A cylindrical jug that carries 2ℓ of water when it is filled to the brim has a base surface with a diameter of 8cm. What is the length of the jug in cm, rounded to two decimal places?

Answer:

The maximum number of possible combinations are 9.

Step-by-step explanation:

There are three types of juices :

Orange, Mango and Blue lemonade

There are three types of biscuits:

Oreo, Skyflakes and Rebisco

So, the number of possible combinations are

= (3 C 1) x (3 C 1)

= 3 x 3 = 9

The maximum number of possible combinations are 9.

I'll use the integrating factor method for the first DE, and undetermined coefficients for the second one.

(a) Multiply both sides by exp(7t ):

exp(7t ) dx/dt + 7 exp(7t ) x = 5 exp(7t ) cos(2t )

The left side is now the derivative of a product:

d/dt [exp(7t ) x] = 5 exp(7t ) cos(2t )

Integrate both sides:

exp(7t ) x = 10/53 exp(7t ) sin(2t ) + 35/53 exp(7t ) cos(2t ) + C

Solve for x :

x = 10/53 sin(2t ) + 35/53 cos(2t ) + C exp(-7t )

(b) Solve the corresonding homogeneous DE:

d²x/dt ² + 6 dx/dt + 8x = 0

has characteristic equation

r ² + 6r + 8 = (r + 4) (r + 2) = 0

with roots at r = -4 and r = -2. So the characteristic solution is

x (char.) = C₁ exp(-4t ) + C₂ exp(-2t )

For the particular solution, assume an ansatz of the form

x (part.) = a cos(3t ) + b sin(3t )

with derivatives

dx/dt = -3a sin(3t ) + 3b cos(3t )

d²x/dt ² = -9a cos(3t ) - 9b sin(3t )

Substitute these into the non-homogeneous DE and solve for the coefficients:

(-9a cos(3t ) - 9b sin(3t ))

… + 6 (-3a sin(3t ) + 3b cos(3t ))

… + 8 (a cos(3t ) + b sin(3t ))

= (-a + 18b) cos(3t ) + (-18a - b) sin(3t ) = 5 sin(3t )

So we have

-a + 18b = 0

-18a - b = 5

==>   a = -18/65 and b = -1/65

so that the particular solution is

x (part.) = -18/65 cos(3t ) - 1/65 sin(3t )

and thus the general solution is

x (gen.) = x (char.) + x (part.)

x = C₁ exp(-4t ) + C₂ exp(-2t ) - 18/65 cos(3t ) - 1/65 sin(3t )

9514 1404 393

Answer:

  (b)  the correct table is marked

Step-by-step explanation:

Direct variation is characterized by the ratio of y to x being a constant for all values in the table. That constant is the constant of proportionality. For the values in the second table (marked), the ratio is ...

  y/x = 8/6 = 12/9 = 16/12 = 4/3

The constant of proportionality is 4/3.

x = 100° (using definition of vertical angles)

Answer:

first one

Step-by-step explanation:

Answer:

the range the score is 59 is the correct answer

Step-by-step explanation:

Range is the largest no minus the smallest no...so 59 is the largest minus 0 the smaller number

Answer:

a = 2

b = 5

Step-by-step explanation:

Given :

(ar^b)^4 = 16r^20 ; a and b are positive integers :

Opening the bracket :

a^4r^4b = 16r^20

a^4 = 16 - - - - - (1)

r^4b = r^20 - - - (2)

a^4 = 16

Take the 4th root of both sides :

(a^4)^(1/4) = 16^1/4

a = 2

From (2)

r^4b = r^20

4b = 20

Divide both sides by 4

4b/4 = 20/4

b = 5

Hence ;

a = 2

b = 5

Answer:

6x6

Step-by-step explanation:

Hello!

The answer is a.

Good luck! :)

Answer:

n>2 2/3

Draw a filled dot at a little more than 2 1/2 and continue the line to the right.

Step-by-step explanation:

Subtract 1/3 from both sides to get

2 2/3

Flip the inequality

n> 2 2/3

I hope this helps!

Answer:

ASA

Step-by-step explanation:

∠ABC ≅ ∠EDF  Angle

BC ≅ DF            Side

∠C ≅ ∠F            Angle

Step-by-step explanation:

Given: [tex]y = -\dfrac{2}{x}[/tex]

Derivative of a power function [tex]x^n[/tex]:

[tex]\dfrac{d}{dx}(x^n) = nx^{n-1}[/tex]

Therefore,

[tex]\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}[/tex]

Answer:

363,000,000

..........

Answer:

B. [tex] y + 5 = 2(x + 2) [/tex]

Step-by-step explanation:

Point-slope equation is given as [tex] y - b = m(x - a) [/tex], where,

(a, b) = (-2, -5)

[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line (-2, -5) and (0, -1),

Slope (m) = (-1 -(-5))/(0 -(-2)) = 4/2

m = 2

✔️To write the equation in point-slope form, substitute a = -2, b = -5, and m = 2 into [tex] y - b = m(x - a) [/tex]

Thus:

[tex] y - (-5) = 2(x - (-2)) [/tex]

[tex] y + 5 = 2(x + 2) [/tex]

23/200

Hope this helps! :)

Answer:

23/2000

Step-by-step explanation:

0.0115 can be written as 115/10000

=23/2000

Please mark me as brainliest.

Answer:

2/7

Step-by-step explanation:

d=2n+3

 [tex]\frac{d-7}{2n-4} = \frac{4}{13}[/tex]

13(2n+3) -91 =8n - 16

26n+39 -91 = 8n-16

18n=36

n=2

d=7

Answer:

40

Step-by-step explanation:

10/x = 25/100

Cross multiply 10 and 100 = 1000.

Then, divide 1000 by 25 = 40.

10/40 = 0.25 = 25%

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

[tex] W(-1, 1) = (x_1, y_1) [/tex]

[tex] X(1, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]

[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]

[tex] WX = \sqrt{4 + 1} [/tex]

[tex] WX = \sqrt{5} [/tex]

[tex] WX = 2.24 [/tex]

✔️Distance between X(1, 2) and Y(2, -4)

Let,

[tex] X(1, 2) = (x_1, y_1) [/tex]

[tex] Y(2, -4) = (x_2, y_2) [/tex]

Plug in the values

[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]

[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]

[tex] XY = \sqrt{1 + 36} [/tex]

[tex] XY = \sqrt{37} [/tex]

[tex] XY = 6.08 [/tex]

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

[tex] Y(2, -4) = (x_1, y_1) [/tex]

[tex] Z(-2, -1) = (x_2, y_2) [/tex]

Plug in the values

[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]

[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]

[tex] YZ = \sqrt{16 + 9} [/tex]

[tex] YZ = \sqrt{25} [/tex]

[tex] YZ = 5 [/tex]

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

[tex] Z(-2, -1) = (x_1, y_1) [/tex]

[tex] W(-1, 1) = (x_2, y_2) [/tex]

Plug in the values

[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]

[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]

[tex] ZW = \sqrt{1 + 4} [/tex]

[tex] ZW = \sqrt{5} [/tex]

[tex] ZW = 2.24 [/tex]

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A.....let P be the number of people that will show up.....so....

The total amount of broccoli needed (in ounces)  =    8P  ounces

Part B

32  =  8P       divide both sides by 8

4 = P            so.....4 people can be fed.....!!!

Step-by-step explanation:

Answer:

189 ft²

Step-by-step explanation:

Here is the formula...

1/2 * 6 * 36 + 81

Hope this helps

Answer:

b and f

Step-by-step explanation:

Answer:

all counting numbers except one

Answer:

i^−3 = i

i^−2 = −1

i^−1 = −i

i^0 = 1

i^1 = i

i^2 = −1

i^3 = −i

i^4 = 1

i^5 = i

i^ 6 = −1

See the pattern

Answer:

[tex]A = 200,000(1+.025) ^{t}[/tex]

[tex]A = 200,000(1+.025) ^{10}[/tex]

Step-by-step explanation:

Answer:

1d = -3

2b = 2

2c = 1

3a = 3

3d = 4

Step-by-step explanation:

Polynomial 1: [tex]x^2-8x+15[/tex]

Multiply the leading coefficient, 1, and the last term, 15. You get: 15.

Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:

Factors of 15: -5 * -3

Addends of -8: -5 + -3

Replace the -8x with -5x - 3x:

[tex]x^2-5x-3x+15[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](x^2-5x)-(3x+15)[/tex]

[tex]x(x-5)-3(x-5)[/tex]

[tex](x-5)(x-3)[/tex]

Looking at the answer (ax + b)(cx + d), d would correspond with -3.

Polynomial 2: [tex]2x^3-8x^2-24x[/tex]

First factor out the x:

[tex]x(2x^{2}-8x-24)[/tex]

Divide the polynomial inside by 2 and place the 2 outside with the x:

[tex]2x(x^2-4x-12)[/tex]

Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:

Factors of -12: -6 * 2

Addends of -4: -6 + 2

Replace the -8x with -6x + 2x:

[tex]2x(x^2-6x+2x-12)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex]2x((x^2-6x)+(2x-12))[/tex]

[tex]2x(x(x-6)+2(x-6))[/tex]

[tex]2x((x+2)(x-6))[/tex]

[tex]2x(x+2)(x-6)[/tex]

Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.

Polynomial 3: [tex]6x^2+14x+4[/tex]

Divide the polynomial by 2:

[tex](2)(3x^2+7x+2)[/tex]

Find the factors of 3*2 and the addends of 7 and see which two numbers match:

Factors of 6: 6 * 1

Addends of 7: 6 + 1

Replace the 7x with 6x + x:

[tex](2)(3x^2+6x+x+2)[/tex]

Put parentheses around the first 2 terms & last 2 terms and factor like so:

[tex](2)((3x^2+6x)+(x+2))[/tex]

[tex](2)(3x(x+2)+(x+2))[/tex]

[tex](2)((3x+1)(x+2))[/tex]

[tex](2)(3x+1)(x+2)[/tex]

Then multiply the 2 with the (x+2) and here's your final answer:

[tex](3x+1)(2x+4))[/tex]

Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.

Hope that helps (●'◡'●)

(This took a while to write, sorry about that)

Answer:

-3,-1

Step-by-step explanation:

x²+4x+3=0

x²+4x=-3

x²+4x+(2)²=-3+(2)²

(x+2)²=-3+4

(x+2)²=1

Take square root of both sides

x+2=±1

x=-2±1

x=-1 or-3

Answer:

19.0%

Step-by-step explanation:

The probability that a student in the sample data is enrolled in painting Given that the student is female is a conditional probability and can be defined as :

Let,

F = Female ; P = painting

P(Painting Given female) = P(P|F) = (PnF) / F

From the table :

(PnF) = 16

F = 84

Hence,

P(P|F) = 16 / 84 = 0.19047 = 0.19047 * 100%

P(P|F) = 19.0%