consider the differential equation dp dt = f(p) where f(p) = −0.4p3 − 1.6p + 3.6.

The particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

What is differential equation?

Differential equations are used to model a wide range of phenomena in science, engineering, and mathematics, including physics, chemistry, biology, economics, and engineering.

Integration is a mathematical concept and technique used to find the integral of a function. The integral of a function is a measure of the area under the curve of the function, between two specified points on the x-axis.

To find the particular solution to the differential equation

[tex]\frac{dy}{da} = (a+1)(y+1)[/tex]

with the initial condition y(4) = 3, we can use separation of variables:

[tex]\frac{dy}{y+1} = (a+1) da[/tex]

Integrating both sides:

[tex]\int \frac{dy}{y+1} = \int (a+1) da\ln |y+1| = \frac{1}{2}a^2 + a + C_1, \text{ where } C_1 \text{ is an arbitrary constant of integration}[/tex]

Solving for y, we get:

[tex]y+1 = Ce^{\frac{1}{2}a^2 + a}[/tex]

where C is another arbitrary constant of integration. We can solve for C using the initial condition y(4) = 3:

[tex]3+1 = Ce^{\frac{1}{2}(4^2) + 4}C = 4e^{10}[/tex]

Substituting back, we get:

[tex]y+1 = 4e^{\frac{1}{2}a^2 + a + 10}y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

Therefore, the particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

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Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

Probability that is established using logic is known as theoretical probability.

Experimental probability is calculated based on the outcomes of numerous iterations of an experiment.

A probability is a number that falls between (and includes) 0 and 1.

If the likelihood of a situation E is represented by P(E), then:

Given:

Total marbles in  bag = 12

theoretical probability P(E) = favourable outcome / total outcome

P(red marble) = 5/12

Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

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Step-by-step explanation:

6.3    goes to  2.52

6.3 : 2.52   = 2.5 :1  = 5 : 2

Answer:

3 one

Step-by-step explanation:

The experimental probability of choosing the name Maya is [tex]23/118[/tex].

and theoretical probability is of choosing name maya is [tex]1/5[/tex]

Probability is a measure of how likely an event is to occur. Many events are impossible to forecast with absolute accuracy. We can only anticipate the possibility of an event occurring, i.e. how probable they are to occur, using it. Probability can range from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of all events in a sample space equals one.

According to the given information:

The experimental probability = [tex]\frac{Number of times an event occur}{ Total number of trials}[/tex]

Here total trials = 118,

The number of times the name maya has been chosen =23 times.

Therefore, experimental probability = [tex]\frac{23}{118}[/tex].

Theoretical probability = [tex]\frac{Number of favourable outcome}{Number of possible otucome}[/tex]

favourable outcome = 1 (Maya)

Possibleble outcome = 5 (Total no of Names in a hat)

And the theoretical possibility of the name maya has been chosen is [tex]1/5[/tex]

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Vertical angles are a pair of opposite angles formed by two intersecting lines. Vertical angles are congruent, meaning they have the same measure.

For example, if two lines intersect and form four angles, the two angles that are opposite each other  are vertical angles.

Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

In other words, they share a ray or line segment, but they don't share any interior points.

Adjacent angles may or may not be congruent, depending on their measurement.

For example, if two angles are next to each other and share a vertex and a side, they are adjacent angles.

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As per the number of gym machines, the type of data is b. quantitative discrete data.

A discrete quantitative variable has a distinct quantitative meaning but can only take particular integer values rather than any value within a period. The number of needle sticks, the number of births, and the number of hospitalisations are a few examples of discrete numeric factors.

Similarly to that, the information given in the question refers to the quantity of gym equipment, which qualifies as quantitative data because it is a numerical assessment. Furthermore, rather than representing a continuous range of values, the data is discrete, which means that it reflects a limited collection of whole integers such as 10, 12, 15, 20, and 22. These numbers are the total number of gym machines that are available.

Complete Question:

the data are the number of machines in a gym. you sample five gyms. one gym has 12 machines, one gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines. what type of data is this?

a. Qualitative data

b. Quantitative discrete data

c. Discreet data

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Answer:

15.625 inches^3

Step-by-step explanation:

The volume of a cube is a simple calculation:

V=a^3

"a" is any edge of the cube.

Therefore, it would be (2.5^3), which would be 15.625 inches^3

The general solution of the given higher-order differential equation is y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2)).

To find the general solution of the given higher-order differential equation, first, let's rewrite the equation in a more standard form:
16y'''' + 16y'' + 4y = 0
Now, we'll solve this fourth-order linear homogeneous differential equation using the characteristic equation method.
1. Write the characteristic equation:
16r^4 + 16r^2 + 4 = 0
2. Divide the equation by 4 to simplify:
4r^4 + 4r^2 + 1 = 0
3. Apply a substitution: let t = r^2, then the equation becomes:
4t^2 + 4t + 1 = 0
4. Solve the quadratic equation for t using the quadratic formula:
t = (-B ± √(B^2 - 4AC)) / 2A
t = (-4 ± √(4^2 - 4(4)(1))) / (2 * 4)
t = (-4 ± √(16 - 16)) / 8
t = -4/8 = -1/2
5. Substitute back r^2 for t:
r^2 = -1/2
6. Solve for r:
r = ±√(-1/2)
r = ±(1/√2)i
7. Since the roots are complex conjugates, the general solution can be written as:
y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2))
where A and B are arbitrary constants determined by the initial conditions of the problem.

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The equation of the line parallel to the line shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3) and the equation of the line perpendicular to the line shown in the graph passing through the point (-2, 3) is y = (-3/2)x.

What is slope?

The slope of a line passing through two points [tex](x_1, y_1) \: and \: (x_2, y_2)[/tex] is given by slope = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Given line passes through (0,-6) and (9,0)

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.

The slope of the line passing through (0,-6) and (9,0) can be found using the slope formula

slope = (change in y) / (change in x)

= (0 - (-6)) / (9 - 0)

= 6 / 9

= 2/3

Therefore, any line parallel to this line will also have a slope of 2/3.

We can now use the point-slope form of a line to find the equation of the line passing through (-2,3) with a slope of 2/3:

y - y1 = m(x - x1) (point-slope form)

where m is the slope, and (x1,y1) is a point on the line.

Substituting the values, we get:

y - 3 = (2/3)(x - (-2))

y - 3 = (2/3)(x + 2)

y - 3 = (2/3)x + (4/3)

y = (2/3)x + (4/3) + 3

y = (2/3)x + (13/3)

Therefore, the equation of the line parallel to the line passing through (0,-6) and (9,0) shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3).

Using the points (0,-6) and (9,0), we can find the slope of the original line:

slope = (0 - (-6)) / (9 - 0) = 6/9 = 2/3

The slope of any line perpendicular to this line will be the negative reciprocal of this slope. So, the slope of the perpendicular line will be:

perpendicular slope = -1 / (2/3) = -3/2

Now we have the slope of the perpendicular line, and we also have a point it passes through: (-2, 3). We can use the point-slope form of a line to write the equation of the perpendicular line: y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is the point it passes through. Plugging in the values we have, we get:

y - 3 = (-3/2)(x - (-2))

Simplifying:

y - 3 = (-3/2)x - 3

y = (-3/2)x + 0

So the equation of the line perpendicular to the line passing through (0,-6) and (9,0), and passing through (-2, 3), is y = (-3/2)x.

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Answer:

A

Step-by-step explanation:

Given:

r (radius) = 2 in

h (height) = 8 in

Find:

A (surface area) - ?

.

First, we have to find the lateral area of the cylinder:

[tex]a(lateral) = 2\pi \times r \times h = 2 \times π\times 2 \times 8 = 32\pi \: {in}^{2} [/tex]

Now, let's find the area of both bases (since a cylinder has 2 identical bases, we have to multiply the area of one base by 2):

[tex]a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times π\times {2}^{2} = 8\pi \: {in}^{2} [/tex]

In order to find the surface area, we have to add both lateral and bases' areas together:

[tex]a(surface) =32\pi + 8\pi = 40\pi \: {in}^{2} [/tex]

Answer:

The answer to your problem is, 4.51 or in option terms A. 4

Step-by-step explanation:

A=π [tex]R^{2}[/tex]

d = 2 r

We would need to solve for D

d = 2 [tex]\sqrt{\frac{A}{tt} } = 2 x \sqrt{\frac{16}{tt} }-around- 4.51352-or-4.51[/tex]

Thus the answer to your problem is, 4.51 or A. 4

Answer:

D. 20 in by 30 in by 10 in

Step-by-step explanation:

The rest of them would equal 600 in³ but answer choice D when multiplied together equaled 6,000 in³.

The area of the triangles are:

Triangle 1: 144√3 unit²

Triangle 2: 64√3 unit²

The area of a triangle is given by the formula:

A = 1/2 * b * h

where b is the base and h is height of the triangle

1st triangle:

The vertical line divides the base into two right triangles.

Considering the right triangle to the right. Let L represent the length of the base. Thus, we can say:

tan 60° = (12√3)/L

√3 = (12√3)/L

(√3)L = 12√3

L = 12

Since b = 2* L

b = 24 units

A = 1/2 * 24 * 12√3

A = 144√3 unit²

2nd triangle:

cos 60° = L/16

0.5 = L/16

L = 0.5 * 16

L = 8 units

b = 2 * 8 = 16 units

h = √(16² - 8²)    (Pythagoras)

h = 8√3 units

A = 1/2 * 16 * 8√3

A = 64√3 unit²

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To make the larger sculpture with each linear dimension 75% greater, the artist needs to use 265.625% or 3.65625 times more clay than the original sculpture.

Let's assume that the original sculpture is a cube with side length x cm. Therefore, its volume would be x³ cm³.

To make the larger sculpture, each linear dimension needs to be increased by 75%, which means that each side length will become 1.75x cm. Thus, the new volume of the sculpture will be (1.75x)³ = 5.378125 x³ cm³.

To find the amount of clay required to make the larger sculpture, we need to find the ratio of the new volume to the original volume (5.378125 x³ cm³) / (x³ cm³) = 5.378125

This means that the artist needs to use 5.378125 times more clay than the original amount used to make the larger sculpture.

Therefore, to find the actual amount of clay needed, we multiply the original amount of clay by 5.378125: n cm³ x 5.378125 = 5.378125n cm³

So, the artist needs to use 3.65625 or 265.625% times more clay than the original sculpture to make the larger sculpture with each linear dimension 75% greater.

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Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

We can solve mathematical equations thanks to algebra's inherent characteristics. Take note that both addition and multiplication adhere to these characteristics.

This Order of Operations is a set of rules that enables mathematicians to solve issues uniformly. In this order:

using the algebraic formula:

(a² - b²) = (a + b)(a - b)

Given expression:

= 1 - 4sin²a

This can be written as:

= 1² - (2sina)²

Now, using identity:

= (1 + 2sina)(1 - 2sina)

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

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Complete question-

Express the given as the product of both values.

1 - 4sin²a

Answer:

[D] No, it is not a polynomial

Step-by-step explanation:

Polynomial- (Have)

Polynomial -(Can't/Don't)

There are 3 different types of polynomials:

As we can see based on the given;

5x²y⁴ + x√3 isn't a polynomial.

As a result, the answer is [D] No, it is not a polynomial

RevyBreeze

option (c) -No, 20 is NOT a reasonable solution because at x=-20,

an equation in which highest power of variable is always 1.

by solving the equation -6+2log(-5x)=-2 :

-6 + 2log(-5x) = -2

2log(-5x) = 4

log(-5x) = 2

-5x = 10^2

-5x = 100

x = -20

So, we found that x = -20 satisfies the equation. However, we need to check whether it is a reasonable solution or not.

Option C is correct: -20 is NOT a reasonable solution because at x = -20, the logarithm is not defined. The logarithm function is defined only for positive real numbers.

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Regenerate response

Answer: 216

Step-by-step explanation:

Brainliest pls:)

Answer:

20

Step-by-step explanation:

7 computers every 5 printers

7/5 = 28/x

Cross multiply

7x = 5*28

7x = 140

x = 20

Or in words,

7 times 4 is 28

5 times 4 is 20, which is your answer

No , because 7 t shirts will cost 56 $ in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have $50 to buy T-shirts.

You can buy 3 T-shirts for $24.

                 You can buy 1 T-shirts for = 24/3 = 8

then 3 + 3 = 6 = 24 + 24 = 48 + 8 =  $56

so, you don't buy 7 t - shirts because you have only $56 .

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Answer:

44

Step-by-step explanation:

come on now.

the perimeter is

2×length + 2×width = 110

width = 4×length

so, we use the second equation in the first :

2×length + 2×(4×length) = 110

2×length + 8×length = 110

10×length = 110

length = 110/10 = 11

width = 4×length = 4×11 = 44

Answer:

x ≈ 8.0

Step-by-step explanation:

Using the tangent of the angle is equal to the opposite over the adjacent

tan(37º) = 6/x

x = 6/tan(37º)

x=7.96226892972

Answer:

Step-by-step explanation:

3 divided by 3/4 can be changes to multiplication

We can solve the equation like 3*4/3

3 divided by 3/4 is 4

Then answer and explanation is in the doc below.

Answer:

  7. shifted right 8 units

  8. shifted left 4 and up 12 units

  9. shifted up 8 units

Step-by-step explanation:

You want to compare the given functions with p(x) = a(x -h)² +k and tell the value and effect of a, h, and k on the vertex.

In the equation for p(x) above, the value 'a' represents a vertical scale factor. It expands the graph vertically by the factor 'a'. If a < 0, the graph is reflected across the x-axis.

The values 'h' and 'k' in the equation for p(x) represent a right shift of the graph by 'h' units and a shift up by 'k' units. That is, the graph is translated by (h, k).

We have h = 8. The graph is shifted right 8 units.

We have (h, k) = (-4, 12). The graph is shifted left 4 units and up 12 units.

The values of the transformation parameters are a = -1/2 and k = 8. The vertical compression and reflection do not affect the vertex. The vertex is shifted up 8 units.

Answer:

x=2

Step-by-step explanation:

Answer: 6x-12= -72

Step-by-step explanation: 12 is a bigger number than 6 and a negative times a positive is always a negative. 6x12 is already 72 but we have to keep the negative so it becomes -72.

Or if its another equation involving x then it's going to be 2. ;)

We know that the sum of the angles of a triangle is 180 degrees. So, we can find the value of angle LNM as follows:

m/L + m/M + m/N = 180 degrees

Substituting the given values, we get:

40 + 41 + m/N = 180

m/N = 99

Now, we can see that angle LNM is greater than both angles L and M. So, we can conclude that:

OMN > NL > LM