A hot air balloon rose from a height of 100 meters to 450 meters in 3
minutes. What was the balloon's rate of change

Answer:

 (x - 8)^2 + y^2 = 3.

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

Here h = 8, k = 0 and r^2 = (√3)^2 = 3

The answer is  (x - 8)^2 + (y - 0)^2 = 3

or (x - 8)^2 + y^2 = 3.

The value of the function at x = 4 is 8.79.

Tangent line approximation is the approximation of any function using a linear function. It is also called as linear approximation.

It allows us to approximate the value of a general function with a more simpler linear function.

Given that,

f(1) = 2

f'(x) = \(\sqrt{x^{2} +2cos x + 3}\)

We have the formula for linear approximation as,

f(x) = f(a) + f'(a) (x - a)

Here x = 4 and a = 1

f(a) = f(1) = 2

f'(a) = f'(1) = \(\sqrt{1^{2} +2cos 1 + 3}\) = 2.254

Substituting,

f(4) = 2 + (2.254) (4 - 1)

     = 8.762 ≈ 8.79

Hence the value of f(4) is 8.79.

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Answer:

Step-by-step explanation:

\(f(x)=\frac{x^{2} - 8 x + 12}{x - 6}\)

VERTICAL ASYMPTOTES

The line x = L is a vertical asymptote of the function \(y=\frac{x^{2} - 8 x + 12}{x - 6}\)

, if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x=6, check:

\(\lim_{x \to 6^+}\left(x - 2\right)=4\)

Since the limit is finite, check another limit.

\(\lim_{x \to 6^-}\left(\frac{x^{2} - 8 x + 12}{x - 6}\right)=4\)

Since the limit is finite, then x=6 is not a vertical asymptote.

HORIZONTAL ASYMPTOTES

Line y=L is a horizontal asymptote of the function y=f(x), if either \(\lim_{x \to \infty} f{\left(x \right)}=L\)

or \(\lim_{x \to -\infty} f{\left(x \right)}=L\) , and L is finite.

Calculate the limits:

\(\lim_{x \to \infty}\left(\frac{x^{2} - 8 x + 12}{x - 6}\right)=\infty\)

\(\lim_{x \to -\infty}\left(\frac{x^{2} - 8 x + 12}{x - 6}\right)=-\infty\)

Thus, there are no horizontal asymptotes.

SLANT ASYMPTOTES

Do polynomial long division \(\frac{x^{2} - 8 x + 12}{x - 6}=x - 2\) Thus, the slant asymptote is y=x−2.

Answer

No vertical asymptotes.

No horizontal asymptotes.

Slant asymptote: y=x−2

(a) The sequence {z_n} converges to 5 - i.

(b) The sequence {z_n} does not converge.

(c) The sequence {z_n} is a sequence of angles. Angles do not form a convergent sequence, so the sequence {z_n} does not converge.

(d) The sequence {z_n} converges to 1.

a. We can prove this using the definition of convergence. A sequence {z_n} converges to a number z if for every ε > 0, there exists an N such that for all n > N, |z_n - z| < ε.

In this case, let ε = 1. Then for all n > 3, |z_n - (5 - i)| = |(n + 1)/(3n) * (5 - i) - (5 - i)| = |(5 - i)/(3n)| < 1/3 < ε.

Therefore, the sequence {z_n} converges to 5 - i.

b. We can prove this using the ratio test. The ratio test states that a geometric sequence converges if the absolute value of the common ratio is less than 1 and diverges if the absolute value of the common ratio is greater than or equal to 1.

In this case, the absolute value of the common ratio is 3/2, which is greater than 1. Therefore, the sequence {z_n} diverges.

c. We can prove this by showing that for any two angles α and β, there exists an integer n such that z_n = α and an integer m such that z_m = β.

Let α = 0 and β = π/2. Then for n = 2, z_n = Arg(-2 + 2i) = π/2. For m = 3, z_m = Arg(-2 + 3i) = 0. Therefore, the sequence {z_n} does not converge.

d. We can prove this using the ratio test. The ratio test states that a geometric sequence converges if the absolute value of the common ratio is less than 1 and diverges if the absolute value of the common ratio is greater than or equal to 1.

In this case, the absolute value of the common ratio is e^(2πi/7), which is less than 1. Therefore, the sequence {z_n} converges.

The sum of the infinite geometric series with first term 1 and common ratio e^(2πi/7) is given by 1/(1 - e^(2πi/7)). This can be simplified to 1. Therefore, the limit of the sequence {z_n} is 1.

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Answer:

plot it on -4

Step-by-step explanation:

Answer: -3

Step-by-step explanation:

Answer:

Probability that a student who passed the test did not  complete the homework = 0.07

Step-by-step explanation:

Given:

Total number of students = 28

Number of students who passed the test = 18

Number of students who completed  the assignment = 23

Number of students who passed the test and also completed the  assignment = 16

To find: probability that a student who passed the test did not  complete the homework

Solution:

Probability refers to chances of occurrence of some event.

Probability = number of favorable outcomes/total number of outcomes

Let A denotes the event that students passed the test and B denotes the event that students completed  the assignment

P(A only) = \(P(A)-P(A\cap B)\)

Here,

\(P(A)=\frac{18}{28}\,,\,P(A\cap B)=\frac{16}{28}\)

So,

\(P(A\,\,only)=\frac{18}{28}-\frac{16}{28}=\frac{2}{28}=\frac{1}{14}=0.07\)

Therefore,

probability that a student who passed the test did not  complete the homework = 0.07

Answer:

2/9

Step-by-step explanation:

Answer:

( 36 + 14 ) / 2 x 5  

I hope im right !

Answer:

For radio = $40.43

Television =  $444.73

Player =  $364.73

Step-by-step explanation:

The computation of the each device cost is shown below:

let us assume the following things

radio be x

television x + 10x

player x + 10x - $80

Now the equation is

x + x + 10x + x + 10x - $80 = $850

3x + 20x - $80 = $850

23x = $930

x = $40.43

For radio = $40.43

Television = $40.43 + 10(40.43)

= $40.43 + $404.3

= $444.73

and, the player would be

= $444.73 - $80

= $364.73

Answer:

Yes

Step-by-step explanation:

2 pennies and 3 dimes = 60 cents

I penny = 1 cent

1 dime = 10 cents

In Korea, tofu is typically offered during breakfast.

Describe breakfast.

The first meal of the day, known as breakfast, is often had in the morning. After an overnight fast, it is a crucial meal that gives the body and brain fuel. Protein and carbs are generally found in breakfast foods such eggs, bacon, oatmeal, toast, pancakes, yoghurt, cereal, and fruits. A nutritious breakfast may boost energy levels, jump-start the metabolism, and enhance focus and memory. A nutritious breakfast can also aid in lowering mid-day snacking and preventing overeating in the evening. Make sure to incorporate breakfast in your daily schedule since eating breakfast is crucial to living a healthy lifestyle.

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The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos(\(\pi\)t).

As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.

Calculation for the cosine function-

The given function is: cosine function, d = acos(bt).

As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.

The total time 't' by the pendulum is 2 sec.

Calculate the angular speed of the pendulum by-

ω = 2\(\pi\)f

   = 2\(\pi\)×(1/2)

ω = \(\pi\) which is 'b' value of the given function.

As given, the distance of the pendulum from the centre is half of the total distance.

a = 12/2

a = 6

Substitute the obtained values in the cosine function, d = acos(bt),

d(t) = 6cos(\(\pi\)t)

Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is  d(t) = 6cos(\(\pi\)t).

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The complete question is -

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).

Answer:

a=6

The period is 2 seconds.

b=pi

t=0.5

d=4.243

Step-by-step explanation:

Answer:

i think it might be A

Step-by-step explanation:

Answer;

12/a

Step-by-step explanation:

Here, we want to reduce the given expression to the lowest term

We have this as;

33/5 * 20/11 * a^2/a^3

= 33/11 * 20/5 * a^2/a^3

= 3 * 4 * 1/a

= 12/a

Answer:

8.94

Step-by-step explanation:

Distance formula:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\)

\(d = \sqrt{(3 - (-5))^2 + (2-6)^2}\)

\(d = \sqrt{(64 + 16)}\)

\(d= \sqrt{80}\)

\(d= 8.94\)

The first digit must be 1. The remaining seven ones must be either 0 or 1.

Therefore, there can be formed \(2^7=128\) different numbers.

Answer:

c)

subtract 5 times the second equation from 2 times the first equation

Step-by-step explanation:

subtract 5 times the second equation from 2 times the first equation

This will make the coefficient of the y variable 10

for both equations

10y - 10y = 0

leaving only x

The measure of BC is 24 cm.

The diagram of circle A with two tangents is given in the attached figure.

The given radius of the circle is 10 cm.

AC = 26 cm

We require to calculate the value of BC.

We have,

AD = AB = 10 cm

We know that the radius of a circle is always perpendicular to the tangent at the point of intersection. It suggests that triangle ABC is a right-angle triangle.

Using the Pythagoras theorem, we get

AB² + BC² = AC²

10² + BC² = 26²

BC² = 676 - 100

BC² = 576

Take square root on both sides,

BC = √576

BC = 24

The measure of BC is 24 cm.

Hence, the correct answer is B.

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--The given question is incomplete; the complete question is

"Circle A has a radius of 10 centimetres. BC and CD are tangent to circle A. If AC = 26 cm, what is BC?

A)20cm

B)24cm

C)26cm

D)2√194cm'--

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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Answer:

no

Step-by-step explanation:

w would have to be bigger or greater than 27. 1 is less than

Answer: yes, 1> 27 is an inequality. This states 1 is greater than 27, which is incorrect the correct solution would be w<27.

hope this helps :)

Answer:

D

Step-by-step explanation:

since it is not in a parentheses with x that means it only affects the y axis, resulting in a vertical compression by a factor of 9

plz, mark me brainliest ;)

Answer:

$32040

Step-by-step explanation:

1=2232

To calculate John's BMI, we need to use the formula BMI = weight (kg) / height (m)^2. When we calculate this, we get a BMI of 36.1.

First, we need to convert John's height and weight to the metric system. His height is 1.75 meters and his weight is 110.5 kilograms.
Next, we can plug those values into the formula: BMI = 110.5 / (1.75)^2.
According to the Centers for Disease Control and Prevention, a BMI of 30 or above is considered obese. Therefore, John falls into the obese category based on his BMI.
It's important to note that BMI is just one measure of health and does not take into account muscle mass or other factors that can affect weight. It's always best to speak with a healthcare professional to determine a healthy weight and lifestyle plan.

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The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.

The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.

Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.

Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.

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Answer:

Step-by-step explanation:

it’s ca

Answer: 29152332 ≡ 0 (mod 3)

Step-by-step explanation:

In modular arithmetic, there is the form a ≡ b (mod m) where b is the remainder.

To solve this problem, we want to divide 29152332 by 3 and find the remainder.

29152332 ÷ 3 = 9717444

Since we get an integer with no remainder, we know the answer is 29152332 ≡ 0 (mod 3).

Of the following one that is not considered a guideline for developing visualizations is vary the scale to conserve space whenever possible. (Option B)

Data and information visualization refers to an interdisciplinary field that focuses on the graphic representation of data and information. It is an efficient way of communicating when the data or information is numerous. It aims to present the data in a clear manner and with a clear purpose. The aim of the texts and labels should be to clarify and not clutter. According to the guidelines for developing visualization, it is not recommended to vary the scale to conserve space whenever possible.

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He have 48 different possible outfits to wear at work with three one-piece jump suits, five pairs of work pants, and eight work shirts.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that.

Here,

5 pants with each of 8 shirts,

=5 x 8

=40 combinations of shirts and pants.

40 shirt/pants outfits + 8 jumpsuits = 48 total outfits.

With three one-piece jumpsuits, five pairs of work pants, and eight work shirts, he has 48 different work-appropriate outfit options.

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The length and width of the rectangle with perimeter 254 yards are 57 and 70 yards respectively.

Perimeter of rectangle is 2(Length + width)

Given,

Perimeter of rectangle = 254 yards

Width = Length+ 13

Consider the Length of the rectangle as "x". Thus, width of the rectangle is x+13 ( as it is 13 yards more than the Length ).

Put the value in the formula.

=> 254 = 2(x+x+13)

=> 254 = 2(2x+13)

=> 254 -26 = 4x

=> 228= 4x

=>  x = 57 (length)

=>  x+13= 70( width)

Therefore, we get length = 57 yards and width = 70 yards.

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We are given an economy with two goods and Leontief consumers who have utility functions that depend on the minimum of the two goods. The initial endowments of the consumers are positive, and we are assuming that the aggregate endowment of the economy has more of the first good than the second. If a price system p=(p1,p2) is an equilibrium with market clearing, we need to show that p1=0 and p2>0.

We start by considering the demand function for a Leontief consumer, which is given by xi1(p) = xi2(p) = (p1 + p2)mi/pi, where mi represents the initial endowment of consumer i and pi represents the price of good i.

Since the aggregate endowment ω=(ω1,ω2) of the economy satisfies ω1 > ω2, we know that the total supply of the first good is greater than the total supply of the second good.

Now, if p1 > 0, then for any positive value of p2, the demand for the second good xi2(p) will be positive for all consumers. This implies that the total demand for the second good will be greater than the total supply, leading to a market imbalance.

To achieve market clearing, where total demand equals total supply, we must have p1 = 0. This is because if p1 = 0, the demand for the first good xi1(p) will be zero for all consumers, and the total supply of the first good will match the total supply. Additionally, p2 must be positive to ensure positive demand for the second good.

Therefore, we have shown that in an equilibrium price system with market clearing, p1 = 0 and p2 > 0, given the initial endowment condition ω1 > ω2.

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Answer: x=90 y=48 z=60

Step-by-step explanation: z=y+12 because they are parallel lines and must be equal alternate interior angles theorem. And y-18+z=90, because they are a right angle. x is 90 degrees because it is also a right angle