Solve for "B" I tried it the way I solved the rest of the equations but I can't get it

- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.

To determine the behavior of the solution for the given differential equation s′′ + bs′ + 6s = 0, we need to analyze the roots of the characteristic equation:

r^2 + br + 6 = 0

For this quadratic equation, the discriminant Δ is given by:

Δ = b^2 - 4(1)(6) = b^2 - 24

The behavior of the solution depends on the value of Δ:

1. Overdamped: If Δ > 0, the solution will be overdamped.
2. Underdamped: If Δ < 0, the solution will be underdamped.
3. Critically damped: If Δ = 0, the solution will be critically damped.

Now, we find the intervals of b for each case:

1. Overdamped (Δ > 0):
b^2 - 24 > 0
This inequality holds for b ∈ (-∞, -2√6) ∪ (2√6, ∞).

2. Underdamped (Δ < 0):
b^2 - 24 < 0
This inequality holds for b ∈ (-2√6, 2√6).

3. Critically damped (Δ = 0):
b^2 - 24 = 0
This equation holds for b = -2√6 and b = 2√6.

In conclusion:
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.

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If Mrs. Smith's estimation only accounted for a 4-week month, it would be incorrect. However, if she factored in the additional 10 days, then her estimation of serving 40,000 people soup with 1 cup per person over 2 weeks is correct.

Soup kitchens are community-based organizations that provide meals, primarily soup, to people in need. These facilities are often run by volunteers and rely heavily on donations from local businesses and individuals to provide food for those who cannot afford it.

Mrs. Smith, the soup kitchen chef, estimates that they will serve 40,000 people soup, giving each person 1 cup of soup over 2 weeks, and with the month having 5 weeks.

To determine if Mrs. Smith's estimation is correct, we need to do some calculations. One cup of soup per person over two weeks means that each person will receive 2 cups of soup in total. Therefore, to serve 40,000 people with 2 cups of soup each, the soup kitchen would need to provide a total of 80,000 cups of soup.

With the month having 5 weeks, it means that there are 10 days extra in the month compared to a standard 4-week month. Therefore, the soup kitchen will need to serve an additional 1/5 of the total amount of soup to cover the additional 10 days.

So, to determine if Mrs. Smith's estimation is correct, we can multiply the total cups of soup needed (80,000) by 1/5, which equals 16,000 cups. We then add this to the original total, which gives us 96,000 cups of soup needed for the month.

In conclusion, if Mrs. Smith's estimation only accounted for a 4-week month, it would be incorrect. However, if she factored in the additional 10 days, then her estimation of serving 40,000 people soup with 1 cup per person over 2 weeks is correct.

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The rate of change of the revenue function R(x) is given by its derivative R'(x) = 190 - 0.8x. To find where the rate of change is equal to 0, we set R'(x) = 0 and solve for x:

190 - 0.8x = 0
0.8x = 190
x = 237.5

Therefore, the revenue function is constant when x = 237.5.
To find the value of x where revenue is constant, we need to find the point where the rate of change of the revenue function R(x) is equal to 0. This can be achieved by finding the derivative of R(x) with respect to x, and then setting it equal to 0.

R(x) = 190x - 0.4x^2

The derivative of R(x) with respect to x is:

R'(x) = dR(x)/dx = 190 - 0.8x

Now, set R'(x) equal to 0 and solve for x:

0 = 190 - 0.8x

0.8x = 190

x = 190 / 0.8

x = 237.5

The revenue function is constant when x = 237.5.

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Answer: C. 54cm^2

Step-by-step explanation:

Break the shape into 2 pieces and multiply the sides. ex. 12 by 2 and 8 by 5 and then add the 2 answers to get 54cm

The probability of getting an even number or a number less than 8 is:

P = 0.83

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.

The numbers that are even or less than 8 are:

{1, 2, 3, 4, 5, 6, 7, 8, 10, 12}

So 10 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 10/12 = 0.83

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The factored form of the equation is 1/2(y - √5)

To factor this expression, we need to look for any common factors that can be pulled out of both terms. We can see that both terms contain a factor of 1/2, so we can factor that out:

1/2(y - 5 1/2)

Now we need to see if there are any further factors that we can find. The term inside the parentheses, y - 5 1/2, cannot be factored any further using real numbers. However, we can write the expression as y - √5, which shows that it involves the square root of 5.

So the final factored form of the expression is:

1/2(y - √5)

This means that if we multiply 1/2 by (y - √5), we get back the original expression 1/2y - 5 1/2.

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Answer:

[tex]y=-\dfrac{8}{x}[/tex]

Step-by-step explanation:

Inverse proportions can be represented by an equation in the form:

[tex]\boxed{y=\dfrac{k}{x}}[/tex]

where:

To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:

[tex]\implies y=\dfrac{k}{x}[/tex]

[tex]\implies 4=\dfrac{k}{-2}[/tex]

[tex]\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)[/tex]

[tex]\implies -8=k[/tex]

[tex]\implies k=-8[/tex]

Therefore, the expression for the graphed function is:

[tex]\boxed{y=-\dfrac{8}{x}}[/tex]

The artist used a total of $0.33 worth of paint for the project.

The artist purchased 2 liters of paint, which is equivalent to 2,000 milliliters of paint. This amount of paint was used to complete a project, and after the project was finished, there were 350 milliliters of paint left over.

To determine how much paint was used for the project, we subtract the amount of leftover paint from the total amount of paint purchased, which gives us 2,000 - 350 = 1,650 milliliters of paint used for the project.

The cost of the paint is 2 cents per milliliter, which is equivalent to $0.02/100 milliliters or $0.0002 per milliliter. To determine the cost of the paint used for the project, we multiply the amount of paint used by the cost per milliliter.

Therefore, the cost of 1,650 milliliters of paint used for the project can be calculated by multiplying 1,650 milliliters by $0.0002 per milliliter, which gives us $0.33.

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Answer:

[tex]2( {3}^{x} ) = 258280326[/tex]

[tex] {3}^{x} = 129140163[/tex]

[tex]x = \frac{ ln(129140163) }{ ln(3) } = 17[/tex]

n = 17 + 1 = 18

[tex]s = \frac{2( 1 - {3}^{18} )}{1 - 3} = 387420488[/tex]

The sum of this finite geometric series is 387,420,488.

To make 132 cookies 3.14 pounds of butter would be used.

It is given that a bakery make 7 dozen cookies using 2 lbs of butter.

We know that 1 lb=1 pound

We know that 1 dozen = 12

7 dozen =7 × 12

= 84 cookies

We have to find how many pounds of butter would be used to make 132 cookies.

Let x be the number of pounds butter would be used to make 132 cookies

84/2 = 132/x

Apply cross multiplication

84x = 264

Divide both side by 84

x = 264/84

Hence, to make 132 cookies 3.14 pounds of butter would be used .

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Firstly, we can simplify the numerator which is 35x raised to the power 5 times y raised to the power 3. To do this, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the numerator simplifies to 35x^5y^3.

Next, we need to simplify the denominator which is 7xy raised to the power 2. Similarly, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the denominator simplifies to 7x^1y^1 (since x and y each have a power of 1).

Now we can divide the numerator by the denominator. To do this, we divide the coefficients (35/7 = 5) and subtract the exponents of the variables with the same base (x^5/x^1 = x^4 and y^3/y^1 = y^2). Therefore, the simplified form of the given expression is 5x^4y^2.

In summary, to simplify the given expression, we used the power and quotient rules of exponents. We multiplied coefficients and added exponents of variables with the same base, and then divided coefficients and subtracted exponents of variables with the same base. The final simplified form is 5x^4y^2.

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The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.

When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.

For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.

Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.

Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.

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Hi! I'd be happy to help you with your question. To find the volume of two laundry detergent boxes, each measuring 12 inches by 8 inches by 3 inches,

you can follow these steps:

Formula: Volume = Length × Width × Height

Step 1: Plug in the values for one box:
Volume = 12 inches × 8 inches × 3 inches

Step 2: Calculate the volume of one box:
Volume = 288 cubic inches

Step 3: Multiply the volume of one box by 2 to find the volume of two boxes:
Total volume = 288 cubic inches × 2

Solution: The total volume of two laundry detergent boxes is 576 cubic inches.

Your answer: The volume of two boxes of detergent is 576 cubic inches.

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The value of x is 32.

A set of angles that are between the two line parallels but on each side of the transverse are referred to as alternate external or exterior angles. The measure of the alternate external or exterior angles is equal.

According to the alternate outside angle theorem, alternate exterior angles are regarded as congruent angles or degrees of equal magnitude when two parallel lines intersected by a transversal.

Given that the lines m and n are parallel, and the angles are [tex](3x-2)^{0}[/tex] and [tex](2x+30)^{0}[/tex].

The given angles are alternate external or exterior angles. So, they must be equal.

[tex](3x-2)^{0} = (2x+30)^{0}[/tex]

Rearrange the above equation to find the value of x as follows,

[tex]3x-2x=30+2[/tex]

[tex]x=32[/tex]

Hence, the value of x is 32.

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The equation that can be written to show the total length of the bandages if they are placed end-to-end is expressed as: 2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3).

In the image given above that shows a line plot for the set of data representing the length of bandages, we have:

Two 1¼ = 2(5/4)

One 1 2/4 = 6/4

Three 1¾ = 3(7/4)

Four 2 = 4(2)

Six 3 = 6(3)

Thus, the equation that will represent the total length of the bandages can be expressed as:

2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3)

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The correct sequence for the samples in order of least variation to greatest variation is:

Sample A: A sample of 10 people

Sample D: A sample of 20 people

Sample B: A sample of 50 people

Sample C: A sample of 100 people

The reason for this sequence is that larger sample sizes tend to provide more accurate estimates of the population parameters, while smaller sample sizes are more prone to random fluctuations and sampling error.

Therefore, sample A (with the smallest sample size of 10) is likely to have the greatest variation from the expected value, while sample C (with the largest sample size of 100) is likely to have the least variation from the expected value.

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The rational function graphed in this problem is given as follows:

B. f(x) = 1/(x - 3) + 2.

From the graph, the asymptotes of the rational function are given as follows:

Considering that the function has a vertical asymptote at x = 3, we have that:

f(x) = 1/(x - 3).

Considering the horizontal asymptote at y = 2, we have that:

f(x) = 1/(x - 3) + 2.

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The probability of selecting a brown M&M from this bag is 0.

Since there are no brown M&Ms mentioned in your bag, the probability of selecting a brown M&M is 0. In probability terms, we can express this as:

Probability of selecting a brown M&M = Number of brown M&Ms / Total number of M&Ms

There are 0 brown M&Ms, and there are a total of 4 green + 6 yellow + 7 purple + 3 red = 20 M&Ms in the bag. So the probability is:

Probability = 0 / 20 = 0

Thus, the probability of selecting a brown M&M from this bag is 0, meaning it's impossible with the given information.

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No, 2352 is not a perfect square.

To find the smallest number by which 2352 must be multiplied so that the product is a perfect square, we need to factorize 2352 into its prime factors.

2352 = 2^4 x 3 x 7^2

To make it a perfect square, we need to multiply it by 2^2 and 7, which gives us:

2352 x 2^2 x 7 = 9408

Now, we can take the square root of 9408:

√9408 = √(2^8 x 3 x 7) = 2^4 x √(3 x 7) = 16√21

Therefore, the smallest number by which 2352 must be multiplied so that the product is a perfect square is 2^2 x 7, which gives us the square root of 9408 as 16√21.

Answer:

The smallest number by which 2352 must be multiplied so that the product is a perfect  square = 3

The square root of the new number = 84

Step-by-step explanation:

√2352 ≈ 48.5 so not a perfect square

Prime factorization of 2352 yields

2352 = 2 x 2 x 2 x 2 x 7 x 7 x 3

In exponential form this is
2⁴ x  7² x 3¹

So
[tex]\sqrt{2352} = \sqrt{2^4 \cdot 7^2 \cdot 3}\\\\= \sqrt{2^4} \cdot \sqrt{7^2} \cdot \sqrt{3}\\\\= 2^2 \cdot 7 \cdot \sqrt{3}\\\\= 28 \sqrt{3}[/tex]

To get rid of the radical in the square root and get a whole number, all you have to do is multiply [tex]\sqrt{2352}[/tex]  by √3

[tex]28 \sqrt{3} \cdot \sqrt{3} = 28\cdot 3 = 84\\\\84^2 = 7056 = 2352 \cdot 3\\[/tex]

This means that if you multiply 2352 by 3 it will become a perfect square

Check:
[tex]2352 \cdot 3 = 7056\\\\\sqrt{7056} = 84[/tex]

The radius of the circle of the equation is 19 units

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

x² + y² = 19²

The equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

using the above as a guide, we have the following:

Center = (a, b) = (0, 0)

Radius = r = 19

Hence, the radius of the circle of the equation is 19 units

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Answer:

There are 6 goldfish in each of the 3 aquariums at Joe's fish store.

Step-by-step explanation:

To find out how many goldfish are in each aquarium, we can divide the total number of goldfish by the number of aquariums:

Therefore, there are 6 goldfish in each of the 3 aquariums at Joe's fish store.

Answer:

The answer to 1+1 is 2.

Answer:

2

Step-by-step explanation:

The perimeter of Rebakh's new mural is 9 meters.

Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.

So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.

Therefore, the perimeter of Rebakh's new mural is 9 meters.

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If the dowel has a radius of 3.5 cm, we can round it to 4 cm and use the formula to find an estimated circumference of C ≈ 2π(4) ≈ 25.1 cm.

When Jayce cuts the cylindrical dowel in parallel to the base, she creates a circular cross section. The circumference of a circle is the distance around its perimeter, and it can be calculated using the formula C = 2πr, where C is the circumference, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.

Since the dowel is cylindrical, its cross section will also be a circle. Therefore, to find the circumference of the horizontal cross section of the dowel, we need to know the radius of the circle.

However, we can estimate the circumference by rounding the radius to the nearest whole number. For example, if the dowel has a radius of 3.5 cm, we can round it to 4 cm and use the formula to find an estimated circumference of C ≈ 2π(4) ≈ 25.1 cm. Rounded to the nearest whole number, the circumference would be 25 cm.

In summary, to find the circumference of the horizontal cross section of a cylindrical dowel that has been cut in parallel to the base, we need to know the radius of the resulting circle. We can estimate the circumference by rounding the radius to the nearest whole number and using the formula C = 2πr.

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To find sin(∠BAC + 30°), we will use the sine addition formula. The sine addition formula is: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

Step 1: Identify the angles A and B in our expression. In this case, A = ∠BAC and B = 30°.

Step 2: Apply the sine addition formula:

sin(∠BAC + 30°) = sin(∠BAC)cos(30°) + cos(∠BAC)sin(30°).

Now you have the expression for sin(∠BAC + 30°). To calculate its value, you will need the values of sin(∠BAC) and cos(∠BAC), which require more information about the triangle.

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Answer:

$626.76

Step-by-step explanation:

The area of the triangle is approximately 31.3049 square inches.

The area of a triangle can be found using the formula: A = (1/2)bh, where b is the length of the base of the triangle, and h is the height (or perpendicular distance from the base to the opposite vertex).

However, in this case, we don't have the height. Instead, we can use

Heron's formula, which only requires the lengths of the three sides of the triangle:

A = √[s(s-a)(s-b)(s-c)],

where a, b, and c are the lengths of the sides of the triangle, and s is the semiperimeter (half the perimeter):  s = (a + b + c)/2.

Using the given values, we have:

s = (7 + 9 + 12)/2 = 14

A = √[14(14-7)(14-9)(14-12)]

A = √[14(7)(5)(2)]

A = √(980)

A ≈ 31.3049 square inches

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Examining the expression the value of r/2c is

We can use algebra to calculate the value of r/2c with 3r/c as the variable.

First, let's reduce the expression 3r / c = 126 by multiplying both sides by c / 3:

3r/c * c/3 = 126 * c/3

r/1 = 42c

Now we can obtain r / 2c by dividing both sides by 2c:

solving for the left hand side of the equation

r /2c = (r/1)/(2c)

solving for the right hand side of the equation

42c = (42c)/(2c) = 21

Equation the left hand side to the right hand side of the equation

r/2c = 21

Therefore, r/2c = 21.

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The closest value to the total cost of Francine's calls is $191.07

To find the total cost of Francine's calls, we need to know the total number of minutes she spent on the phone. We can calculate this by adding up the lengths of all 11 calls:

Total minutes = 11 + 14 + 12 + 20 + 25 + 16 + 11 + 22 + 18 + 19 + 15 = 193

The total cost of Francine's calls can then be found by multiplying the total number of minutes by the cost per minute:

Total cost = 193 * 0.99

= 191.07

Therefore, the closest value to the total cost of Francine's calls is $191.07.

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