Find the critical points of the autonomous differential equation dy /dx = y 2 − y 3 , sketch a phase portrait, and sketch a solution with initial condition y(0) = 4

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

The answer is B because of the graph being 1/2

Given:

The figure of a right angle triangle.

To find:

The value which is equal to r÷q.

Solution:

In the given right triangle, the length of the hypotenuse is q units.

For angle x degrees, perpendicular is p units and base is r units.

For angle y degrees, perpendicular is r units and base is p units.

In a right angle triangle,

\(\sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)

\(\cos \theta=\dfrac{Base}{Hypotenuse}\)

So,

\(\sin y=\dfrac{r}{q}\)

\(\cos x=\dfrac{r}{q}\)

Therefore, the value of r÷q is equal to siny or cosx. So, the correct option is C.

The answer to this problem is cos x since sin y is not in the options

Data;

To solve this problem, we have to identify that for angle y, r is the opposite and q is the hypothenuse.

\(sin y = \frac{r}{q}\)

for angle x, r is the adjacent and q is the hypothenuse

\(cos x = \frac{r}{q}\)

The answer to this problem is cos x since sin y is not in the options.

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Answer:

53

Step-by-step explanation:

c=42+11

c=53

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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By the Work out the  estimate for the value of 92 × 1.63 is approximately equal to 180.

To calculate an estimate for the value of 92 × 1.63, we can use the rounding method.

Rounding means to replace a number with another number that is approximately equal to it and has fewer digits.

For example, we can round 1.63 to 1.6 and 92 to 90, as follows:

92 × 1.63 ≈ 90 × 1.6

To get an estimate of the value 92 × 1.63, round the number to the nearest integer and perform the multiplication.

Round 92 to the nearest integer:

92 ≈ 90

Round 1.63 to the nearest integer:

1.63 ≈ 2

Multiplied and rounded numbers:

90 × 2 = 180

So the estimate for the value of 92 × 1.63 is 180.

We can also use the multiplication table to get an approximate answer as follows:

90 × 2 = 180, 90 × 1.5 = 135, and 90 × 0.1 = 9

Thus, 92 × 1.63 is approximately equal to 180.

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Answer:

V=L x W x H

(4.7)(5.2)(4.7)(5)

=574.34 inch

Answer:

the answer is 140.6

Step-by-step explanation:

got it right on quiz

The coordinates of X'' is (-4, 7) after the transformation

From the question, we have the following parameters that can be used in our computation:

X = (4, -7)

Then, we have the transformations to be

X'' = R y axis (R x axis(X))

This transformation means that

Mathematically, this is represented as

(x, y) = (-x, -y)

Substitute the known values in the above equation, so, we have the following representation

(x, y) = (-4, 7)

Hence, the image is (-4, 7)

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Answer:

The sheet should be turned up 7.5cm on each side to obtain maximum volume.

Step-by-step explanation:

If we make a rectangular eavesdrop, by bending the sheet along dotted line, then.

Height of eaves trough = x cm

Length of eaves trough = 600 cm

Width of eaves trough =  (30 - 2x) cm

We know that Volume is given by:

V = Length · Width · Height

V = (x)(30 - 2x)(600)

V = -1200x² + 18000x

To maximize the volume, we take the derivative and put it equal to zero.

\(\frac{dV}{dx} =\frac{d}{dx}( -1200x^2 +18000x)=0\\\frac{d}{dx}( -1200x^2 +18000x) = 0\\-(2)1200x+18000=0\\-2400x+18000=0\\x=\frac{18000}{2400}\\ x=7.5cm\)

Greetings from Brasil...

Let's place the triangle in a Cartesian Plane - see attached figure.

We have:

A(1; 2)

B(3; 1)

C(6; 3)

1 - rotation

Specifically for a 90° rotation, we will use the expression

then

A'(-2; 1)

B'(-1; 3)

C'(-3; 6)

2 - translation

For a translation, we will add n units in all coordinates. (instead of adding, we could too subtract)

Let's consider n = 2, so

A''(3; 4)

B''(5; 3)

C''(8; 5)

3 - reflection

No way. We have to draw the original figure and reflect it.  Let's use the Y axis as the reflection axis.

See the attachments

Answer:

See attachments.

Step-by-step explanation:

Rotation, translation and reflection are all examples of transformations  A transformation is a way by which the size or position of a shape is changed.

(See attachment 1)

Rotation turns a shape around a fixed point called the center of rotation.

(See attachment 2)

A translation moves a shape left, right, up or down.

Every point on the original shape is translated (moved) the same distance in the same direction.

(See attachment 3)

A shape can be reflected across a line of reflection.

Every point on the reflected shape is the same distance from the line of reflection as the corresponding points on the original shape.

The lines joining the points on the original shape and the corresponding points on the reflected shape are perpendicular to the line of reflection.

All three transformations have been drawn on one grid in attachment 4.

The Law of Large Numbers is a fundamental concept in probability theory and statistics stating the number of trials of a random event increases, the average of the outcomes approaches the expected value of the event. It's better to use 500 trials.

In other words, as we repeat an experiment a large number of times, the proportion of times that a certain outcome occurs will converge to its probability of occurrence. This is an important concept in statistical inference, as it helps to ensure that the results of a sample are representative of the population from which it was drawn.

Now, if you were using the relative frequency of an event to estimate the probability of the event, it would be better to use 500 trials rather than 100 trials. The reason is that the larger the number of trials, the more accurate the estimate of the probability is likely to be.

Using a larger sample size reduces the impact of random variation and provides a more precise estimate of the true probability. The Law of Large Numbers tells us that as the sample size increases, the relative frequency of the event should converge to the true probability, so a larger sample size will generally give a more reliable estimate

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The number on the third term and the eleventh term will be 22 and 46, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

In a game, the number of dominos in different lines structures an A.P. Assuming that the quantity of dominos in the third and eleventh cell together is 68 and the quantity of dominos in the eleventh cell is 24 a bigger number than of the third cell.

Let 'x' be the third number and 'y' be the eleventh number. Then the equations are given below.

x + y = 68          ...1

y = x + 24          ...2

From equations 1 and 2, then we have

x + x + 24 = 68

2x = 44

x = 22

Then the value of the variable 'y' will be given as,

y = 22 + 24

y = 46

The number on the third term and the eleventh term will be 22 and 46, respectively.

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The first law of thermodynamics, mathematically expressed as:

ΔU = Q - W

Where:

ΔU represents the change in internal energy of the system,

Q represents the heat added to the system, and

W represents the work done by the system.

The first law of thermodynamics, also known as the law of energy conservation, states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The term "internal energy" (ΔU) refers to the total energy possessed by the system, including the kinetic and potential energy of its molecules. It is a measure of the system's thermal energy.

The term "heat" (Q) represents the transfer of energy between the system and its surroundings due to temperature difference. It is a form of energy transfer that occurs spontaneously from higher temperature regions to lower temperature regions.

The term "work" (W) represents the energy transfer resulting from forces applied to the system, causing displacement. It can take different forms, such as mechanical work, electrical work, or expansion work.

For different scenarios, the explicit form of the energy balance equation can be derived by considering the specific types of work and heat involved in the system. By drawing appropriate schematics, one can identify the relevant forms of work and heat transfer. Examples include:

Adiabatic Process: In this scenario, no heat transfer occurs (Q = 0). The energy balance equation simplifies to ΔU = -W, where the work done by the system contributes to the change in internal energy.

Isothermal Process: In this case, the temperature remains constant (ΔU = 0). The energy balance equation becomes Q = W, indicating that the heat added to the system is fully converted into work.

Isobaric Process: Here, the pressure remains constant. The energy balance equation can be written as ΔU = Q - PΔV, where P is the constant pressure and ΔV is the change in volume. This equation accounts for both heat transfer and work done against the constant pressure.

Therefore, by applying appropriate schematics and considering the specific conditions of a given scenario, one can deduce the explicit form of the energy balance equation and understand the interplay between heat, work, and the change in internal energy.

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Hence, at the stage \(1,073,741,824\) it reached nearest to \(1,000,000,000\).

What is the circle?

A circle is a round-shaped figure that has no corners or edges.

In geometry, a circle can be defined as a closed, two-dimensional curved shape.

So, the calculation is:-

Now, Multiplying by \(2\)

\(2 * 2 = 4\)

\(4 * 2 = 8\)

\(8 * 2 = 16\)

\(16 * 2 = 32\)

\(32 * 2 = 64\)

\(64 * 2 = 128\)

\(128 * 2 = 256\)

\(256 * 2 = 512\)

\(512 * 2 = 1,024\)

\(1,024 * 2 = 2,048\)

\(2,048 * 2 = 4,096\)

\(4,096 * 2 = 8,192\)

\(8,192 * 2 = 16,384\)

\(16,384 * 2 = 32,768\)

\(32,768 * 2 = 65,536\)

\(65,536 * 2 = 131,072\)

\(131,072 * 2 = 262,144\)

\(262,144 * 2 = 524,288\)

\(524,288 * 2 = 1,048,576\)

\(1,048,576 * 2 = 2,097,152\)

\(2,097,152 * 2 = 4,194,304\)

\(4,194,304 * 2 = 8,388,608\)

\(8,388,608 * 2 = 16,777,216\)

\(16,777,216 * 2 = 33,554,432\)

\(33,554,432 * 2 = 67,108,864\)

\(67,108,864*2 = 134,217,728\)

\(134,217,728* 2 = 268,435,456\)

\(268,435,456 * 2 = 536,870,912\)

\(536,870,912* 2 = 1,073,741,824\)

Hence, at the stage \(1,073,741,824\) it reached nearest to \(1,000,000,000\).

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The area of the shaded rectangle is 18 square units.

The shaded region is the framed rectangle, and the white part is the frame.

We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:

Now, if we remove the frame, we will remove 2*2 units = 4 units for each measure (because for each measure we have the frame in both sides).

So the measures for the shaded rectangle are:

And the area of a rectangle is given by the product between the width and length, then we have:

A = (3 units)*(6 units) = 18 square units.

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Answer:2479

Step-by-step explanation: subtract 2,994 and 515 and you would get 2479

Answer: 3509 treats

Step-by-step explanation:

If I'm understanding correctly, we need to add the desserts together right?

\(2994+515\\=3509\)treats in total

Answer:

y=-1/2x+0

Step-by-step explanation:

First, find the slope by choosing two points and counting up and over (rise over run). Then, find where the line crosses the y-axis to get the y-intercept.

For the two points, let's choose (0,0) and (-2,1). You can either count up and over to get slope, or you can use the slope formula which is y2-y1/x2-1x.

1-0/-2-0 = -1/2.

Since this line represents a negative slope, your slope is -1/2.

Now, looking at the graph, you can see that the line crosses the y-axis at 0. This is your y-intercept.

Answer:

the answer is c. y=3x-6

Step-by-step explanation:

The answer is C. when you plug in your equation you should get a decimal but make sure to round up or down to the nearest WHOLE number so it would be C.

Answer: Option A is correct, What is the average time a car is in the system?

Answer: 1/30-24= ⅙ * 60 min =10 min

Step-by-step explanation:

Answer:

3.75 cups of flour

2.5 cups of sugar

1.25 cups of butter

Step-by-step explanation:

Hello!

Let the amount of sugar used be x:

The total sum of ingredients should be 7.5 cups, so we can add x, 1.5x, and 0.5x and set it to 7.5.

Clifford needs 2.5 cups of sugar.

The amount of flour can be found by multiplying 2.5 by 1.5: 3.75 cups

The amount of butter can be found by multiplying 2.5 by 0.5: 1.25

Clifford needs 3.75 cups of flour, 2.5 cups of sugar, and 1.25 cups of butter.

Answer:

f² - 11f - 12

Step-by-step explanation:

(f-12)(f+1) = f² + 1f - 12f - 12

The probability that the mean IQ score of a sample of 40 people falls between 95 and 99 can be calculated using the central limit theorem.

According to the central limit theorem, the distribution of sample means approximates a normal distribution, regardless of the shape of the population distribution, when the sample size is large enough.

In this case, the sample size is 40, which is considered large enough for the central limit theorem to apply. The mean of the sample means is equal to the population mean, which is 100. The standard deviation of the sample means, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size, i.e., 15/√40.

To find the probability, we need to calculate the z-scores for the lower and upper limits of the desired range and then find the corresponding probabilities from the standard normal distribution table. The z-score for 95 is calculated as (95 - 100) / (15/√40) = -2.041, and the z-score for 99 is calculated as (99 - 100) / (15/√40) = -0.447.

Using the z-scores, we can find the corresponding probabilities from the standard normal distribution table. The probability that the mean IQ score of the sample is between 95 and 99 is then equal to the probability of the z-score being between -2.041 and -0.447. By looking up these z-scores in the standard normal distribution table, we find that the probability is approximately 0.104.

Therefore, the correct answer is (a) 0.104.

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The number of cakes Jas can make in an hour are 55/12 cakes.

It is given in the question that it takes Jas 2/5 hours to make 11/6 cakes.

We have to find the number of cakes made by Jas in an hour.

All we had to do in this question is multiply the numbers of hours by its reciprocal to get 1 hour.

Hence, according to the data given in the question, we can write,

Number of cakes made by Jas in (2/5)*(5/2) hour = 1 hour = (11/6)*(5/2) = 55/12 cakes.

Hence, the number of cakes made by Jas in an hour is 55/12 cakes.

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Answer:

36

Step-by-step explanation:

6 to the second power or 6^2 is equivalent or equal to 36, 6x6, 36/1, 36/36

Or if you were looking for just the answer, 36.

Hope that helped (lol)

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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Answer:

sum the previous two terms and then multiply

The formula to calculate the distance:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute and solve:

d = √(-5(-2))² + (-4-1)²

d = √7² + (-5)² = √49 + 25

d = √74 ====> Alternative "A"