im stuck on this need a bit of help

To find the implicit solution for dy/dx = x^2/(1-y^2), we can start by separating the variables and integrating both sides.

dy/(1-y^2) = x^2 dx

To integrate the left-hand side, we can use partial fractions:

dy/(1-y^2) = (1/2) * (1/(1+y) + 1/(1-y)) dy

Integrating both sides, we get:

(1/2) * ln|1+y| - (1/2) * ln|1-y| = (1/3) * x^3 + C

Where C is the constant of integration.

We can simplify this expression by combining the natural logs:

ln|1+y| - ln|1-y| = (2/3) * x^3 + C'

Where C' is a new constant of integration.

Finally, we can use the logarithmic identity ln(a) - ln(b) = ln(a/b) to get the implicit solution:

ln|(1+y)/(1-y)| = (2/3) * x^3 + C''

Where C'' is a final constant of integration.

Therefore, the implicit solution for dy/dx = x^2/(1-y^2) is ln|(1+y)/(1-y)| = (2/3) * x^3 + C''.

Given the differential equation:

dy/dx = x^2 / (1 - y^2)

To find an implicit solution, we can use separation of variables. Rearrange the equation to separate the variables x and y:

(1 - y^2) dy = x^2 dx

Now, integrate both sides with respect to their respective variables:

∫(1 - y^2) dy = ∫x^2 dx

The result of the integrations is:

y - (1/3)y^3 = (1/3)x^3 + C

This is the implicit solution to the given differential equation, where C is the integration constant.

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Answer:

a. I would put 20 stuffed animals in the bin, out of which 10 would be teddy bears.

So that the probability is 10/20 = 1/2

b. I could remove 8 other animals from 12 to have 4. So that the total number of stuffed animals is 8. 4/8 = 1/2

Step-by-step explanation:

a. Probability =

number of required outcomes / number of possible outcomes

If in the bin there are 10 teddy bears out of 20 stuffed animals,

Then the probability of picking a teddy bear = 10/20 = 1/2.

b. If on returning, there are 4 teddy bears and 12 other animals, I could simply remove 8 of the other animals to have 4 other animals and a total of 8 stuffed animals.

Probability = 4/8 = 1/2

Answer:

C. 1

Step-by-step explanation:

h = r * sin(θ) formula expresses the car's horizontal distance (h) to the right of the center of the race track in terms of θ.

To write a formula expressing the car's horizontal distance (h) to the right of the center of the race track in terms of θ (measured from the 12 o'clock position), you can use the following formula:

h = r * sin(θ)

Here's the step-by-step explanation:

1. Consider the race track as a circle with a radius r.
2. Place the car at an angle θ from the 12 o'clock position.
3. Draw a line from the center of the circle to the car's position (this is the radius, r).
4. Draw a horizontal line from the car's position to the vertical line that passes through the center of the circle.
5. Notice that you have now formed a right triangle, with the horizontal distance h as one of the legs, r as the hypotenuse, and θ as the angle between the hypotenuse and the horizontal leg.
6. Since sin(θ) = opposite side (h) / hypotenuse (r), you can rearrange the formula to find h:

h = r * sin(θ)

This formula expresses the car's horizontal distance (h) to the right of the center of the race track in terms of θ.

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A is the correct answer!

Answer:

the value of x is 5/7 which is in fraction

Answer:  x = 5/7

Step-by-step explanation:  2x/3 + x/2 =5/6

To use a least common denominator, divide LCD by the original denominator and multiply the original numerator by the result.

for 2x/3  6÷3=2  2×2x=4x so that becomes 4x/6

for x/2    6÷2=3  3× (invisible) 1 = 3x, so that becomes 3x/6

combine 4x/6 + 3x/6 = 7x/6  

Back to the original equation, substituting the calculated term:

7x/6 = 5/6   Multiply both sides by 6 to simplify (6)(7x/6) = (6)(5/6) 6's "cancel"

7x = 5 .  Divide both sides by 7 to solve for x  7x/7 = 5/7

x = 5/7

Using Pythagorean theorem, it is proved that BC is the mean proportional between AB and BD in right triangle ABC.

To prove that BC is the mean proportional between AB and BD in right triangle ABC, we need to show that the ratio of BC to AB is equal to the ratio of AB to BD.

Let's denote the length of AB as a, BC as b, and BD as c.

From the definition of mean proportionality, we have the following relationship:

\(b^2 = a * c\)

Now, let's consider triangle ABC and triangle CBD separately.

In triangle ABC:

Using the Pythagorean theorem, we have:

\(AC^2 = AB^2 - BC^2\)

In triangle CBD:

Using the Pythagorean theorem, we have:

\(BD^2 = BC^2 + CD^2\)

Since CD is the altitude to the hypotenuse AB, we know that:

CD * AD = BC * BD

Rearranging the equation:

CD = (BC * BD) / AD

Substituting \(CD^2\) into the equation for \(BD^2\):

\(BD^2 = BC^2 + ((BC * BD) / AD)^2\\BD^2 = BC^2 + (BC^2 * BD^2) / AD^2\\BD^2 = BC^2 + (BC^2 * BD^2) / (AB^2 - BC^2)\)

Now, let's substitute the value of AD from the equation CD * AD = BC * BD:

\(BD^2 = BC^2 + (BC^2 * BD^2) / (AB^2 - BC^2)\\BD^2 * (AB^2 - BC^2) = BC^2 * (AB^2 - BC^2) + BC^2 * BD^2\\BD^2 * AB^2 - BD^2 * BC^2 = BC^2 * AB^2\\BD^2 * AB^2 = BC^2 * (AB^2 + BC^2)\)

Now, we can divide both sides of the equation by \(AB^2\):

\(BD^2 = BC^2 + BC^4\)

Substituting \(BC^2\) with \(a^2\):

\(BD^2 = a^2 + a^4\)

Therefore, BC is the mean proportional between AB and BD in right triangle ABC, as BC = \(\sqrt{a^2 + a^4}\).

This proves that BC is the mean proportional between AB and BD in right triangle ABC.

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An expression that is equivalent to ∛18⁴ is (b) (18)³/⁴

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

∛18⁴

Applying the law of indices, we have

∛18⁴ = (18⁴)¹/³

Evaluate

So, we have

∛18⁴ = (18)³/⁴

Hence, the solution is (18)³/⁴

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A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

Um im not sure

Step-by-step explanation:

Its probly A if im doing it write

Answer:

Step-by-step explanation:

it will always be true as long as it is adittion the r is the unknown number just add 15 plus what equals 25

The answer is Numeric.

What measurement scale is this?

There are mainly two types of variables

Numerical(quantitative): observations that can be measured in numerical form

Agin two types: ratio scale and interval scale

Categorical(qualitative ): named categories

Again two types: Ordinal or nominal

Her in the given an example,

Measured time of race have  numerical observations

The measurement scale is Numeric.

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For this case we have the following variables:

x: represents time, in seconds at the start of the test.

y: represents the speed, in miles per hour.

We have then that:

x = 0 ---> y = 0

x = 12 ---> y = 0

Answer:

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

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Answer: Check out the graph below

The graph is a straight line through the points (0,6) and (1,8)

====================================

Explanation:

Plug in x = 0 to find that...

y = 2x+6

y = 2(0)+6

y = 0 + 6

y = 6

The point (0,6) is on the line

---------

Repeat for x = 1

y = 2x+6

y = 2(1)+6

y = 2 + 6

y = 8

The point (1,8) is also on the line

---------

Now plot the two points together on the same xy grid.

Draw a straight line through the two points. Stretch the line as far as you can in either direction. See below. I used GeoGebra to make the graph. It's a free graphing app.

Desmos is another useful free graphing tool. There are many options if you don't have a graphing calculator.

Answer:

D) maximum height = 26 feet and minimum height = 8 feet

Step-by-step explanation:

100% on edge

Answer:D on edge

Step-by-step explanation:

the guy above is right .

The probability of getting an even number is 1/2 while the probability of getting a factor of 6 is 1/6

The probability of an even number

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of even numbers, x = 3

The probability of getting an even number is then calculated as

P(Even) = Number of even numbers/Sample size

This gives

P(Even) = 3/6 = 1/2

The probability of a factor of 6

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of factor of 6, x = 1

The probability of getting a factor of 6 is then calculated as

P(factor) = Number of factor of 6/Sample size

This gives

P(factor) = 1/6

Hence, the probability is 1/2 and 1/6

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Answer:

x + 3x + 5x = 180

9x = 180

x = 20

20 kg cement, 60 kg sand, 100 kg gravel

Talil does not have enough cement (he has only 15 kg cement--he needs 20 kg cement). He does have enough sand and gravel.

Answer:

Maybe, there is a chance, but I don't know for sure.

It might matter, but I wouldn't worry or stress about it too much.

My only advice to you is do not procrastinate and if you need help don't be afraid to ask.

Answer:

It matters but not like you think.

GPA, extracurricular activities, and SAT/ACT are the biggies. Truthfully it won't change a thing if you took accelerated pre-algebra versus normal. In fact, spoiler alert, the SAT/ACT (I'm assuming your american) will matter more than your courses ever did. I took two years of college physics in highschool and i made more off my SAT. Not only that, but an A in an easy class looks better than a C in a hard one on transcripts.

My advise is slow down, relax, and learn it well. Better to learn the concept fully in normal so that you can apply it, than half learn it in advance and struggle in future applications. After all, math ALWAYS builds. Take it slow, take it easy.

I would recommend talking to a school guidance counselor about your academic stress. Im sure their professional insight will help put you at ease. It may also help to get you going in the right direction so that you achieve your goals.

Good luck. Enjoy life

that it is important for likert-type scale response choices to be balanced at the ends of the response continuum. This means that there should be an equal number of positive and negative response options to avoid any bias or skew in the results.

An explanation for this is that if there are too many positive or negative response options, respondents may feel pressured to choose a certain option even if it doesn't accurately reflect their true opinion. This can result in inaccurate data and can skew the results of the survey or study.

balancing the response choices on a likert-type scale is crucial for obtaining accurate and unbiased data. By having an equal number of positive and negative options, respondents are more likely to provide honest and accurate responses.

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The inequality 4/3|1/4x+3|<4 are Ox>-13 and x < -11 or Ox<-24 and x > 0

We can begin by isolating the absolute value on one side of the inequality:

4/3|1/4x+3|<4

|1/4x+3|<3/2

We can then split this inequality into two cases, one for when 1/4x+3 is positive and one for when it is negative:

1/4x+3>0: 1/4x+3>3/2, so multiplying both sides by 4, we get x>-13 and x<-11

1/4x+3<0: 1/4x+3<-3/2, so multiplying both sides by -4, we get x<-24 and x>0

So, the solution is: Ox>-13 and x < -11 or Ox<-24 and x > 0

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The three possible values for a are:

a = -5^(1/3)/2

a = (5^(1/3)/4) - (5^(1/3)/4)isqrt(3)

a = (5^(1/3)/4) + (5^(1/3)/4)isqrt(3)

To find the coefficient of x^3 in the expansion of (2+x)(3-ax)^4, we can use the binomial theorem or Pascal's triangle to expand the expression.

However, since we are only interested in the coefficient of x^3, we can use the following approach:

The coefficient of x^3 in the expansion of (2+x)(3-ax)^4 will be the sum of the products of the coefficients of x and x^3 in the two factors, i.e.,

coefficient of x^3 = (coefficient of x in 2+x) * (coefficient of x^3 in (3-ax)^4) + (coefficient of x^3 in 2+x) * (coefficient of x^2 in (3-ax)^4)

The coefficient of x in 2+x is 1, and the coefficient of x^3 in (3-ax)^4 can be found using the binomial theorem:

coefficient of x^3 in (3-ax)^4 = (4 choose 3) * (3)^1 * (-a)^3 = -36a^3

The coefficient of x^3 in 2+x is 0 since there is no x^3 term in 2+x.

The coefficient of x^2 in (3-ax)^4 can also be found using the binomial theorem:

coefficient of x^2 in (3-ax)^4 = (4 choose 2) * (3)^2 * (-a)^2 = 54a^2

Substituting these values into the equation above, we get:

30 = 1 * (-36a^3) + 0 * 54a^2

Simplifying, we get:

-36a^3 = 30

Dividing both sides by -36, we get:

a^3 = -5/6

Taking the cube root of both sides, we get:

a = -5^(1/3)/2

This is one possible value for a.

Since a^3 = (-5/6) has three cube roots (one real and two complex), there are two more possible values for a, which can be found by multiplying the real cube root by the complex cube roots of unity (which are -1/2 + isqrt(3)/2 and -1/2 - isqrt(3)/2):

a = (-5^(1/3)/2) * (-1/2 + i*sqrt(3)/2) = (5^(1/3)/4) - (5^(1/3)/4)isqrt(3)

a = (-5^(1/3)/2) * (-1/2 - i*sqrt(3)/2) = (5^(1/3)/4) + (5^(1/3)/4)isqrt(3)

Therefore, the three possible values for a are:

a = -5^(1/3)/2

a = (5^(1/3)/4) - (5^(1/3)/4)isqrt(3)

a = (5^(1/3)/4) + (5^(1/3)/4)isqrt(3)

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The missing angle for x by the measures add up to 90° is 53°

Complementary angles are pairs of angles whose measures add up to 90°. In this problem, we are given two angles, one of which measures 37°, and the other of which has an unknown measure that we will call x. We are also told that these angles are complementary, which means that their measures add up to 90°.

So, we can set up an equation to represent this relationship:

37 + x = 90

We can simplify this equation by subtracting 37 from both sides:

x = 90 - 37

x = 53

Now we know that the measure of the second angle is 53°. But we can go further and solve for x to get a more complete solution.

In the problem statement, we are also given an expression for the second angle in terms of x:

5x + 3

We know that this angle measures 53°, so we can set up another equation to represent this relationship:

5x + 3 = 53

We can solve for x by first subtracting 3 from both sides:

5x = 50

Then, we can divide both sides by 5 to isolate x:

x = 10

Now we know that x has a value of 10, and we can substitute this value back into the expression for the second angle to find its measure:

= 5x + 3

= 5(10) + 3 = 53

Therefore, the missing angle is 53°, and x has a value of 10.

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Answer:

yeet

Step-by-step explanation:

yeet yeet yeet yeet yeet yeet yeet yeet yeet eet yett yeet yeet yeet yeet yeet yeet yeet yeet yeety

Answer:

Step-by-step explanation:

Use the Law of Sines to solve the triangle. (Round your answers to two decimal places.)

A = 73°, a = 39, b = 24

The radius of the inner tube is r2 = 25 mm. Therefore, the hydraulic diameter of the annulus is given by,Dh = 4 A/PWhere, A is the cross-sectional area of the flow path in the annulus and P is the wetted perimeter.

The pressure drop per unit length in annulus when the water at 21°C is flowing with a velocity of 0.30 m/s in the annulus between a tube with an outer diameter of 22 mm and another with an internal diameter of 50 mm in a concentric tube heat exchanger can be calculated using the following formula:

∆p/L = fρV²/2gWhere,∆p/L = Pressure drop per unit length in annulusf = Friction factorρ = Density of waterV = Velocity of waterg = Acceleration due to gravity.

Here, the density of water at 21°C is 997 kg/m³f = 0.014 (from Darcy Weisbach equation or Moody chart).

The radius of the outer tube is r1 = 11 mm.

A = π/4 (D² - d²) = π/4 (0.050² - 0.022²) = 1.159 x 10⁻³ m²P = π (D + d) / 2 = π (0.050 + 0.022) / 2 = 0.143 mTherefore, Dh = 4 x 1.159 x 10⁻³ / 0.143 = 0.032 m.

Now, the Reynolds number can be calculated as,Re = ρVDh/µWhere, µ is the dynamic viscosity of water at 21°C which is 1.003 x 10⁻³ Ns/m²Re = 997 x 0.30 x 0.032 / (1.003 x 10⁻³) = 94,965.2.

Now, the friction factor can be obtained from the Moody chart or by using the Colebrook equation which is given by,1 / √f = -2.0 log (2.51 / (Re √f) + ε/Dh/3.7)Where, ε is the roughness height of the tubes.

Here, we can assume that the tubes are smooth. Therefore, ε = 0Substituting the values of Re and ε/Dh in the above equation, we get,f = 0.014Here, ∆p/L = fρV²/2g = 0.014 x 997 x (0.30)² / (2 x 9.81) = 0.064 Pa/m

Given data:Velocity of water, V = 0.30 m/sDensity of water, ρ = 997 kg/m³Outer diameter of tube, D1 = 22 mm.

Internal diameter of tube, D2 = 50 mmTemperature of water, T = 21 °C.

First, we need to calculate the hydraulic diameter of the annulus which is given by,Dh = 4 A/PWhere, A is the cross-sectional area of the flow path in the annulus and P is the wetted perimeter.

The cross-sectional area of the flow path in the annulus is given by,A = π/4 (D1² - D2²)The wetted perimeter is given by,P = π (D1 + D2) / 2Now, we can calculate Dh and substitute it in the formula for friction factor which can be obtained from the Moody chart or by using the Colebrook equation.

Here, we can assume that the tubes are smooth since the surface roughness is not given.After obtaining the value of friction factor, we can use it to calculate the pressure drop per unit length in annulus using the following formula:

∆p/L = fρV²/2gWhere, f is the friction factor, ρ is the density of water, V is the velocity of water, and g is the acceleration due to gravity.

Finally, we can substitute the values in the formula to obtain the pressure drop per unit length in annulus.

Therefore, the pressure drop per unit length in annulus when the water at 21°C is flowing with a velocity of 0.30 m/s in the annulus between a tube with an outer diameter of 22 mm and another with an internal diameter of 50 mm in a concentric tube heat exchanger is 0.064 Pa/m.

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Answer:

\(8<\sqrt{66}<9\)

Step-by-step explanation:

\(64<66<81 \implies 8<\sqrt{66}<9\)