give me any equation in the comments

The family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P) on an appropriate interval of definition.

In the first paragraph, we summarize that the family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P). This equation represents the rate of change of the variable P with respect to time t, and the solution provides a relationship between P and t. In the second paragraph, we explain why this family of functions satisfies the given differential equation.

To verify the solution, we can substitute P = C1e^t / (1 + C1e^t) into the differential equation dP/dt = P(1 - P) and see if both sides are equal. Taking the derivative of P with respect to t, we have:

dP/dt = [d/dt (C1e^t / (1 + C1e^t))] = C1e^t(1 + C1e^t) - C1e^t(1 - C1e^t) / (1 + C1e^t)^2

      = C1e^t + C1e^(2t) - C1e^t + C1e^(2t) / (1 + C1e^t)^2

      = 2C1e^(2t) / (1 + C1e^t)^2.

On the other hand, evaluating P(1 - P), we get:

P(1 - P) = (C1e^t / (1 + C1e^t)) * (1 - C1e^t / (1 + C1e^t))

        = (C1e^t / (1 + C1e^t)) * (1 - C1e^t + C1e^t / (1 + C1e^t))

        = (C1e^t - C1e^(2t) + C1e^t) / (1 + C1e^t)

        = (2C1e^t - C1e^(2t)) / (1 + C1e^t)

        = 2C1e^t / (1 + C1e^t) - C1e^(2t) / (1 + C1e^t).

Comparing the two sides, we see that dP/dt = P(1 - P), which means the family of functions P = C1e^t / (1 + C1e^t) is indeed a solution to the given differential equation.

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The order of the angles from the least measure to greatest measure is ∠HGB, ∠ECD, ∠FGH and ∠GBH. The solution has been obtained by using the properties of angles.

What is an angle?

When two rays or lines share an endpoint, they form an angle, which is a figure in plane geometry.

We are given that CEFH is a parallelogram. We know that the adjacent angles of a parallelogram are supplementary.

So,

⇒∠FEC + ∠HCE = 180°

⇒124° + ∠HCE = 180°

⇒∠HCE = 56°

We know that angles on a straight line form a linear pair.

So,

⇒∠BCH + ∠HCE + ∠ECD = 180°

⇒90° + 56° + ∠ECD = 180°

⇒∠ECD = 34°

We know that the opposite angles of a parallelogram are equal.

So,

⇒∠FEC = ∠FHC

⇒∠FHC = 124°

Now,

⇒∠FHC + ∠FHG = 180°

⇒∠FHG = 56°

Using the angle sum property of triangle, we get

⇒∠FHG + ∠FGH + ∠GFH = 180°

⇒56° + ∠FGH + 87° = 180°

⇒∠FGH = 37°

∠GHB = 124°     (Vertically opposite angles)

∠CHB = 56°     (Vertically opposite angles)

Using the angle sum property of triangle, we get

⇒∠BCH + ∠CHB + ∠HBC = 180°

⇒90° + 56° + ∠HBC = 180°

⇒∠HBC = 34°

∠GBH = 44°    (Straight line angle)

∠HGB = 12°     (Angle sum property of triangle)

Hence, order of the angles from the least measure to greatest measure is ∠HGB, ∠ECD, ∠FGH and ∠GBH.

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The length of an arc, s, intersected by a central angle of 3 radians in a circle with a radius of 4 in. is s = three-fourths inches.

The length of the arc is the distance between the two points lying on a curve.

We know that the 2 radian is 360°, therefore, it will cover the complete circumference of the circle. Now, calculating the value of 1 radian,

\(2\pi\) \(radian=2\pi r\)

\(1\) \(radian=\frac{2\pi r}{2\pi }\)

\(1\) \(radian=r\)

As we know the value of 1 radian, therefore, to find the value of 3 radians simply multiply it by 3,

\(1\) \(radian=r\)

\(3\) \(radian=3*r\)

\(3\) \(radian=3r\)

We know the value of the radius of the circle, therefore,

\(3\) \(radian=3r\)

\(3\) \(radian=3*4\) \(in.\)

Hence, the length of an arc, s, intersected by a central angle of 3 radians in a circle with a radius of 4 in. is s = three-fourths inches.

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Answer:

ANSWER IS D ON EDGE 23'

Step-by-step explanation:

GUY ABOVE IS WRONG THE ANSWER IS s=4x3

Answer:

Let me hep you then :)

Step-by-step explanation:

7/9 x 3/7 = 1/3 or 0.3

Have a nice day <3

Answer:

Fraction Form = 1/3

Decimal Form= 0.3 repeating or just 0.3

Step-by-step explanation:

Heres a free Quote  for you- “Believe you can and you're halfway there.”

Ally will be able to cover 285 miles for the trip

Ally wants to rent the car for one day

The rents costs $35 and $0.35 per mile

Ally has $134.75 to spend for the trip

The number of miles Ally can drive for the trip can be calculated as follows

134.75 - 35

= 99.75

99.75/0.35

= 285

Hence Ally will be able to drive 285 miles for the trip  

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Answer:

48÷4=g

Step-by-step explanation:

Answer:

g=48 divided by 4

Step-by-step explanation:

Answer:

-2w-18

Step-by-step explanation:

first get rid of the () by multiplying. -3w-18+w then combine like terms. -2w-18

Answer:

-3(w+6)+w

-3w-3×6+w

-2w-18

or

-2(w-9)

Answer:

C; D; E

Step-by-step explanation:

✔️Angles in a straight line = 180°

Therefore, m<5 + m<6 = 180° is correct.

✔️Exterior angle of a triangle = the sum of the opposite interior angels based on the exterior angle theorem of a triangle.

Therefore,

m<2 + m<3 = m<6 is correct.

✔️The sum of m<2 + m<3 + m<5 = 180° is correct. This is true based on the sum of triangle theorem.

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Answer:

B: 3/4a + 1/2b - 3

Step-by-step explanation:

Answer:

y>= -27/16

Step-by-step explanation:

I just put in the calculator

Answer:

B)  Write out the relation in an x-y table and check that each x-value corresponds to the only one x - value

Answer: 227

Step-by-step explanation:

To find the 46th term of the sequence, we need to first determine the pattern of the sequence. We can see that the sequence increases by 5 between each consecutive term. Therefore, the common difference of the sequence is 5.

Using this information, we can find the \(n\)th term of the sequence using the formula:

\(\Large \boxed{an = a1 + d(n-1)}\)

where

Using the given terms, we have:

To find the 46th term, we substitute \(n = 46\) into the formula:

Therefore, the 46th term of the sequence is 227.

________________________________________________________

To find the pattern in the sequence, we can observe that each term is obtained by adding 5 to the previous term. Therefore, we can write the recursive formula for the sequence as:

\(\large a_1 = 2\)

\(\large a_n = a_{n-1} + 5\)

To find the 46th term, we can use the recursive formula to generate each term until we reach the desired term:

\(\large a_1 = 2\)

\(\large a_2 = a_1 + 5 = 2 + 5 = 7\)

\(\large a_3 = a_2 + 5 = 7 + 5 = 12\)

\(\large a_4 = a_3 + 5 = 12 + 5 = 17\)

\(\vdots\)

\(\large a_{46} = a_{45} + 5 \approx \boxed{227}\)

\(\therefore\) The 46th term of the sequence is approximately 227.

We can also write the explicit formula for the sequence as:

\(\large a_n = 5n - 3\)

To verify that this formula generates the same sequence as the recursive formula, we can substitute the value of n = 1, 2, 3, etc. and compare the results.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

The age of Michelle is 30 years old (option A).

The mathematical operation that would be used to determine the required value is multiplication. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is ×.

The first step is to determine Fiona's age.

Fiona's age = Madeline's age x 2

Fiona's age = 5 x 2 = 10

The second step is to determine Michelle's age.

Michelle's age = Fiona's age x 3

Michelle's age = 10 x 3

Michelle's age = 30

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An 86 grade is typically a B+ letter grade in most educational systems that use a letter grade system. It is also sometimes considered a 3.3 on a 4.0 scale.

In most educational systems, a grade is a number or letter that represents the level of achievement of a student in a particular course or subject. The most common grading systems used in schools and universities are the letter grade system and the numerical grade system.

In the letter grade system, grades are typically assigned as A, B, C, D, or F. The numerical scale most commonly used is a 4.0 scale, where an A is equal to 4.0, a B is equal to 3.0, a C is equal to 2.0, and so on.

An 86 grade is considered a B+ letter grade in most educational systems that use a letter grade system. It is also sometimes considered a 3.3 on a 4.0 scale, which is just above a B but below an A-. This grade usually indicates that the student has performed well in the course, but not quite at the level of an A student.

It's important to note that the grading system and the grades cut offs could vary from school to school, college to college, and country to country. Some schools use a different grading system and different grade cut-offs.

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Answer:

its 8

Step-by-step explanation:

4/5 ÷ 1/10

4×10/5×1=40/5

8×5/1×5=8/1=8

hope this helps

Answer:

8

Step-by-step explanation:

turn division into mulitplictaion the mulitplie

Answer:

B. a^3√a

Explanation: I got it right

Answer:

\(a^{3}\sqrt{a}\)

Step-by-step explanation:

Answer in question

True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

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The formation's height is 31 meters to the closest meter.

In mathematics, height is defined as the vertical distance between an object's top and bottom. It is also referred to as 'altitude.' The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry.

Height, altitude, and elevation all refer to the vertical distance between the top and bottom of something or between a base and anything above it. Height is a standard bodily measurement that is commonly measured in feet (ft) + inches (in) in the United States and centimeters (cm) abroad. Because they are length measurements, the SI unit would be meters.

We can use the tangent function to calculate the formation's height, h.

tan ( 36°) = h/43

Here, we have to multiply both sides by 43 we get,

43tan (36°)= h

h=31m

Therefore, the height of the formation to the nearest meter is 31m.

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Answer: 120

Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question

25 x 4.8 = 120

After answering the presented question, we can conclude that As a equation result, the mass of   \(9.3 \times 1024\) glucose molecules is roughly \(2777.4\) grammes.

Glucose has a molecular weight of about  \(180\) grammes per mole (g/mol).

To calculate the mass of  \(9.3\times 1024\) glucose molecules, we must first determine the number of moles of glucose in   \(9.3 \times 1024\) molecules. We can achieve this using Avogadro's number:

Every substance contains \(6.022 \times 10^2^3\) molecules in 1 mole.

As a result, the number of moles of glucose in \(9.3x10^2^4\)  molecules is as follows:

\(15.43 moles = 9.3\times 1024\) molecules / \(6.022 \times 1023\) molecules/mol

Using its molecular weight, we can then compute the mass of \(15.43\) moles of glucose:

Mass = number of moles multiplied by molecular weight

\(15.43 mol \times 180 g/mol = mass\)

\(2777.4\)gramme mass

Therefore, the mass of  \(9.3 \times 1024\) glucose molecules are roughly \(2777.4\)grammes.

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Answer:

√61

Step-by-step explanation:

→ Find the distance between y coordinates

2 --4 = 6

→ Find distance between x coordinates

2--3 = 5

→ Find distance

√6² + 5² = √36 + 25 = √61

A four-dimensional hypercube is bipartite, and it can be colored with a blue-red coloring scheme.

A four-dimensional hypercube, also known as a tesseract, is a geometric shape in four dimensions that extends the concept of a cube in three dimensions. It can be visualized as a cube within a cube, connected by edges.

To determine if the four-dimensional hypercube is bipartite, we need to check if it is possible to color its nodes with two colors (e.g., blue and red) such that no two adjacent nodes have the same color.

In the case of a four-dimensional hypercube, it is indeed bipartite. We can apply a blue-red coloring scheme as follows:

Start by coloring one vertex (node) with the color blue. Then, assign the color red to all the vertices that are one edge away from the blue vertex. Next, assign the color blue to all the vertices that are two edges away from the blue vertex. Continue this alternating pattern of colors until all the vertices are colored.

Since the four-dimensional hypercube is a regular structure with each vertex connected to exactly four other vertices, this coloring scheme ensures that no two adjacent vertices have the same color, making it bipartite.

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Each cube in the pattern has an area of 3 square inches.

To determine the area of each cube in the pattern, we need to find the area of each rhombus formed by the pattern.

The pattern consists of rhombuses, and we know that the diagonals of each rhombus are 2 inches and 3 inches.

The formula to find the area of a rhombus is given by:

Area = (d1 * d2) / 2,

where d1 and d2 are the lengths of the diagonals.

In this case, d1 = 2 inches and d2 = 3 inches.

Plugging the values into the formula, we get:

Area = (2 * 3) / 2

= 6 / 2

= 3 square inches.

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Answer:

21 Miles. Hope your enjoying Middle School!

Step-by-step explanation:

The straight line that is parallel to 3x + y = -3 and passes through point (3,2) is  y = -3x + 11.

We find the slope of the given line: 3x +  y= -3 can be rearranged to y = -3x - 3, which is in the slope-intercept form y = mx + b. The slope of this line is -3.

Since parallel lines have the same slope, the slope of the line we are looking for is also -3.

We use the point-slope form of an equation, y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through.

Plug in the values we have: y - 2 = -3(x - 3)

We simplify the equation: y - 2 = -3x + 9 => y = -3x + 11

Therefore, the equation of the line parallel to 3x +y=-3 through the point (3,2) is y = -3x + 11.

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I'll assume the ODE is

\(y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}\)

Solve the homogeneous ODE,

\(y'' - 3y' + 2y = 0\)

The characteristic equation

\(r^2 - 3r + 2 = (r - 1) (r - 2) = 0\)

has roots at \(r=1\) and \(r=2\). Then the characteristic solution is

\(y = C_1 e^x + C_2 e^{2x}\)

For nonhomogeneous ODE (1),

\(y'' - 3y' + 2y = e^x\)

consider the ansatz particular solution

\(y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x\)

Substituting this into (1) gives

\(a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1\)

For the nonhomogeneous ODE (2),

\(y'' - 3y' + 2y = e^{2x}\)

take the ansatz

\(y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}\)

Substitute (2) into the ODE to get

\(b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1\)

Lastly, for the nonhomogeneous ODE (3)

\(y'' - 3y' + 2y = e^{-x}\)

take the ansatz

\(y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}\)

and solve for \(c\).

\(ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16\)

Then the general solution to the ODE is

\(\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}\)

Answer:

1/17 + 4i/17

Step-by-step explanation: