/tex]

[tex]y = 5[/tex]

_________________________________

[tex]10z - 5 = 3z + 9[/tex]

Plus sides 5

[tex]10z - 5 + 5 = 3z + 9 + 5[/tex]

[tex]10z = 3z + 14[/tex]

Subtract sides -3z

[tex]10z - 3z = 3z - 3z + 14[/tex]

[tex]7z = 14[/tex]

Divided sides by 7

[tex] \frac{7}{7}z = \frac{14}{7} \\ [/tex]

[tex]z = 2[/tex]

_________________________________

And we're done....♥️♥️♥️♥️♥️

Answer:

n = 70

Step-by-step explanation:

-8 + n = 62

      n = 70

Answer:

17

Step-by-step explanation:

d = √( (x₂ - x₁)² + (y₂ - y₁)² )

   = √( (14 - 6)² + (19 - 4)² )

   = √( 8² + 15² )

   = √( 64 + 225 )

   =  [tex]\sqrt{289}[/tex]

   = 17

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:

Step-by-step explanation:

E = 10:15 C = 4:5 F = 1:10 D = 1:2 R = 1:3 I = 30: 80 G = 16:48  N = 20: 40

A = 2:1 T = 6:10 S= 9:12 H = 9 O = 1: 11

(wouldve explained them but im in class :)

false false false false false

Answer:

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

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

Answer:

[tex]Probability = 0.023[/tex]

Step-by-step explanation:

Given

Represent the given probability with P(Gene)

[tex]P(Gene) = 39\%[/tex]

[tex]Children = 4[/tex]

Since all 4 children get the disease, the required probability is calculated as thus:

[tex]Probability = P(Gene)^4[/tex]

[tex]Probability = 39\%^4[/tex]

Convert % to decimal

[tex]Probability = 0.39^4[/tex]

[tex]Probability = 0.02313441[/tex]

[tex]Probability = 0.023[/tex] Approximated

Answer:

d

Step-by-step explanation:

i looked it up