For the differential equation s" + bs' +9s = 0, find the values of b that make the general solution overdamped, underdamped, or critically damped. (For each, give an interval or intervals for b for which the equation is as indicated. Thus if the the equation is overdamped for all b in the range -1

Let's solve this step by step.

Let's denote the length of the interstate as "x".

According to the given information, one side of the town is 1/2 the length of the interstate, which means its length is (1/2)x.

Another side of the town is 2/3 the length of the interstate, which means its length is (2/3)x.The perimeter of the town is the sum of the lengths of all three sides:

Perimeter = (1/2)x + (2/3)x + x

We know that the perimeter is 104 km, so we can set up the equation:

104 = (1/2)x + (2/3)x + x

To simplify the equation, let's find the common denominator of 2 and 3, which is 6:

104 = (3/6)x + (4/6)x + (6/6)x

Now, we can add the fractions:

104 = (13/6)x

To isolate x, we multiply both sides of the equation by 6/13:

104 * (6/13) = x

48 = x

So, the length of the interstate is 48 km.

Now we can find the lengths of the other two sides of the town:Length of one side = (1/2) * 48 = 24 km

Length of the other side = (2/3) * 48 = 32 km

Therefore, the length of the side not bordered by the interstate are 24 km and 32 km, respectively.

Given that the town is triangular in shape with a perimeter of 104 km, one side of the town is half the length of the interstate, while the other side is two-thirds the length of the interstate. By solving the equations derived from these conditions, we find that the length of each of the two sides not bordered by the interstate is 24 km and 32 km, respectively.

Let's denote the length of the interstate as "x" km. According to the given information, one side of the town is half the length of the interstate, so its length is x/2 km. The other side is two-thirds the length of the interstate, making it (2/3)x km.

Since the town is triangular, the sum of all three sides must equal the perimeter of the town, which is 104 km. Therefore, we can write the equation:

x + x/2 + (2/3)x = 104

To solve for x, we can simplify the equation:

(6/6)x + (3/6)x + (4/6)x = 104

(13/6)x = 104

To isolate x, we multiply both sides by 6/13:

x = (6/13) * 104

x = 48 km

Now that we have the length of the interstate, we can determine the lengths of the other two sides. One side is half the length of the interstate, so it is (1/2) * 48 = 24 km. The other side is two-thirds the length of the interstate, so it is (2/3) * 48 = 32 km.

Therefore, the length of each of the two sides of the town not bordered by the interstate is 24 km and 32 km, respectively.

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Answer:

1000 feet²

Step-by-step explanation:

Given that,

Width of a parallelogram is 40 feet

Height of the parallelogram is 25 feet

We need to find the area of the intersection that forms a parallelogram. The formula for the area of a parallelogram is given by :

A = base × height

A = 40 × 25

A = 1000 feet²

So, the area of the parallelogram is 1000 feet²

Safety data sheets (SDS) are not only required when there are 10 gallons. This statement is false. SDS, also known as material safety data sheets (MSDS), are required for hazardous substances, regardless of the quantity.

Safety data sheets provide detailed information about the potential hazards, handling, and emergency measures for substances. They are required under various regulations, such as the Occupational Safety and Health Administration (OSHA) Hazard Communication Standard (HCS) in the United States.

The quantity of the substance does not determine the need for an SDS. For example, even if a small amount of a highly hazardous substance is present, an SDS is still necessary for safety reasons.

SDS help workers and emergency personnel understand the risks associated with a substance and how to handle it safely. It is essential to follow proper safety protocols and provide SDS for hazardous substances, regardless of the quantity.

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The smallest number by which 3^6 * 3^5 must be multiplied (or divided) to become a perfect square is 2.

To find the smallest number by which 3^6 * 3^5 must be multiplied (or divided) so that the product (or quotient) becomes a perfect square,

First, let's simplify the expression 3^6 * 3^5 by using the exponent rule for multiplication. When we multiply numbers with the same base, we add the exponents:

3^6 * 3^5 = 3^(6+5) = 3^11.

Now, we have 3^11. To make this expression a perfect square, we need the exponent to be an even number. In this case, we want the exponent of 3 to be divisible by 2.

The smallest number by which we can multiply 3^11 to make it a perfect square is 2. By multiplying 3^11 by 2, we get:

2 * 3^11 = (2^2) * (3^11) = (2*3)^11 = 6^11.

Now, 6^11 is a perfect square because the exponent of 6 (11) is divisible by 2. Therefore, the smallest number by which 3^6 * 3^5 must be multiplied to become a perfect square is 2.


To find the smallest number by which 3^6 * 3^5 must be multiplied (or divided) so that the product (or quotient) becomes a perfect square, we need to simplify the expression 3^6 * 3^5. By applying the exponent rule for multiplication, we can add the exponents:

3^6 * 3^5 = 3^(6+5) = 3^11.

Now, we have the expression 3^11. To make it a perfect square, we need the exponent of 3 to be divisible by 2. Since 11 is an odd number, we need to multiply or divide 3^11 by a number that will make the exponent even.

The smallest number by which we can multiply 3^11 to make it a perfect square is 2. By multiplying 3^11 by 2, we get:

2 * 3^11 = (2^1) * (3^11) = (2*3)^11 = 6^11.

Now, 6^11 is a perfect square because the exponent of 6 (11) is divisible by 2.

Therefore, the smallest number by which 3^6 * 3^5 must be multiplied (or divided) to become a perfect square is 2.

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A square could be called a rectangle since it has four right angles.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°. Observe the rectangle given below to see its shape, sides and angles.

So,  Every square is a rectangle because it is a quadrilateral with all four angles right angles.

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Answer:

1/3

Step-by-step explanation:

The simplest form of 2/6 is 1/3. You can do 2/6*.5/.5 to get 1/3

You can do other fractions such as 4/12, 8/24, as long as it the numerator maintains a ratio of 1:3

The value of the arc length and area are 11. 2ft and 44.2 ft² respectively

To determine the arc length, we use the formula;

s = 2πr(θ/360)

Such that the parameters of the formula are expressed as;

Substitute the values, we get;

s = 2 × 3.14 × 8 × (80/360)

Divide the values, we get;

s = 50. 24(0. 22)

Multiply the values, we have;

s = 11. 2ft

The area of the sector is expressed as;

(θ/360º) × πr2

Substitute the values

80/360 × 3.14 ×8²

Find the square and multiply

0. 22 × 200. 96

Multiply

44.2 ft²

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If a differentiable function f: ℝ³ ⟶ ℝ has an absolute maximum value K ≠ 0 and an absolute minimum m, then the function f must have a critical point where the derivative of the function is zero (or undefined).

Given that, suppose f : ℝ³ ⟶ ℝ is a differentiable function which has an absolute maximum value K ≠ 0 and an absolute minimum m.

Since f is continuous on a compact set, it follows that f has a global maximum and a global minimum. We are given that f has an absolute maximum value K ≠ 0 and an absolute minimum m. Then there exists a point a ∈ ℝ³ such that f(a) = K and a point b ∈ ℝ³ such that f(b) = m.Then f(x) ≤ K and f(x) ≥ m for all x ∈ ℝ³.

Since f(x) ≤ K, it follows that there exists a sequence {x_n} ⊆ ℝ³ such that f(x_n) → K as n → ∞. Similarly, since f(x) ≥ m, it follows that there exists a sequence {y_n} ⊆ ℝ³ such that f(y_n) → m as n → ∞.Since ℝ³ is a compact set, there exists a subsequence {x_nk} and a subsequence {y_nk} that converge to points a' and b' respectively. Since f is continuous, it follows that f(a') = K and f(b') = m.

Since a' is a limit point of {x_nk}, it follows that a' is a critical point of f, i.e., ∇f(a') = 0 (or undefined). Similarly, b' is a critical point of f. Therefore, f has at least two critical points where the derivative of the function is zero (or undefined). Hence, the statement is true.

Therefore, the above explanation is verified that if a differentiable function f: ℝ³ ⟶ ℝ has an absolute maximum value K ≠ 0 and an absolute minimum m, then the function f must have a critical point where the derivative of the function is zero (or undefined).

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Answer:

Your answer is: k = 5+12/x

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )

Answer:

y= 30 + 3.50

Step-by-step explanation:

lol I think you're Giselle for my school but that's what the answer it im pretty sure.

Answer:

m=3n/4

Step-by-step explanation:

4m+2n=5n subtract 2n from both sides

4m= 5n-2n combine like terms

4m=3n divide by 4

m=3n/4

brainliest plz <3

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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Answer:

c 3 and 6

Step-by-step explanation:

edg2020

Answer:

C 6 and 3, not 3 and 6

Step-by-step explanation:

got it wrong and saw the answer

Answer:

-3231a-5326b

Step-by-step explanation:

I subtracted the a's but you can't subtract the b with anything so .....yea

Given:

The equation of polynomial is

\(2x^3-5x^2+1=0\)

To find:

All rational roots of the polynomial.

Solution:

According to the rational root theorem, all the possible rational roots of a polynomial are defined as

\(x=\dfrac{p}{q}\)

where, p is a factor of constant term and q is factor of leading coefficient.

We have,

\(2x^3-5x^2+1=0\)

Here, leading coefficient is 2 and constant term is 1.

Factors of 1 are ±1.

Factors of 2 are ±1, ±2.

Using rational root theorem, we get

\(x=\pm \dfrac{1}{1},\pm \dfrac{1}{2}\)

\(x=\pm 1,\pm \dfrac{1}{2}\)

Therefore, all possible rational roots of the given polynomial are \(\pm 1,\pm \dfrac{1}{2}\).

The standard normal distribution  becomes smaller.

What is standard deviation?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

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Answer:

4d=48

Step-by-step explanation:

Answer

x=4

Explanation

-4 = x -8

add 8 to both sides

-4+8 = x

x=4

Answer: (3,6)

Rewrite in vertex form and use this form to find the vertex (h,k)

Answer:

(3,6)

Step-by-step explanation:

f(x) = |x| is a V-shaped graph with the vertex at (0,0). It is called a parent graph, because its super basic.

f(x) = |x - 3| + 6

has had two changes made to it. The "- 3" that's in there close to the x slides the graph over to the right 3 units. This is kind of the opposite of what you might think. Minus3 shifts right. (Plus3 would shift left)

The +6 tacked on to the end shifts the whole graph UP 6.

That slides the graph RIGHT3 and UP6. So the vertex lands at (3,6). See image.

Answer:

B

Step-by-step explanation:

Here, we want to get the value of m

The value of m can be obtained by multiplying the first factors of the first two polynomial, subtracting the first factor of the third and equating to 18

So what we have will be;

m * 6 - 6 = 18

6m -6 = 18

6m = 18 + 6

6m = 24

m = 24/6

m = 4

The two possible functions is F(x)= \frac{x^4}{12}+3x^2 and F(x)= \frac{x^4}{12}+3x^2+x.

The derivative of the first derivative of the given function is known as the second order derivative. We can learn about the slope of the tangent at a particular position or the instantaneous rate of change of a function at that point from the first-order derivative at that point.

F”(x)= x^2+6

F’(x)= \int f"(x) dx

       = \int( x^2+6) dx

       = \frac{x^3}{3}+6x+c_1                                  c_1 is the integral constant.

F(x)= \int f\prime(x) dx

      = \int f (\frac{x^3}{3}+6x+c_1) dx

      = \frac{x^4}{12}+3x^2+c_1x+c_2

(i) if c_1=0 , and c_2=0

   F(x)= \frac{x^4}{12}+3x^2

(ii) if c_1=1, and c_2=0

        F(x)= \frac{x^4}{12}+3x^2+x

Therefore the two possible functions is F(x)= \frac{x^4}{12}+3x^2 and F(x)= \frac{x^4}{12}+3x^2+x

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Answer: 5$ took test

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 is the answer

Answer:

56

Step-by-step explanation:

Answer:

parabola On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6). On a coordinate plane, a parabola opens up.

Step-by-step explanation:

Answer: C) the third graph

Step-by-step explanation: i got 100% on my quiz, hope this helps!!

EXAMPLE QUESTION+ANSWER;-

16 - [5 - 2 { 14  of  2 - (8/4 * 2 - 1 + 3 } ]

= 16 - [5 - 2 { 14  of  2 - (2 * 2 - 1 + 3 } ]

= 16 - [5 - 2 { 14  of  2 - (4 - 1 + 3 } ]  

= 16 - [5 - 2 { 14  of  2 - (3 + 3 } ]

= 16 - [5 - 2 { 14  of  2 - 6} ]

= 16 - [5 - 2 { 28  - 6} ]

= 16 - [5 - 2 {22} ]

= 16 - [5 - 44]

= 16 + 30

= 55

Answer: 55

The probability of seeing five heads in a row when picking a random coin from the box and tossing it five times is approximately 0.29677.

The required probability that the coin is fair given that we observed five heads in a row is approximately 0.05338.

The probability of flipping five heads in a row with a fair coin is,

⇒ (1/2)⁵ = 1/32,

Since the probability of flipping heads on any given toss is 1/2, and each toss is independent.

Then the probability of flipping five heads in a row with a loaded coin (p head = 0.9) be,

⇒ (0.9)⁵ = 0.59049,

Since the probability of flipping heads on any given toss is 0.9, and each toss is independent.

Now, to find the probability of seeing five heads in a row when picking a random coin from the box and tossing it five times,

Use the law of total probability,

Let F denote the event that the coin is fair,

And L denote the event that the coin is loaded.

Then, the probability of seeing five heads in a row is:

⇒P(5 heads) = P(5 heads | F) P(F) + P(5 heads | L) P(L)

                     = (1/32) (1/2) + (0.59049) (1/2)

                      = 0.29677

Therefore,

The probability of seeing five heads in a row when picking a random coin from the box and tossing it five times is approximately 0.29677.

Proceed the second question:

We have to find the probability that the coin is fair given that we observed five heads in a row.

Let H denote the event that we observed five heads in a row, and let F and L have the same meanings as before.

Then, by Bayes' theorem, we have:

P(F | H) = P(H | F) P(F) / P(H)

We already have P(H | F) and P(H) in the previous question,

So we just need to compute P(F).

Since half of the coins are fair, we have:

P(F) = 1/2

Putting it all together, we get:

P(F | H) = (1/32) (1/2) / 0.29677

            = 0.05338

Therefore, the required probability is approximately 0.05338.

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Answer:

25

Step-by-step explanation:

Cross multiply

23/x=92/100

x=25

There were approximately 25 questions on the test.

To determine the number of questions on the test, we can set up a proportion based on Charles' correct answers and the grade received.

Let x be the total number of questions on the test.

We can set up the proportion:

23 (Charles' correct answers) / x (total number of questions) = 92% (grade as a decimal: 0.92)

This can be written as:

23 / x = 0.92

To solve for x, we can multiply both sides of the equation by x:

23 = 0.92 * x

Dividing both sides by 0.92:

23 / 0.92 = x

x ≈ 25

Therefore, there were approximately 25 questions on the test.

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