100 Points

Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x, with initial condition y(1) = 1.

Answer:

all real numbers.

Step-by-step explanation:

9x - 8y = 1

18x - 16y = 2

if you look at the first equation, you can figure out what y equals.

9x - 8y = 1

add 8y to both sides

9x = 1 + 8y

subtract 1 from both sides

9x - 1 = 8y

divide both sides by 8

[tex]\frac{9x - 1}{8}[/tex] = y

now, substitute y in the second equation.

18x - 16y = 2

18x - 16([tex]\frac{9x - 1}{8}[/tex]) = 2

18x - 2(9x - 1) = 2

18x - 18x +2 = 2

2 = 2

the answer is all real numbers, because regardless of what x equals, 2 will always equal 2.

Answer:

y equals to x plus 9

Step-by-step explanation:

-x+y=9

so, y=x+9

Answer:11/c

Step-by-step explanation:

Answer:

  B.  (3, –1)

Step-by-step explanation:

Reflection in the line y=-x is described by the transformation ...

  (x, y) ⇒ (-y, -x)

Then the point of interest becomes ...

  F(1, -3) ⇒ F'(3, -1) . . . . matches choice B

Answer:

The correct answer is B

Step-by-step explanation:

This is correct because it is correct

20 - (+7) + - (6)

Answer: 7

Answer:

Answer is 7

20-(+7)+(-6)= ?

(20-7)-6

13-6

7

Answer:

25

Step-by-step explanation:

Answer:

6 gallons of 10% ethanol gas and 3 gallons of the E70 fuel.

Step-by-step explanation:

Let the volume of 10% ethanol gas be x gallons and the volume of 70% be y gallons.

The resulting mixture ( 9 gallons) must have a strength of 30% ethanol.

SO WE HAVE THE SYSTEM:

x + y = 9

0.10x + 0.70y = 0.30 * 9

0.10x + 0.70y = 2.7

Multiplying the first equation by -0.10:

-0.10x - 0.10y = -0.9

Adding the last 2 equations:

0 + 0.60y = 1.8

y = 1.8 / 0.6 = 3 gallons.

So x = 9 - 3 = 6 gallons.

6 gallons of 10% ethanol gas and 3 gallons of the E70 fuel.

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.

Let the volume of 10% ethanol gas be x gallons and the volume of 70% be y gallons.

The resulting mixture ( 9 gallons) must have a strength of 30% ethanol.

x + y = 9

0.10x + 0.70y = 0.30 * 9

0.10x + 0.70y = 2.7

Multiplying the first equation by -0.10:

-0.10x - 0.10y = -0.9

Adding the last 2 equations:

0 + 0.60y = 1.8

y = 1.8 / 0.6 = 3 gallons.

So x = 9 - 3 = 6 gallons.

To know more about an expression follow

https://brainly.com/question/17277463

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Answer:

63 units^2

Step-by-step explanation:

the area of the rectangle is 48 units^2

l*h=a

6*8=a

48=a

The area of the triangle is  15 units^2

b*h/2=a

6*5/2=a

30/2=a

15=a

Let me know if you have any further questions, hope this helped!

9514 1404 393

Answer:

  18 weeks

Step-by-step explanation:

We are given the (time, population) pairs (0, 5) and (7, 47). With these values, we can use the two-point form of the equation of a line to write the equation of the linear model.

  p = (p2 -p1)/(t2 -t1)(t -t1) +p1

  p = (47 -5)/(7 -0)(t -0) +5

  p = 6t +5 . . . . . the linear model matching the given points.

For p = 113, the time (number of weeks) is ...

  113 = 6t +5

  108 = 6t . . . . . . subtract 5

  18 = t . . . . . . . . . divide by 6

After 18 weeks, the beetle population will reach 113.

Answer:

Step-by-step explanation:

3.9

Replace y(x) with 4:

4 = 4x

Divide both sides by 4:

x = 1

Answer:

9. is true

10. is false

hope this helps

Step-by-step explanation:

Step-by-step explanation:

9 is true and 10 is true as well

Step-by-step explanation:

8 cups total a day

1 bottle holds 2 cups (Celeste drinks 4 bottles a day = 8 cups) 

If she drank 1.5 bottles already, she needs to drink 2.5 bottles 

Let x be the number of bottles she needs to drink to have at least 8 cups 

The inequality is x >= 2.5 bottles

Answer:

$17

Step-by-step explanation:

So first

The total money John have is $20

then he earned $5 which means $20+$5 = $25

After that he spent $10 = $25- $10 = $15

Again earned $5 = $15+$5=$20

At last spent $3 = $20-$3=$17

Hence the total money he owe or have left is $17

Answer:

7/12ths

Step-by-step explanation:

2/3rds of the way full would be 8/12. Since she started at 1/12th of a tank, 7/12ths was added. (:

Answer:

24

Step-by-step explanation:

area of a triangle = 1/2 ( base length * height )

given base length : 6

given height : 8

area of triangle = 1/2(8*6)

==> multiply 8 and 6

area of triangle = 1/2(48)

==> multiply 1/2 and 48

area of triangle = 24 square units

Answer:

26 inches

Step-by-step explanation:

You need to add 3+5+7+7+4= 26 because you need to find the area of the figure which the inches are area to add and get how many inches in the figure. Sorry if you don't get it but the answer is 26 inches.

Answer:

h =12

Step-by-step explanation:

[tex]In\: \triangle ABC, \: \angle ABC = 90\degree \: \&\:\\ BD\perp AC[/tex]

Therefore, by geometric mean property:

[tex]BD = \sqrt {AD\times CD} \\

h = \sqrt {(AC-CD) \times CD} \\

h = \sqrt {(25-16) \times 16} \\

h = \sqrt {9 \times 16} \\

h = \sqrt {144} \\

\huge \red {\boxed {h = 12}} \\

[/tex]

Answer:

Step-by-step explanation:

12

To find the slope, we must know the equation

 --> [tex]slope = \frac{y2-y1}{x2-x1}\\[/tex]

Now using the information given, (-2,1) and (2,6), let's plug that into the equation

--> [tex]slope = \frac{6-1}{2--2} = \frac{5}{4}[/tex]

In this case, the slope is 5/4

Hope that helped!

Answer:

[tex]\rn\hookrightarrow 5/4[/tex]

Step-by-step explanation:

[tex]Solution,\\\\Let,\\(x_1,y_1)=(-2,1)\\\\(x_2,y_2)=(2,6)\\\\Now,\\\\\rn\hookrightarrow Slope=\frac{y_2-y_1}{x_2-x_1}\\\\\rn\hookrightarrow Slope=\frac{6-1}{2-(-2)} \\\\\rn\hookrightarrow Slope=\frac{5}{4}[/tex]

Answer:

I need to know the equation, but if you have to cube them then you will find your answer right away if you google how to cube numbers.

Step-by-step explanation:

Sorry for the bad answer.

[tex]Your answer it W^2 = 1024/4 = 256.[/tex]

Step-by-step explanation:

Answer:

y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

Step-by-step explanation:

Solve 2 x + y(x) + (dy(x))/(dx) (x - 2 y(x)) = 0:

Let P(x, y) = 2 x + y and Q(x, y) = x - 2 y.

This is an exact equation, because (dP(x, y))/(dy) = 1 = (dQ(x, y))/(dx).

Define f(x, y) such that (df(x, y))/(dx) = P(x, y) and (df(x, y))/(dy) = Q(x, y).

Then, the solution will be given by f(x, y) = c_1, where c_1 is an arbitrary constant.

Integrate (df(x, y))/(dx) with respect to x in order to find f(x, y):

f(x, y) = integral(2 x + y) dx = x^2 + x y + g(y) where g(y) is an arbitrary function of y.

Differentiate f(x, y) with respect to y in order to find g(y):

(df(x, y))/(dy) = d/(dy) (x^2 + y x + g(y)) = x + (dg(y))/(dy)

Substitute into (df(x, y))/(dy) = Q(x, y):

x + (dg(y))/(dy) = x - 2 y

Solve for (dg(y))/(dy):

(dg(y))/(dy) = -2 y

Integrate (dg(y))/(dy) with respect to y:

g(y) = integral-2 y dy = -y^2

Substitute g(y) into f(x, y):

f(x, y) = x^2 - y^2 + y x

The solution is f(x, y) = c_1:

x^2 - y^2 + y x = c_1

Solve for y:

y(x) = 1/2 (x - sqrt(5 x^2 - 4 c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 - 4 c_1))

Simplify the arbitrary constants:

Answer:  y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

Answer:

Step-by-step explanation:

The fraction will represent the number of shaded squares over the total number of squares. You have correctly identified it as 98/100. That fraction can be reduced, if you like, to 49/50.

The pronunciation of your fraction is "ninety-eight hundredths." The decimal number with that same pronunciation is 0.98.

The symbol % and the symbol /100 have identical meaning. This makes them essentially interchangeable.

  98/100 = 98%

Your numbers are ...

  98/100 (or 49/50), 0.98, and 98%.

_____

Additional comment

We have shown you that % is a shorthand way to write /100. There is another similar symbol: ‰ is shorthand for /1000.

1/100 is one percent. 1/1000 is one mil.

Answer:

xy=6

Step-by-step explanation:

sin θ= opposite side÷ hypotenuse

sin 30°= xy÷12

sin 30°=1/2

Therefore,

1/2=xy÷12

1/2×12=xy

xy=6

Answer:

4 1/3 feet

Step-by-step explanation:

11 3/8 - 3 1/8 = 8 2/3

8 2/3 / 2 = 4 1/3