Determine which function is a solution to the differential equation xy ' + 2y = 0.

e^2x
x^2
x^-2
None of these

Thus far, I have ruled out option a.

Thank you!

Answers

Answer 1

Answer:

x⁻²

Step-by-step explanation:

If y = e²ˣ, y' = 2e²ˣ.

2xe²ˣ + 2e²ˣ ≠ 0

If y = x², y' = 2x.

2x² + 2x² ≠ 0

If y = x⁻², y' = -2x⁻³.

-2x⁻² + 2x⁻² = 0

Answer 2

The x^-2 function is a solution to the differential equation

[tex]xy ' + 2y = 0.[/tex]

We have given,

The differential equation[tex]xy ' + 2y = 0.[/tex]

What is the differential equation?

A differential equation is an equation with one or more derivatives of a function. The derivative of the function is given by dy/dx.

If [tex]y = e^{2x}, y' = 2e^{2x}.[/tex]

[tex]2xe^2x + 2e^2x[/tex]≠0

If [tex]y = x^2, y' = 2x.[/tex]

[tex]2x^2 + 2x^2[/tex]≠0

If[tex]y = x^-2, y' = -2x^-3.[/tex]

[tex]-2x^-2 + 2x^-2= 0[/tex]

Therefore, the x^-2 function is a solution to the differential equation

[tex]xy ' + 2y = 0.[/tex]

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Related Questions

Pleaaaase hellp me will mark u brainly for both answers!!!
Thank u if u do really appreciate it.

Answers

Answer:

1. Option A is correct (A = length x width)

2. Option B is correct ( A = base x height/2)

Hope this helps

:)

Please answer.....................................

Answers

Answer:

1.25 + r = 4

1.25 - 1.25 + r = 4 - 1.25

r = 2.75

first option is the answer

Step-by-step explanation:

1. subtract 1.25 from both sides

Idk what it is plz help me

Answers

Answer:

1) Starting height is 6.25

2) after 20 years it would be 30

1.25(20)=25+5=30

3) 76 years

Answer:

a) 5 feet

b) 30 feet

c) 76 years

Step-by-step explanation:

a) 5 feet. If t is 0, it'll still be 5 feet

b) 30 feet

1.25*20+5=

25+5=

30

c) 76 years

100 = 1.25t+5

1.25t=95

t=76

pls help asappp you will get brainliest

Answers

Answer:

32 units.

Step-by-step explanation:

look up a picture of a 306090 triangle, it will make sense :)

Answer:

32

Step-by-step explanation:

cos 30 = [tex]\frac{\sqrt{3} }{2}[/tex]

[tex]\frac{\sqrt{3} }{2}[/tex] = 16[tex]\sqrt{3}[/tex] / n

n = 16[tex]\sqrt{3}[/tex] * [tex]\frac{2}\sqrt{3} }[/tex]

n = 32 units

A soda manufacturer knows that sales of soda increase during the summer. To make sure that they get a large portion of the sales, they decide to offer a contest throughout the spring. The contest is pretty simple: when you open your bottle of soda, if it says, “You win!” under the cap, you get another bottle of their soda for free. The chance of winning a free soda is 1 in 12. Lucky Lucy bought five sodas and won a free one with four of the caps. What’s the probability of that happening? Theoretically, how many sodas would you have to buy before having a greater than 50% chance of winning a free soda?

Answers

Answer:

a.) Probability = 1/5

b.) 10 soda

Step-by-step explanation:

Probability is a game of chance.

The initial chance = 1/12

If Lucky Lucy bought five sodas and won a free one with four of the caps. The probability of that happening will be 1/5

Having a greater than 50% chance of winning a free soda means having probability greater than half. That is,

Probability > 1/2

You would have to buy (12 - 2) soda. Which is equal to 10.

Use a proportion to convert 32 fluid ounces to cups. [Hint: Use the conversion factor 8 fl oz = 1 c.]

Answers

Answer:

4 cups

Step-by-step explanation:

in order to convert 32 ounces into cups, you must divide 32 by 8. this will give you 4, your answer.

If this helps, please mark me brainliest. :)

Answer:

4 cups

Step-by-step explanation:

32/x = 8/1

8x = 32

x = 4

Rhonda used unit cubes to make a rectangular prism. What is the volume of the prism? Prism with length as 7 unit cubes, height as 3 unit cubes and width as 2 unit cubes. A. 14 cubic units B. 21 cubic units C. 42 cubic units D. 63 cubic units

Answers

Answer:

42 cubic units

Step-by-step explanation:

A rectangle prism formula is V = l x h x w.

The length is 7

The height is 3

The width is 2

Then multiply 7, 3, and 2 together (7 x 3 x 2) = 42

The volume of the Rhonda rectangular prism will be 42 cubic units thus option (C) is correct.

What is volume?

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

The volume of the rectangular prism is given as,

V = length × height × width

Put length as 7 unit cubes, height as 3 unit cubes, and width as 2 unit cubes.

V = 7 x 3 x 2 = 42 units³.

Hence "The Rhonda rectangular prism will have a volume of 42 cubic units".

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Write in point-slope form an equation of the line that passes through the point
(3,−5) with slope -4

Answers

A horizontal line through y=−53. Explanation: Write the equation in the form y=mx+c because then we can read off the slope and the y-intercept ...

Answer:

Step-by-step explanation:

does anyone know the answer to this ?please

Answers

Answer:B

Step-by-step explanation:

Would a piece of wood with a mass of 48 grams and a volume of 47.4 cm^3 float in water?

Answers

The piece of wood would sink.

Given that water has a density of 1 g/cm^3 the piece of wood would have to be lower than such density. A bigger density would then mean said object would sink.

To find the density of the piece of wood you need to know the density formula which is d= m/v, m being mass and v being volume. With the givens of mass and volume you just need to plug your values in to get 48/47.4=d. Dividing would then equate to about 1.02, which exceeds the density of water, therefore sinking.

An easy way to find the answer to this is if you see that the volume is greater than the mass then it will float, if less then it will sink. If they are the same number then you can suggest that it depends on the water’s buoyancy.

The piece of wood would sink if a piece of wood with a mass of 48 grams and a volume of 47.4 cubic cm, and a density is 1 g/cm³.

What is density?

It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.

We have:

Mass of the piece of wood = 48 grams

The volume of the piece of wood = 47.4 cubic cm

As we know, from the definition of density, density is the mass-to-volume ratio.

d = mass/volume

d = 48/47.4

d = 1.01 g/cm³ ≈ 1 g/cm³

As we know,

It will float if the volume is larger than the mass and sink if the reverse is true.

Thus, the piece of wood would sink if a piece of wood with a mass of 48 grams and a volume of 47.4 cubic cm, and a density is 1 g/cm³.

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Mariam bought 8 gallon of gas for $31.12. How much would she pay for 11
gallons of gas at this same rate?

Answers

Answer:

$42.79

Step-by-step explanation:

Divide $31.12 by 8 to get how much money you pay for 1 gallon and multiply it by 11 to get how much to pay for 11 gallons.

Zugo delivers muffins for the Pastry-and-Muffin company. Each muffin is packed in its own
little box. An individual muffin box has the shape of a cube, measuring three inches on
each side. Zugo packs the individual muffin boxes into a larger box. The larger box is also
in the shape of a cube, measuring two feet on each side. How many of the individual
muffin boxes can fit into the larger box?

Answers

Answer:

  512

Step-by-step explanation:

You can figure this a couple of ways.

1) Figure the number of muffin boxes that goes into each dimension of the larger box:

  (2 ft)/(3 in) = (24 in)/(3 in) = 8 . . . . muffin boxes in each direction.

Then the total number of muffin boxes that will fit in a larger box is ...

  8×8×8 = 512

512 muffin boxes can fit into the larger box.

__

2) The volume of a muffin box in cubic feet is ...

  ((3 in)/(12 in/ft))^3 = (1/4 ft)^3 = 1/64 ft^3

The volume of a larger box in cubic feet is ...

  (2 ft)^3 = 8 ft^3

Then the number of smaller boxes that will fit in the larger box is ...

  (8 ft^3)/(1/64 ft^3) = 8×64 = 512

512 muffin boxes can fit into the larger box.

I need help with this, I don't understand how to do this.

Answers

Simple..A cyrcle first of all is a 360 degree angle...as a result

X=360-115-105-60

X=80 degrees

A rectangular playground is 10m longer than it is wide.The area of the playground is 1400m² Calculate the width and length of the playground. solve using quadratic formula please?

Answers

Answer:

[tex] 1400 = x(x+10)= x^2 +10x[/tex]

We can rewrite this expression like this:

[tex] x^2 +10 x -1400 =0[/tex]

And we can use the quadratic formula given by:

[tex] x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where [tex] a =1 , b=10 , c= -1400[/tex]

And replacing we got:

[tex] x = \frac{-10 \pm \sqrt{10^2 -4(10)(-1400)}}{2*1}[/tex]

And solving we got:

[tex] x_1 =32.75 , x_2 = -42.75[/tex]

And since the value can't be negative the answer would be x = 32.75 and the value of y = 32.75+10 =42.75

Step-by-step explanation:

For this case we know that we have a rectangular playground and the area can be founded with this formula:

[tex] A = xy[/tex]

Where x represent the width and y the length. From the problem we know that A =1400 m^2 and the heigth is 10m longer than the wide so we can write this condition as:

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

And replacing this formula into the area we got:

[tex] 1400 = x(x+10)= x^2 +10x[/tex]

We can rewrite this expression like this:

[tex] x^2 +10 x -1400 =0[/tex]

And we can use the quadratic formula given by:

[tex] x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where [tex] a =1 , b=10 , c= -1400[/tex]

And replacing we got:

[tex] x = \frac{-10 \pm \sqrt{10^2 -4(10)(-1400)}}{2*1}[/tex]

And solving we got:

[tex] x_1 =32.75 , x_2 = -42.75[/tex]

And since the value can't be negative the answer would be x = 32.75 and the value of y = 32.75+10 =42.75

Answer:

Step-by-step explanation:

Given Data:

Area = 1400m²

L = 4+w

W= w

Area = L * W

1400 = ( 4+W) W ²

1400 = 4w + w ²

w ² + 4w - 1400 = 0

- b ± √ b ² - 4ac / 2a

Where;

a = 1

b = 4

c = -1400

- 4 ± √4² - 4(1)(-1400) / 2(1)

= - 4 ± 74.94 /2

= - 4 + 74.94 / 2 or - 4 - 74.94 / 2

= 35.47 or - 39.47

Solve the long division

Answers

Answer:

1. 158

2. 120.125

3. 148.6

4. 158.6

Step-by-step explanation:

You divide the number inside by the number outside

Someone be a homie cause I’m really tryin on this math shi thank youuuu

Answers

Answer:

The area of the shaded region is equal to difference of the sector contains that shaded region and the triangle.

The area of sector:

A_S = pi x radius^2 x 123/360

       = pi x 18.6^2 x 123/360

       = 371.346 (m2)

The area of triangle:

A_T = base x height x (1/2)

       = (18.6 x sin(123/2) x 2) x (18.6 x cos(123/2)) x (1/2)

       = 145.073 (m2)

=> Area of shaded region:

A = 371.346 - 145.073 = 226.273 = ~226.3 (m2)

Hope this helps!

:)

Answer:

First give me points and make me winner, then we can discuss the answer.

Step-by-step explanation:

y−5/3 = 4/5

HELP ME!!

Answers

Answer:

Y=37/15

Step-by-step explanation:

Y=5/3+4/5

Y=(25+12)/15

Y=37/15

Hope you understand

Circle $A$ has a diameter of 12 inches and circle $B$ has a diameter of 22 inches. What is the ratio of the area of circle $A$ to the area of circle $B$? Express your answer as a common fraction.

Answers

Answer:

36/121

Step-by-step explanation:

The other person is wrong, don't listen to him. I have done this problem before.

What are the solutions of the quadratic equation? x^2-9x+18=0

Answers

Answer:

x=6   x=3

Step-by-step explanation:

x^2-9x+18=0

Factor

What 2 numbers multiply to 18 and add to -9

-6*-3 = 18

-6-3 = -9

(x-6) (x-3) =0

Using the zero product property

x-6 =0  x-3 =0

x=6   x=3

If I have a package deal if $80 what is the shipping price? PLEASE HELP

Answers

17 dollar and 54 cents

How do you remove all perfect squares from inside the square root - 108

Answers

Answer:

6dquare 2

Step-by-step explanation:

The square root of 108 in radical form is 6√(3). In general, to find √(a) in radical form, when a is not a perfect square, we use the.

what is 2/3 ÷ 4/5 = ?

Answers

Answer:

this is the answer:5/6.

Answer:

= 5/6

Step-by-step explanation:

2/6 ÷ 4/5

= 2/6 × 5/4

= 10/24

= 5/6

One side of a rectangle is 7 inches long. Another side of the rectangle is 19 inches long. What are the lengths of the other 2 sides of the rectangle?

Answers

Answer:

7 and 19 its a rectangle so it has 2 congruent sides

Step-by-step explanation:

can anyone write me the steps of how to graph y=(x-9)^, please?

Answers

Answer:

first step is to put the (x-9)^2 into a standard form which is y=x^2−18x+81 then choose two integers larger than the x-value of the vertex point.next choose two integers smaller than the x-value of the vertex point. lastly substitute these values in place of "x" in the equation and solve for "y".

Step-by-step explanation:

x | y

7 | 4

8 | 1

9 | 0

10 | 1

11 | 4

4=(11-9)^2

1=(10-9)^2

0=(9-9)^2

1=(8-9)^2

4=(7-9)^2

What would be the value of x in x+5=-3x-9

Answers

-3 because it shows the value right there

Answer  -3

Step-by-step explanation:

what is a measure of an angle between the perpendicular
bisectors of two adjacent sides of a regular polygon 3
Sides ?​

Answers

Answer:

2/5*180=72

360/72=5

as simple as that you just need to read on polygons

Step-by-step explanation:

pls give me brainlyist

Which of the following values is a solution to the inequality? 12 – 5x > -8

Answers

Answer:

x < 4

Step-by-step explanation:

12 – 5x > -8

Subtract 12 from each side

12-12 – 5x > -8-12

-5x> -20

Divide each side by -5, remembering to flip the inequality

-5x/-5 < -20/-5

x < 4

There are 197 oak trees in the park. There are 27 more pine trees than oak trees in the park how many trees are there in all

Answers

just add.................

197 + 27 = 224

hope this helps

Yeah.. the answer is 224

Which of the following describe the growth rate of the exponential function in the graph below?

Answers

Answer:

B)

Step-by-step explanation:

Let's check each answer:

A is incorrect. If that were the case, (0,1) to (1,3) would be (0,1) to (1,5) instead

B is correct. The y-coordinate gets multiplied by 3 each time (0,1)->(1,1*3)->(2,3*3)->(4,3*3*3)

C is incorrect. If that were the case, (1,3) to (2,9) would be (1,3) to (2,7) instead.

D is incorrect. If that were the case, (0,1) to (1,3) would be (0,1) to (1,4) instead.

Therefore, the correct answer is B.

Answer:

Its B :)

Step-by-step explanation:

I j took the unit quiz lol

someone plz help it looks easy but I dont understand

Answers

Answer:

Step-by-step explanation:

(√8)²=8,2²+2²=8

√8→2 units,2 units

(√7)²=7,(√5)²+(√2)²=5+2=7

√7→√5 units,√2 units

(√5)²=5,2²+1²=5

√5→2 units ,1 unit

3²=9,2²+(√5)²=9

3→2 units,√5 units.

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