Solve the separable differential equation y' = 3yx^2?. Leave your answer in implicit form. Use c for the constant of integration. log |y| = x^3 + c .

Answer:

$360

Step-by-step explanation:

Find 3% of 500 = 15

Multiply 15 by 24 = 360

The correct answer is option c. 1/(x² + 2x - 3). To determine which expression is equivalent to the given expression, let's simplify it step by step:

The given expression is (x³ - 2x - 3) ÷ (x² + 2x - 3).

Option a. 1/(x² - 2x - 3):

This option is not equivalent to the given expression because it represents the reciprocal of the quadratic denominator, which is different from the given expression.

Option b. 1/(x² - 4x + 3):

This option is not equivalent to the given expression because the signs of the quadratic terms are different. The given expression has a positive quadratic term, while this option has a negative quadratic term.

Option c. 1/(x² + 2x - 3):

This option is equivalent to the given expression because it represents the reciprocal of the quadratic denominator with the same signs for the quadratic terms.

Option d. x/(3x - 1):

This option is not equivalent to the given expression because it lacks the term x³ in the numerator.

Therefore, the correct answer is option c. 1/(x² + 2x - 3).

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a. the Laplace transform of a(t) is (28/s^2) + (3/s) + (4/s). b. the Laplace transform of b(t) is 5/s - 10/(s + 2) - 10/(s^3 + 2s^2).

a. To find the Laplace transform of a(t) = 28t + 3 + 4u(t), where u(t) is the unit step function, we can apply the linearity property and the transform of elementary functions.

Applying the linearity property, we can split the transform into three parts:

L{28t} + L{3} + L{4u(t)}

Using the transform of t (L{t} = 1/s^2), we get:

28/s^2 + 3/s + 4/s

Simplifying, we can combine the terms:

(28/s^2) + (3/s) + (4/s)

Therefore, the Laplace transform of a(t) is:

(28/s^2) + (3/s) + (4/s).

b. To find the Laplace transform of b(t) = 5 - 5e^(-2t)(1 + 2t), we can again apply the linearity property and the transform of elementary functions.

Applying the linearity property, we can split the transform into two parts:

L{5} - L{5e^(-2t)(1 + 2t)}

The transform of 5 is simply 5/s.

For the second part, we need to use the transform of e^(-at) and t.

The transform of e^(-at) is 1/(s + a), and the transform of t is 1/s^2.

Using these formulas, we get:

-5/(s + 2)(1 + 2/s^2)

Simplifying and combining terms, we have:

5/s - 10/(s + 2) - 10/(s^3 + 2s^2)

Therefore, the Laplace transform of b(t) is:

5/s - 10/(s + 2) - 10/(s^3 + 2s^2).

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Answer:

multiply 75.4 by 60 =4,524

Answer:

You did not take the picture correctly, try taking it again

Step-by-step explanation:

I can’t seeeee

Answer:

She will make a total commission of $1130+$325=$1445

Then 5% of $1445= $1445×5%=$72,75

a) If there are at least 10 bagels of each type, we can calculate the number of different selections of 10 bagels by using the concept of combinations. Since there are 5 types of bagels and we need to select 10 bagels, the calculation can be done as follows:

[tex]\(\binom{10+5-1}{10} = \binom{14}{10}\)[/tex]

b) If there are 3 chocolate chip and 2 cinnamon raisin bagels, and at least 10 of the other three types, we can calculate the number of different selections of 10 bagels using the same concept of combinations. In this case, we have 3 types of bagels (excluding chocolate chip and cinnamon raisin) with at least 10 bagels each. So the calculation becomes:

[tex]\(\binom{10+3-1}{10} = \binom{12}{10}\)[/tex]

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Answer:

please give more information

Step-by-step explanation:

Answer:

6(x - 3 ) = 6x - 18

2(3x - 3) = 6x - 6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The exact value of A in the general solution is 87/2 and B is 0

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

y = Ax² + Bx + C

The differential equation is given as

y' = 87x

When y = Ax² + Bx + C is differentiated, we have

y' = 2Ax + B

So, we have

87x = 2Ax + B

By comparing both sides of the equation, we have

2Ax = 87x

B = 0

So, we have

2A = 87

B = 0

Divide both sides of 2A = 87 by 2

A = 87/2

B = 0

Hence, the value of A in the general solution is 87/2 and B is 0

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Answer:

2/5x7

Step-by-step explanation:

The opposite sides are parallel.

Their angle measures add to 360°

hmmm I dunno sorry ......

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OWA OWA??

Answer:

The first choice is the correct one.

Step-by-step explanation:

The first choice is the correct one.  It starts with the base salary and then is multiplied by (1 + 0.02)^t, which is the correct formula for compounding once per year.

Answer:

The answer is in the link

Step-by-step explanation:

quntyfcjb/crown!.com :))))

Answer:

13 mm

Step-by-step explanation:

V = πr²h

4,939.22 mm³ = 3.14 × (11 mm)²h

4,939.22 mm³ = 3.14 × (11 mm)²h

h = 13 mm

Answer: 13 mm

Answer:

7. 13.25mm

8. 83.25 mm

9. 551.55 mm²

Step-by-step explanation:

The shape of a coin is circular.

A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps.

7. What is the radius?

The formula for radius = Diameter/2

= 26.5 mm/2

= 13.25 mm

8. What is the circumference?

The formula for the circumference of a circle = 2πr

= 2× π × 13.25mm

= 83.25220532 mm

Approximately to the nearest hundredth = 83.25 mm

9. What is the area?​

The formula for the area of a circle = πr²

= π × (13.25mm)²

= 551.54586025 mm²

Approximately to the nearest hundredth = 551.55 mm²

Answer:

There would be infinite solutions because the equations are exactly the same.

I hope this answered your question

Answer:

-84

Step-by-step explanation:

Since m=-4, we can plug -4 into the expression and use PEMDAS

7(m - 8)

7((-4)-8)

7(-12)

-84

Answer:

138 + 27.6 = 165.6

Step-by-step explanation:

Please give brainliest

There is only 1 permutation in S9 with a cycle structure of [tex]3^3[/tex].

To find the number of permutations of S9 with a cycle structure of [tex]3^3[/tex], we can use the concept of cycle index.

In a permutation with a cycle structure of[tex]3^3[/tex], we have three cycles of length 3. The cycle index of S9 with respect to cycles of length 3 can be determined using the Polya enumeration theorem.

The cycle index of S9 with respect to cycles of length 3 is given by:

[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3[/tex]

Expanding this expression, we get:

[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3\\\= (t1^9 + 3t1^6t3^3 + 3t1^3t3^6 + t3^9)[/tex]

To count the number of permutations with the desired cycle structure, we need to find the coefficient of the term [tex]t1^9t3^9[/tex].

From the expanded form, we see that the coefficient  [tex]t1^9t3^9[/tex] is 1.

Therefore, there is only one permutation in S9 with a cycle structure of [tex]3^3[/tex]

In summary, there is 1 permutation of S9 that has a cycle structure of [tex]3^3[/tex].

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Step-by-step explanation:

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Answer:

the first one

Step-by-step explanation:

Answer:

y = -2x + 3

Step-by-step explanation:

If you do rise/run, you recognize that the slope of the line is -6/3, which = -2. You can also see that the y-intercept of the line is at 3.

The equation of a line is represented by y=mx+b, with m being the slope and b being the y-intercept value.

Just plug in -2 as m and 3 as b in y=mx + b, and you will get your answer.

Answer:

A. Increasing by 4%.

Step-by-step explanation:

Answer:

A) The price of product A is increasing by 3% per year.

(B) The product A recorded a greater percentage change in price over the previous year.

Step-by-step explanation:

(A)

The function representing the price, in dollars, of product A after x years is:

FA(x)=0.69*(1.03)x

The function  FA(x)can be written as:

FA(x)=0.69*1+(0.03)x

The function FA(x) is similar to the exponential growth function, y=a(1+r)x .

Here r is the growth rate.

Thus, it can be said that the price of product A is increasing by 3% per year.

(B)

Consider the data of product B for the year 3 and 4.

The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.

Compute the percent price change from year 3 to 4 as follows:

10406.04-10303.01/10303.01*100

which is 0.999%

~1%

The price of product B is increasing by 1% per year.

Thus, the product A recorded a greater percentage change in price over the previous year.

Step-by-step explanation:

d=2r

πr^2

10/2=r

5=r

5^2π

25π=78.5398

Hope that helps :)