what is the general solution to the differential equation dydx=8e4x2cos(2y) ?

The volume of the cylindrical tin can is approximately 4288.65 cubic centimeters.

To find the volume of a cylindrical tin can, we can use the formula V = π\(r^2\)h, where V represents the volume, r is the radius, and h is the height of the cylinder. In this case, the given radius is 8 cm and the height is 21.2 cm.

Calculate the base area

The base area of the cylinder can be found using the formula A = π\(r^2\). Plugging in the given radius, we have A = π\((8 cm)^2\). Simplifying this, we get A = 64π \(cm^2\).

Multiply the base area by the height

Next, we multiply the base area by the height of the cylinder. Multiplying 64π \(cm^2\) by 21.2 cm gives us the volume V = 1356.8π \(cm^3\).

Approximate the value of π and calculate the volume

To find the approximate value of the volume, we substitute the value of π as 3.14. Multiplying 1356.8π \(cm^3\) by 3.14, we get V ≈ 4269.632\(cm^3\).

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Answer:

B

Step-by-step explanation:

The Pythagoras theorem states that \(c^{2} = a^{2} + b^{2\), where \(c\) is the hypotenuse and a and b are the adjacent and opposite sides of the hypotenuse. If we made \(a\) the subject of the expression, the expression will be re-written as \(a^{2} = c^{2} - b^{2}\), which is the correct answer.

The correct answer is V = E - F. This equation allows us to calculate the amount of variable expenses (V) by subtracting the fixed expenses (F) from the total expenses (E).

To rearrange the total expense equation E = F + V and calculate the amount of variable expenses (V), we need to isolate V on one side of the equation. By subtracting F from both sides, we can find the expression for V:

E - F = F + V - F

Simplifying further:

E - F = V

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The effective mass on the opposite end of the lever is 4 kg and distance is given, which is incorrect as option D is 25 kg otherwise all option is correct .

In the given scenario, a 2 kg mass is placed at the end of a lever, which is 20 cm from the pivoting point. If the mass is transferred to the other side of the lever, which is 10 cm from the pivot,

Let's find out.The effective mass on the opposite end of the lever can be found using the following formula:

= Mass × distance of its center of gravity from the pivot

Let M be the effective mass that we have to find. Then, we have:

2 kg × 20 cm

= M × 10 cm40 cm

= 10 M4

= MM

= 4

Therefore, the effective mass is 4 kg. Hence, option D. 25 kg is incorrect as the effective mass is 4 kg.

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Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

Volume of the sphere/Volume of the cylinder

= {(4/3)πr³}/{2πr³}

= 2/3.

Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

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For the complete question, refer to the attachment.

To evaluate the given integral using Green's theorem, we need to express it in the flux form.  The result of the integral is -r/6.

Green's theorem states that for a region R bounded by a simple closed curve C, the flux of the vector field F = (P, Q) across C is equal to the double integral of the curl of F over R.

In this case, we have the vector field F = (r^2xy, 1/2y^3), where r is the position vector (x, y).

The flux form of Green's theorem is:

\(∫∫R (curl F) · dA = ∫∫R (∂Q/∂x - ∂P/∂y) dA\)

Let's calculate the curl of F:

∂Q/∂x = 0

∂P/∂y = 2rxy

So, the curl of F is given by\((∂Q/∂x - ∂P/∂y) = 0 - 2rxy = -2rxy.\)

Now, let's evaluate the integral using the flux form of Green's theorem:

∫∫R (-2rxy) dA

Since the region R is a triangle with vertices (0,0), (1,0), and (0,1), we can express it as:

\(R = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}\)

Now, we can rewrite the integral:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Let's evaluate the inner integral first:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Now, evaluate the outer integral:

\(∫₀¹ -r(x-x²) dx = -r(x²/2 - x³/3) ∣₀¹ = -r(1/2 - 1/3) = -r(3/6 - 2/6) = -r(1/6) = -r/6\)

Therefore, the result of the integral is -r/6.

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The y - intercept of the graph represent the initial radius of the algae, the average rate of change is 0.63

1. Since the radius of the algae is increasing with time, a reasonable domain to plot the growth function would be the set of positive real numbers. In other words, d should be greater than or equal to zero.

2. The y-intercept of the graph of the function f(d) represents the initial radius of the algae, or the radius of the algae on day 0.

3. The average rate of change of the function f(d) from d = 4 to d = 11 is:

average rate of change = [f(11) - f(4)] / (11 - 4)

Substituting the given function, we get:

average rate of change = [7(1.06)^11 - 7(1.06)^4] / 7

average rate of change - 0.64

This represents the average increase in the radius of the algae per day between days 4 and 11.

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Answer:100 grams of A mixed with 80 grams of B will provide the daily diet for a single animal.

Step-by-step explanation:

Step 1

The requirement for each animal is given as 50g of protein  and 12g of fat

let mix A  be represent as   containing  0.10A protein and 0.08A fat

and mix B be represented as containing 0.5B protein and 0.05B  fat

Therefore for Protein , we have   0.10A + 0.5B= 50----- Equation 1

And for fat , we have   0.08A + 0.05B= 12-------Equation 2

Step 2-- Solving

0.10A + 0.5B= 50----- Equation 1

0.08A + 0.05B= 12-------Equation 2

multiplying equation 1 by 10 and equation 2 by 100 we have

1A+ 5B=500-------Equation 3

8A+ 5B= 1200-------Equation 4

Subtracting equation 3 from equation 4

7A= 700

A = 700/7= 100

Puting value of A = 100 IN  EQUATION 3

1(100) + 5B= 500

5B= 500-100

B=400/5= 80

Therefore 100 grams of A mixed with 80 grams of B will provide the daily diet for a single animal.

The s-orbital is spherical in shape, while the p-orbitals are composed of two lobes that are directed at an angle of 120 degrees apart.

It is composed of three atomic orbitals: one s-orbital and two p-orbitals. The s-orbital is spherical in shape, while the p-orbitals are composed of two lobes that are directed at an angle of 120 degrees apart. The combination of these three orbitals forms a hybrid orbital that is shaped like a flat trigonal planar, with a bond angle of 120 degrees. This hybrid orbital is known as the sp2 hybrid orbital.

The "s" in sp2 stands for the s-orbital, which is a single, spherical orbital. The "p" represents the two p-orbitals, which have two lobes and form an angle of 120 degrees with each other. The "2" in sp2 indicates that two p-orbitals are involved in the hybridization process. The hybridization of the s and two p-orbitals creates the sp2 hybrid orbital, which is trigonal planar in shape.

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Answer:

equal or balanced

Step-by-step explanation

the = demonstrates the amounts need to be the same

Answer: Balanced.

Step-by-step explanation:

For an equation each side shall be equal (balanced) or else it's NOT an equation.

Answer:54 cm

Step-by-step explanation:

Given

Rods are joined to form a square

Perimeter of square is \(72\ cm\)

Suppose a is the length of each rod so

Perimeter is \(4 a\)

\(\therefore 4a=72\)

\(\Rightarrow a=\frac{72}{4}\)

\(\Rightarrow a=18\ cm\)

Now if rods are joined to form a square then

Perimeter is the sum of sides

Perimeter of (equilateral)triangle\(=3a\)

\(\Rightarrow =3\times 18\)

\(\Rightarrow =54\ cm\)

Answer: y + 4 = 1/2(x - 1)

Step-by-step explanation:

The form of a straight line quation is y=mx+b, where m is the slope [(1/2) in this case] and b is the y-intercept (the value of y when x=0).  We can already eliminate two of the options (2nd and 4th) since those slopes are 2.

To decide between y - 4 = 1/2(x +1) and y + 4 = 1/2(x - 1), we can see which equation is true for the point (1,-4):

Does y - 4 = 1/2(x +1) work for (1,-4)?  [i.e., will y = -4 when x=1?]

y-4 = 1/2(1+1)?

y = 5         NO

-----------------------------

Does y + 4 = 1/2(x - 1) work for (1,-4)?    [i.e., will y = -4 when x=1?]

y+4 = 1/2(1-1)

y = -4       YES  

The equation is y + 4 = 1/2(x - 1)

To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:

Let u = y,

v = y',

w = y".

Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:

du/dx = y' = v,

dv/dx = y" = w,

dw/dx = y"'.

Now we can rewrite the given differential equation in terms of u, v, and w:

u - w - 4u + 4u = 0.

Simplifying the equation, we get:

-3u - w = 0.

This equation can be expressed as a system of first-order linear differential equations as follows:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

Now we have a companion system of linear equations:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.

The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.

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Answer:

1.x=7,  2.x=7,  3.x=7,  4.x=1,  5.x=20,  6.x=9,  7.x=100,  8.x=9

Step-by-step explanation:

hope this helps :<)

Thus,  the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

To solve this problem, we need to use algebraic equations. Let's start by assigning variables to the unknown quantities. Let x be the number of purses sold and y be the number of blouses sold.

From the problem, we know that the blouses cost $28 each and the purses cost $39 each. Therefore, the total revenue from selling x purses and y blouses is given by:

Revenue = 28y + 39x

We also know that the store sold three times as many blouses as purses. Therefore, we can write:
y = 3x

Now we can substitute y = 3x into the revenue equation and solve for x:
1107 = 28y + 39x
1107 = 28(3x) + 39x
1107 = 84x + 39x
1107 = 123x
x = 9

So the store sold 9 purses. To find the number of blouses, we can use the equation y = 3x:
y = 3x = 3(9) = 27

Therefore, the store sold 27 blouses.

In summary, the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

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Answer:

uh still (7,3)

Step-by-step explanation:

did you attach the wrong picture

I'm sorry but did you add the wrong picture or leave the rest of the graph out?

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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Answer:

To women, it was a steed upon which they rode into a new world. All this triggered a backlash from many (male) doctors and onlookers, who cited all sorts of reasons to dissuade women from riding bikes. It would lead to not only bicycle face, but also exhaustion, insomnia, heart palpitations, headaches, and depression. During the late 19th and early 20th centuries, women began to escape some of their restrictions by riding bycicles. Despite strong opposition from men, women cycled on, and the bicycle became an instrument of change that subverted the status quo and became a powerful symbol of women's emancipation.

Step-by-step explanation:

The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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Answer:

1%

Step-by-step explanation:

Interest gain would be   9880 - 9500 = 380 dollars

9500 * i * 4 yrs = 380

  i = .01     or  1%

Answer:

x is 8

Step-by-step explanation:

combine like terms so 112 + 12 is 124 and 4x + 3x is 7x. subtract 124 from 180 and you get 56. 7x divided by 7 is x and 56 divided by 7 is 8 so x = 8

Answer:

r >= Q

Step-by-step explanation:

THE LAST ONE

Answer:

r-q

Step-by-step explanation:

Answer:

There are six possible outcomes when rolling a die, and three of them are prime numbers (2, 3, and 5). Therefore, the probability of rolling a prime number on a single die is 3/6, or 1/2.

The probability of rolling a 5 on the red die is 1/6, since there is only one face with a 5 out of the six faces.

To find the probability that the red die lands on a 5 and the blue die lands on a prime number, we need to multiply the probabilities of these two events occurring:

P(red die lands on 5 AND blue die lands on prime number) = P(red die lands on 5) x P(blue die lands on prime number)

P(red die lands on 5 AND blue die lands on prime number) = (1/6) x (1/2)

P(red die lands on 5 AND blue die lands on prime number) = 1/12

Therefore, the probability that the red die lands on a 5 and the blue die lands on a prime number is 1/12 or approximately 0.083 or 8.3%.

Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)

Answer: (My view) 6.

Step-by-step explanation: Letting "n" be the number of pictures taken. The probability of no one look at the camera for n photos is of (3/4)^n.

Hence, the probability of at least one photo be the picture craven is of:

(1 - (3/4)^n), and since the likelihood of that being equal to 4/5, it's feasible to assume that (1 - (3/4)^n) = 4/5, solving for that would give:

(3/4)^n = 1/5. Notice that the proposal can also be interpreted as "The number of pictures needed such that the probability of a picture NOT including one with everyone looking at the camera is at most 1/5",

Therefore, (3/4)^n < 1/5;

To solve for that:

n = 1:

3/4 > 1/5,

n = 2:

9/16 > 1/5

n = 3

27/64 > 1/5

n = 4

81/256 > 1/5

n = 5

243/1024 > 1/5

But finally:

n = 6

729/4096 < 1/5

For at least 6 pictures she must take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera.

Let p define the probability of success in a Bernoulli trial, and P define the probability Sara wants to reach "at least" and n be defined as the number of trials. Then,

= 1 - (1 - p)ⁿ ≥ P

= (1 - p)ⁿ ≤ 1 - P

= n ≥ ln(1-P)/ln(1-p)

= n ≥ ln (0.2) / ln (0.75)

=5.6

Hence for at least n=6 photos, there is at least a chance of 4/5 that everyone is looking at the camera.

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Answer:

6

Step-by-step explanation:

We want to use the distance formula for this problem

\(\sqrt{(x_{2} -x_{1} )^{2} +(y_{2}-y_{1}) ^{2} }\)

\(\sqrt{(-8+8)^{2} +(-2-4)^{2} }\)

\(\sqrt{0+36}\)

The distance between these two points is 6

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

Substitute a = 4 and b = - 1 into the expression

\(\frac{5-2(4+3(-1))}{2}\)

= \(\frac{5-2(4-3)}{2}\)

= \(\frac{5-2(1)}{2}\)

= \(\frac{5-2}{2}\)

= \(\frac{3}{2}\)

Answer:

d

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

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