Please help me with question 20. Thank you.

(a) The differential equation is separable, so we separate the variables and integrate:

[tex](x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx[/tex]

[tex]\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx[/tex]

[tex]\ln|y| = x - \ln|x+1| + C[/tex]

When x = 0, we have y = 2, so we solve for the constant C :

[tex]\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)[/tex]

Then the particular solution to the DE is

[tex]\ln|y| = x - \ln|x+1| + \ln(2)[/tex]

We can go on to solve explicitly for y in terms of x :

[tex]e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}[/tex]

(b) The curves y = x² and y = 2x - x² intersect for

[tex]x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1[/tex]

and the bounded region is the set

[tex]\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}[/tex]

The area of this region is

[tex]\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}[/tex]

Answe

about 30-45 Percent.

Step-by-step explanation:

Answer:

104, with the assumption that "an alphabet" is the English alphabet

Step-by-step explanation:

26*4

Answer:

168 inches

Step-by-step explanation:

To find the fence made each day by Libby, we will divide 56 by 4.

convert the length of fence into inches.

1 foot = 12 inches.

Answer:

  49°

Step-by-step explanation:

The marked angles are "vertical" angles. They have the same measure.

  ∠TGF = ∠HGM = 49°

_____

You don't need to know the value of p to answer this question. It is 7.

Answer:

∠TGF = 49°

Step-by-step explanation:

From the diagram, we get that ∠TGF is equal to ∠MGH because they are  vertical angles.

Hence,

⇒ ∠TGF = ∠MGH

⇒ ∠TGF = 49°

Answer:

Do not put A and I more than once, we already measured it before.

10 letters in all

Find how many there are per letter

C - 1/10

A - 2/10

L - 1/10

I - 2/10

F - 1/10

O - 1/10

R - 1/10

N - 1/10

Answer:

its correct so you don't need to do anything

Step-by-step explanation:

The solution is, result of subtraction = 81.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

Nyla compared 790 and 709.

so, we have,

790 - 709

=81

Hence, The solution is, result of subtraction = 81.

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Answer:

13188mm^2

Step-by-step explanation:

D=60mm
H=136mm
L=140mm
then v=1/3xd^2x h= 1/3x3.14x60^2x136
SA=tc pl/2
=3.14x60x140= 13188mm^2
hope this helps!

Answer:

Step 1: 8 + 16x Step 2: 4(4) + 4(12x) Step 3: 4(4 + 12x) Step 4: Dimensions of the rectangle are 4 and 4 + 12x In which step did the student first make an error and what is the correct step? Step 3; 4 + (4 + 12x) Step 3; 4 + (4 ⋅ 12x) Step 2; 4(2) + 4(4x) Step 2; 4(2) + 4x(2)

Answer:

Answer: 3, 3 of them are translated

Answer:

B. 3 triangles are congruent to ABC

Step-by-step explanation:

From the picture, triangle ABC is not a right triangle. The length of AB is graphed with a length of 4. From point C to segment AB is a height of 3. The triangle in quadrant I (top right) has both of these dimensions.

Similarly, the triangle on the x-axis (positive side) below it (between Q1 and Q4) is also congruent to ABC.

The triangle fully in quadrant III (bottom left) is congruent to ABC with a height of 3 and base length of 4.

The triangle in the bottom right corner (Q4) has a height of 4, therefore it is not congruent to ABC which has a height of 3.

The triangle on the x-axis (negative left side) is also not congruent to ABC. It may have a height of 3 and base length 4, but the angles are different which means the other side lengths don't correspond to ABC.

[+ I'm not sure if your teacher would consider this a real answer but I figured I'd mention that in proofs tri.ABC is also congruent to tri.ABC.]

The initial angular velocity of the star will be [tex]w=2.4\times 10^{-6} \ \frac{rad}{sec}[/tex].

Angular velocity refers to how fast an object rotates or revolves relative to another point. It is a rate of change of angle.

Here for the 30 days period the angular velocity will be calculated as:

[tex]W=\dfrac{2\pi}{T}=\dfrac{2\times \pi}{30\times 24\times 3600}=2.4\times 10^{-6} \ \frac{rad}{sec}[/tex]

So the initial angular velocity of the star will be [tex]2.4\times 10^{-6} \frac{rad}{sec}[/tex]

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Answer:

A 9.47% discount was given

Step-by-step explanation:

The question is asking us to find how much percent of 475 is 45. Therefore we do the following:

[tex] \frac{45}{475} \times \frac{100}{1} = \frac{4500}{475} [/tex]

after dividing we get 9.473 which is approximately 9.47%

To check if what we got is correct we do the opposite and instead find 9.47% of 475.

[tex] \frac{475}{1} \times \frac{9.47}{100} = \frac{4498.25}{100} [/tex]

After dividing we find that is equal to 44.98 which is approximately 45.

The answer is: [tex]z_1-z_2[/tex]= 4-4([tex]\sqrt{3i}[/tex]-4i)

The correct option is: (D)

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).

Since we have given : [tex]z_1[/tex]==4-4[tex]\sqrt{3i}[/tex] and [tex]z_2[/tex]= -16i

The difference of z1 - z2 would be:

So,

[tex]z_1-z_2[/tex] = 4-4[tex]\sqrt{3i}[/tex] - (-16i)

[tex]z_1-z_2[/tex] =4-4[tex]\sqrt{3i}[/tex]+16i

[tex]z_1-z_2[/tex] =4-4([tex]\sqrt{3i}[/tex] -4i)

Hence, [tex]z_1-z_2[/tex]= 4-4([tex]\sqrt{3i}[/tex]-4i)

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Answer:

4 – 4( StartRoot 3 EndRoot – 4)i

it's C.

Step-by-step explanation:

took the L for yall bc my shtoopid ahh thought it was D, which is 4 + 4

Length of sides:

Surface Area:

(perimeter of base)(length) + (base)(height)

(8+10+6)(4)+(8)(6)

(24)(4)+48

96+48

144 ft²

The regular polygon must have 12 sides so the smallest angle of rotational symmetry is 30°

We know that the smallest angle of rotational symmetry is 30°, then the exterior angles must measure that.

Remember that the sum of the exterior angles of a regular polygon must be equal to 360°, then we have:

360° = n*30°

Where n is the number of sides

Solving for n we get:

n = 360°/30° = 12

We conclude that the regular polygon has 12 sides.

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Answer: B. 12

Step-by-step explanation: On Edge!!!

Answer:

y>1/3x-3

Step-by-step explanation:

The slope for this equation is 1/3x-3. Because the line is dashed, we know that we're dealing with either < or >. The shading goes upwards, so it's greater than. That means, we would get y>1/3x-3.

Hope this helps!

Answer: The student may overestimate support for a plastic bag ban because the wording of the question may influence adults to support a ban.

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

let's look at the change from the red point to the blue point

thus, (x₁, y₁) = red point = (-4, 1) and (x₂, y₂) = blue point = (-2, 0)

note that (x₁, y₁) and (x₂, y₂) can be interchanged

slope = change in y / change in x = (y₂-y₁)/(x₂-x₁) = (0-1) / (-2-(-4)) = -1/2 as our slope

Answer:

[tex]a=\sqrt[3]{\frac{27}{64}} = 0.75[/tex]

edge length = 0.75

Equation: [tex]a=\sqrt[3]{V}[/tex]

Answer:

About 30-34 hours i estamate

Step-by-step explanation:

Alonso should work for 38 hours to earn $554.80.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Alonso earned $204.40 at his job when he worked for 14 hours.
Let Alonso per hour be x,
x = 204.40 / 14
x = 14.6

Now,
Alonso works for hours to earn $554.80,
= total pay/pay of an hour
= $554.80 / 14.6

= 38

Alonso should work for 38 hours to earn $554.80.

Thus, Alonso should work for 38 hours to earn $554.80.

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If 10 inches is equal to 25.4 centimeters. Then the 45 inches will be equal to 114.3 centimeters.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.

A 10 inches long piece of string is approximately 25.4 centimeters long.

If the length of the string is 45 inches. Then the length in cm will be

Let x be the length. Then we have

x/45 = 25.4/10

    x = 114.3 cm

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Answer:

445455

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Answer:

4394

5200 X 0.12 = 624 --> 5200 - 624 = 4576

5200 X 0.035 = 182

4576 - 182 = 4394

Answer:

The answer would be 9.1104335791443.

See attached. We can draw a right triangles contained within both shapes.

The triangle has height x (same as the cylinder), base 2r (same as the diameter of the cylinder), and hypotenuse 6 (same as the diameter of the sphere).

Since it's a right triangle, the Pythagorean theorem holds and we have

x² + (2r)² = 6²

which we solve for r to get

x² + 4r² = 36

4r² = 36 - x²

r² = 9 - x²/4

r = √(9 - x²/4)

Then the volume of the cylinder, whose height is x and whose base has radius r, is

π r² x = π (9 - x²/4) x = (36x - x³) π/4

Hi Student!

The first step that we need to take to solving this problem (and almost any problem), is to concentrate the important information for the problem that is provided.  Looking at the problem we can see that we are trying to determine what the length of the radius is.  In order to solve this problem we are provided with the area of a sector of 361.6 meters squared and a central angle of 288 degrees.

Now that we have the important information taken care of, we can move onto the part of actually solving the problem.  We must first convert our degrees to radians because the equation that we will be using can only use radians for the angle and not degrees.  We can simply convert our angle to radians by multiplying it by π/180.

[tex]288\ degrees\ *\ \frac{\pi }{180\ degrees}[/tex]

[tex]288\ degrees\ *\ \frac{3.14}{180\ degrees}[/tex]

[tex]\frac{288\ degrees\ *\ 3.14}{180\ degrees}[/tex]

[tex]5.024\ radians[/tex]

After completing this step, we have converted our degrees to radians and now we can move onto the step where we plug in our information into an equation and solve for our unknown.

[tex]Sector\ Area = radius^2\ *\ \frac{angle}{2}[/tex]

[tex]361.6\ m^2 = radius^2\ *\ \frac{5.024}{2}[/tex]

[tex]361.6\ m^2 = radius^2\ *\ 2.512[/tex]

[tex]\frac{361.6\ m^2}{2.512} = \frac{radius^2\ *\ 2.512}{2.512}[/tex]

[tex]143.949\ m^2 = radius^2[/tex]

[tex]\sqrt{143.949\ m^2} = \sqrt{radius^2}[/tex]

[tex]12\ m = radius[/tex]

Therefore, after solving our equation for our unknown, we can see that our radius is really close to 12 meters (so we can just round up as the problem stated).