Determine the intervals on which the following function is continuous. f(x) = x + 6/x^2 - 36 The function is continuous on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)

the boundary condition at a perfectly insulated surface is expressed mathematically as (0) -k = 0 depending on the physical characteristics of the surface.

A boundary condition is a mathematical expression that describes the behavior of a physical system at its boundaries, such as a surface.

Mathematically, a perfectly insulated surface is represented as an isothermal surface, meaning that the temperature is constant across the surface.

This is described by the equation (0) = 0, where эт represents the rate of heat transfer at the surface.

In other words, a perfectly insulated surface does not allow heat to flow through it.

This equation shows that the heat transfer is in the opposite direction of the temperature gradient at the surface.

Finally, the boundary condition at a perfectly insulated surface can also be expressed as эт (0,) -k = 0, which means that the heat transfer at the surface is equal to zero and there is no net heat transfer at the surface.

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The rocket peaks at 5000 meters above sea-level.

The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:

h'(t) = -10t + 1000

h'(t) = 0 => t = 100

So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:

h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000

Therefore, The rocket peaks at 5000 meters above sea-level.

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The rocket peaks at 5000 meters above sea-level.

The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:

h'(t) = -10t + 1000

h'(t) = 0 => t = 100

So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:

h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000

Therefore, The rocket peaks at 5000 meters above sea-level.

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On the NASA space shuttles, a substance called kevlar epoxy is employed. This epoxy's strands underwent testing for 90% breaking strength.

Mean, Range, variance, standard deviation

A) Formula for range is;

Range = Highest term - Lowest term

Range = 7.89 - 0.02

Range = 7.87

B) Sum of all the given 50 epoxy samples is gotten to be;

∑X = 62.12

From online statistics calculator, we have; ∑X² = 164.3516

C) Formula for sample mean here is;

x' = ∑x/n

x' = 62.12/50

x' = 1.24

Formula for variance is;

σ² = [∑x² - [(∑x)²/n]]/(n - 1)

σ² = (164.3516 - (62.12²/50))/(50 - 1)

σ² = 1.78

Formula for the standard deviation is;

σ = √variance = √1.78

σ = 1.334

D) Formula for coefficient of variation is;

CV = (σ/x') * 100

CV = (1.33379/1.2424) * 100

CV = 107.356

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The area of the unshaded region in the given diagram is 64π in²

From the question, we are to determine the area of the unshaded region in the given diagram

Area of the unshaded region = Area of the medium circle - Area of the small circle

The formula for calculating the area of a circle is given as

A = πr²

Where A is the

and r is the radius

From the diagram,

Radius of the medium circle = 6 in + 4 in

Radius of the medium circle = 10 in

and

Radius of the small circle = 6 in

Thus,

Area of the unshaded region = π(10)² - π(6)² in²

Area of the unshaded region = 100π - 36π in²

Area of the unshaded region = 64π in²

Hence, the area is 64π in²

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<1 = 45 degrees- are supplementary angles.

<2 = 95 degrees -  vertical angles.

<3 = 40 degrees because 1, 2, and 3 form a triangle.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Using the provided figure, we can

Because <1 and the angle with a measure of 135 degrees are supplementary angles, m<1 = 45 degrees.

and, Because <2 and the angle measuring 95 degrees are vertical angles, m<2 = 95 degrees.

Also, Because 1, 2, and 3 make a triangle, m<3 = 40 degrees.

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Answer:

Step-by-step explanation:

im sorry Im only in 6th grade and I cant help you

Answer: I can not give an answer because you have not given enough information to answer it. If you could add a picture it would be greatly appreciated.

Jackson spent 4.60+p more than Tim in buying fruits.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, two friends shop for fresh fruit. Jackson buys a watermelon for ​$7.85 and 3 pounds of cherries.

Let the variable p to represent the​ price, in​ dollars, per pound of cherries.

So, the total cost is 7.85+3p

Tim buys a pineapple for ​$3.25 and 2 pounds of cherries.

Here, the total cost is 3.25+2p

Difference in there price is 7.85+3p -(3.25+2p)

4.60+p

Therefore, Jackson spent 4.60+p more than Tim in buying fruits.

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In this case, the limit is 0, so the series is indeed convergent.

The Root Test is used to determine the convergence or divergence of a series. and it is used the Root Test, we start by finding the nth root of each term in the series.

In this case, the series is

=> [∞] n = 1 4 1 1 n n²,

so we calculate the nth root of each term:

[tex]= > (1/n^{2} )^{1/n}[/tex]

Then, we take the limit of this expression as n approaches infinity, to find the value of the root.

If this limit is less than 1, the series is convergent. If the limit is greater than or equal to 1, the series is divergent.

In this case, the limit of [tex](1/n^{2} )^{1/n}[/tex] as n approaches infinity is 0, which is less than 1. This means that the series is convergent.

To confirm this, we can evaluate the limit of the absolute value of each term as n approaches infinity, using the formula

=> lim n → [∞] n |aⁿ|.

If this limit is finite, then the series is convergent.

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At the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Given that the function is:

f(x) = 5x + 7

To evaluate the function at the specified values substitute the value in x:

a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33

b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10

c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52

Hence, at the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.

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The equivalent ratios are given as follows:

Hence the coordinates are given as follows:

As the constant of the proportional relationship is of 3, starting from the origin, the points are plotted always moving one unit right (x) and three units up (y).

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Then the constant is obtained as follows:

k = y/x.

For this problem, the constant is given as follows:

k = 21/7 = 24/8 = 27/9 = 3.

(representing the equivalent ratios).

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Answer:

1256 miles

Step-by-step explanation:

the Pizza Hut driver has a circle with a radius of 20 which is the area he can cover. you're looking for the area of the circle, and the formula for the area of a circle is pi * r * r

If you substitute, you have 3.14*20*20, which is 1256

Answer:

ABD =30 +45

ABD=75

75°is the answer

Answer: 3/2 miles

Step-by-step explanation: Area of Park = Length * Width

Width = Area / Length= (6/8) / (1/2) = (6/8) * (2/1) = 3/2 miles.

The length of the segment MN = 5.4 unit

The length of the line segment bridging two points on a plane is known as the distance between the points.

The length of the segment MN = The distance from (-1, 2) and (4, 0).

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

The length of the segment MN = √{(4+ 1)² + (0 - 2)²}

The length of the segment MN = √{5)² + (2)²}

The length of the segment MN = √{29} = 5.385

Therefore, the length is 5.4 unit.

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All three students could be correct if they recorded the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces.

In order for all three students to be correct, they would have to be recording the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces. This would explain why each student has a different answer, as they are all measuring the mass in different units. The only way to ensure accuracy would be to measure the mass in the same unit of measurement, so that all students have the same answer.

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The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.

(a) Neither - This expression can be written as ¬(p ∨ q) ∧ (q ∨ ¬p), which is neither a tautology nor a contradiction.

(b) Contradiction - This expression can be written as (p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.

(c) Tautology - This expression can be written as (p ∨ q) ∧ p, which is a tautology because it is equivalent to p, which is always true.

(d) Contradiction - This expression can be written as (p ∨ q) ∧ ¬p, which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.

(e) Contradiction - This expression can be written as (¬p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (¬p ∨ q) ∧ (¬p), which is a false statement.

(f) Tautology - This expression can be written as (¬p ∨ q) ∧ (¬p ∨ q), which is a tautology because it is equivalent to (¬p ∨ q), which is always true.

The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.

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Side angle side formula is used to prove congruent triangles.

What are congruent triangles?

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has a symbol ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

Side angle side rule:

The triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

There are four rules of congruent triangles.

1) Side angle side

2) Side side side

3) Angle angle angle

4) Angle side angle

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48 will be the value to ensure that A′ is asymptotically faster than A.

The recurrence relation T(n)=7T(n/2)+n2 is given by the question, and its answer is the asymptotic complexity master theorem T(n)=(nlog49base4).

Therefore, the recurrence relation T′(n)=T′(n/4)+n2 can be used to express the complexity in general.

As a result, the relationship is as follows: a=, b=4, f(n)=n2.

For a value of the >16, nloga base b=nlog base 4, and the >0, f(n)=O(nlog).

As a result, for n > 16, T′(n) = (n log base 4)

Now since A is getting asymptotically faster than A', A must hold:

Base 4 (nlog) nlog49 base 4 Since the base is equal to e, we can calculate the power as follows: log base 4 log49 base 4. Thus, after solving, we will obtain 49.

Therefore, 48 will be the value to ensure that A′ is asymptotically faster than A.

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Distance is a scalar quantity that represents the total length of the path traveled by an object . It can be thought of as the magnitude of the displacement, which is the change in position of an object.

Displacement, on the other hand, is a vector quantity that represents the change in position of an object, taking into account the direction of travel. It is the shortest distance between the initial and final position of an object.

The distance traveled by the woman is the total length of her trip from her house to her office and back. It is equal to 2 * 10 km = 20 km.

Displacement is the final position of an object relative to its initial position, taking into account only the direction, and not the distance traveled. At 6:25 PM, the woman is back at her house, which is her initial position, so her displacement is 0 km.

So the correct answer is:

Distance traveled = 20 km

Displacement = 0 km

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The values of the trigonometric functions of t are Sin(t)=0.2, Cos(t) = -5/12, Csc(t) = 5,Sec(t) = -12/5, Cot(t) = -5/12 and  the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5π/7 rad is 8.86 m

To find the values of the trigonometric functions of t, the tan(t) value was used to calculate the sin(t) value by using the relationship sin²(t) + cos²(t) = 1. The other trigonometric functions were calculated by using the relationship among the trigonometric functions.

Sin(t) = √(1 - (tan(t))^2) = √(1 - (-12/5)^2) = √(1 - 144/25) = √(25/25 - 144/25)   = √(1/25) = 0.2

Csc(t)= 1/0.2= 5

The radius of the circle was then determined by using the arc length and the angle subtended at the center. The arc length was divided by the subtended angle to find the radius. The result was rounded off to two decimal places.

Radius r = (20m)/(5π/7)   = (20m*7)/(5π)   = 28/π = 8.86 m

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If PQ subtends angle at the circle's center, then let PQ be an arc with radius r and a center at O. Thus, the arc length of PQ is given by PQ = /360° (2r),  where is a degree.

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Blinding refers to the nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.

Blinding is a technique used in experimental design to reduce bias and improve the validity of results. It refers to the practice of not revealing to the experimental units (e.g., participants, animals) or the experimenters which treatment they are receiving in a controlled experiment. Blinding is used to eliminate potential sources of bias that might influence the results of the experiment.

For example, if the participants are aware of the treatment they are receiving, they might behave differently and affect the results. Similarly, experimenters might unconsciously treat participants differently based on their knowledge of the treatment, which could also affect the results.

Blinding is the practice of keeping the therapy that an experimental unit is getting a secret. In a single-blind experiment, the experimental unit (also known as the subject) is kept in the dark regarding the therapy that he or she is getting.

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Complete question:

                refers to nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.

Answer:

3x-9+34+24=180 (because the sum of angle of triangle is 180 )

3x+49=180

3x=180-49

3x=131

x=131÷3

x=43.67

The given statement can be justify by using angle inscribed theorem. The angle inscribed theorem define as the angle inscribed in a circle is half of the center angle which subtends same arc of the circle.

What is inscribed angle?

When two chords intersect on a circle, an inscribed angle is the angle that is created inside the circle. It can alternatively be described as the angle formed at a particular point on a circle by two specified points. Alternatively, two chords of the circle sharing an endpoint define an inscribed angle.

Angle inscribed theorem

As per the inscribed angle theorem angle inscribed in a circle is half of the center angle so the angle would be  or .

In geometry right angle is

Thus, the second corollary, that an angle inscribed in a semicircle is a right angle.

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The formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).

Given n balls, m of which are red and n - m are blue, if a collection of n < min{m, n - m} balls is taken out at random without replacement, the probability that exactly k balls are red can be calculated using the Hypergeometric Distribution. The formula for the probability that exactly k balls are red is given by: P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n)

where C(n, k) denotes the number of combinations of n things taken k at a time, and is given by: C(n, k) = n! / (k! * (n - k)!).

Therefore, the formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:

P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).

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The probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).

What is probability?

Calculating probability is a method of determining how likely something is to occur. The probability scale runs from 0 to 1, where 0 denotes impossible and 1 denotes certainty.

We are given that a single die is rolled 100 times.

So, the outcomes can be {1,2,3,4,5,6}

Now,

P(odd) = Probability of odd numbers

Odd numbers are 1, 3 and 5

So, P(odd) = 3/6 = 1/2

P(>4) = Probability of numbers greater than 4

Numbers greater than 4 are 5 and 6

So, P(>4) = 2/6 = 1/3

P(prime) = Probability of prime numbers

Prime numbers are 1, 2, 3 and 5

So, P(prime) = 4/6 = 2/3

P(8) = Probability of number 8

In a dice, the maximum number is 6

So, P(8) = 0

Hence, the probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).

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Answer:

-32, 64, -128

Step-by-step explanation:

Each term is -2 times the previous term. This means the next term is

(-2) x 16 = -32

Then,

(-2) x (-32) = 64

and lastly,

(-2) x 64 = -128