A pebble is dropped into a pond, and the resulting ripple travels 3 ft/sec. How fast is the area inside the ripple increasing when the ripple is 8 feet in diameter?

Answer:

Step-by-step explanation:

The general equation is y = mx + b

You already have m which is the slope. So the general equation becomes y = -5x + b

The point is meant to find b

x = - 4

y = 7

7 = - 5*-4 + b

7 = 20 + b                         Subtract 20 from  both sides.

7 - 20 = 20-20 + b           Combine

- 13 = b

Answer: y = - 5x - 13

Answer:

30 - 2xx = x

Step-by-step explanation:

Answer:

A= 30 - 2x

Step-by-step explanation:

Answer:

D. She used the beach's ball's diameter when she should have used the radius

Step-by-step explanation:

To find the volume of the beach ball, using the volume of a sphere is the right formula to use, which is ⁴/3πr³.

The formula she used is correct.

Since the diameter of the ball is assumed to be 12 inches, what is needed to find the volume is the radius.

Radius (r) = ½(diameter) = ½(12) = 6 in.

This is where Emily made a mistake.

She used the diameter of the beach ball instead of its radius (r) which is needed in the equation.

She should have gotten,

V = ⁴/3(3.14)(6)² = 904.32 cubic inches

The derivative of the function f(x) = x^2 - 3x + 3 at the number a is f'(a) = 2a - 3.

To find the derivative of the function f(x) = x^2 - 3x + 3 at the number a, we can use the definition of the derivative:

\(f'(a) = lim(h - > 0) [f(a + h) - f(a)] / h\)

Plugging in the function \(f(x) = x^2 - 3x + 3\):

\(f'(a) = lim(h - > 0) [(a + h)^2 - 3(a + h) + 3 - (a^2 - 3a + 3)] / h\)

Expanding and simplifying:

\(f'(a) = lim(h - > 0) [a^2 + 2ah + h^2 - 3a - 3h + 3 - a^2 + 3a - 3] / h\)

Canceling out terms:

\(f'(a) = lim(h - > 0) [2ah + h^2 - 3h] / h\)

Now we can factor out an h from the numerator:

\(f'(a) = lim(h - > 0) h(2a + h - 3) / h\)

Canceling out an h from the numerator and denominator:

\(f'(a) = lim(h - > 0) 2a + h - 3\)

Taking the limit as h approaches 0:

\(f'(a) = 2a - 3\)

Therefore, the derivative of the function f(x) = x^2 - 3x + 3 at the number a is f'(a) = 2a - 3.

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Answer:

ewan hahahahahahhhahaahahahah

1

The exact value of tan(π4) tan ( π 4 ) is 1 .

Answer:

Step-by-step explanation:

As,

Landslide, also called landslip, the movement downslope of a mass of rock, debris, earth, or soil (soil being a mixture of earth and debris).

Landslides occur when gravitational and other types of shear stresses within a slope exceed the shear strength (resistance to shearing) of the materials that form the slope.

Answer:

Landslide                              

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The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer:

$25.76

Step-by-step explanation:

$1.12×23ft=$25.76

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

The FALSE statement is e. Mail questionnaires typically provide more sample control than telephone or personal interviews.

The FALSE statement is e. Mail questionnaires typically provide more sample control than telephone or personal interviews. While mail questionnaires have their advantages, such as ease of administration and cost-effectiveness, they generally provide less sample control compared to telephone or personal interviews.

In mail surveys, there is a lack of direct interaction with the respondents, making it challenging to ensure the desired sample representation and control over non-response. On the other hand, telephone and personal interviews allow for real-time communication, clarification of questions, and potential probing, which can lead to better sample control and higher response rates.

Therefore, statement e is false, and it is important to consider the strengths and limitations of different survey methods when choosing the most appropriate approach for research purposes.

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The complementary angles will be 65.6° and 24.4°.

What exactly are complementary angles?

Supplementary and complementary angles are defined by the sum of two angles. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined. If the total of two angles is 180 degrees, they are considered to be supplementary angles since they produce a linear angle when combined.

Now,

Let x be a angle then its complementary angle will be 90°-x as sum of complementary angles is equal to 90°.

as given

90°-x-x=18.8°

9--2x=18.8

2x=71.2

x=65.6° and 90-x°=24.4°

hence,

                The complementary angles will be 65.6° and 24.4°.

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Nominal wage changes have no impact on the economy's output in the long run. The long-run equilibrium output is determined by factors such as technology, productivity, and the availability of resources. Nominal wages alone do not directly affect the economy's output in the long run.

In the long run, the economy reaches a state of equilibrium where the aggregate price level and real GDP stabilize. The long-run aggregate supply (LRAS) curve represents the level of output that can be sustained without causing inflationary or deflationary pressures. It is determined by factors such as the available resources, technology, and productivity.

Nominal wages refer to the wages stated in current dollars, without adjusting for inflation. While changes in nominal wages can affect the distribution of income and purchasing power in the short run, they do not impact the economy's output in the long run. This is because nominal wage changes do not alter the underlying factors that determine the economy's productive capacity and potential output.

Therefore, the correct answer is that nominal wages have no impact on output in the long run. The long-run equilibrium level of output is determined by factors beyond nominal wage changes, such as technology, productivity, and the availability of resources.

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As a result, (b) is the spot on the circle (15,20).

Learn how to apply the Pythagorean theorem to determine the separation between two locations using the distance calculation. The Pythagorean formula can be rewritten as d=(((x 2-x 1)²+(y 2-y 1)²) to calculate the separation between any two locations.

We can use the distance formula to determine if a point is on the circle. The distance between the center of the circle and any point on the circle should be equal to the radius of the circle.

Let's test each point to see if it lies on the circle:

(a) (21,12)

Distance from center of circle:

d = √((21-15)² + (12-20)²) = 10.77

The distance from the center of the circle to point (21,12) is greater than the radius of the circle, so this point does not lie on the circle.

(b) (15,20)

Distance from center of circle:

d = √((15-15)² + (20-20)²) = 0

The distance from the center of the circle to point (15,20) is equal to the radius of the circle, so this point lies on the circle.

(c) (14,7)

Distance from center of circle:

d = √((14-15)² + (7-20)²) = 13.04

The distance from the center of the circle to point (14,7) is greater than the radius of the circle, so this point does not lie on the circle.

(d) (25,25)

Distance from center of circle:

d = √((25-15)² + (25-20)²) = 11.18

The distance from the center of the circle to point (25,25) is greater than the radius of the circle, so this point does not lie on the circle.

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Answer:

12.05

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(2 - 1)² + [4 - (-8)]²

√(1)² + (12)²

√(1) + (144)

√145

12.05

For the utility function U(x, y) = \(x^(4/1) * y^(4/3)\), the indifference curve equations for U = 1, U = 2, and U = 3 are derived. The shape of the indifference curves resembles rectangular hyperbolas.

For the utility function U(x, y) = \(x^(4/1) * y^(4/3)\), we derive the indifference curve equations for U = 1, U = 2, and U = 3. By setting the utility function equal to these values, we can solve for the corresponding relationships between x and y.

The resulting equations form rectangular hyperbolas, where the ratio of x to y remains constant along each curve. These curves are concave and exhibit diminishing marginal rates of substitution.

For the utility function U(x, y) = y - 2x, we derive the indifference curve equations for U = 1, U = 2, and U = 3. By setting the utility function equal to these values, we can solve for the relationships between x and y.

The resulting equations represent straight lines with a slope of 2, indicating a constant marginal rate of substitution between x and y. These indifference curves show a positive linear relationship between the two goods.

Both utility functions satisfy the assumptions of completeness, transitivity, and monotonicity. Completeness implies that the consumer can rank all bundles of goods, transitivity ensures consistent preferences, and monotonicity states that more of a good is preferred to less.

The derived indifference curves reflect these assumptions by providing a consistent ranking of bundles based on utility. The shapes of the indifference curves are well-defined, allowing for clear visual representations of the preferences of the consumer.

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Answer:

Step-by-step explanation:

x= fund that got 7%

y= fund that got 3%

x+y=3000

.07x+.03y=142

y=3000-x

.07x+.03(3000-x)=142

.07x+90-.03x=142

.04x=52

x= 1300

x+y=3000

1300+y=3000

y=1700

1300 in the fund that earned 7%

1700 in the fund that earned 3%

The t-value for a 98% confidence level with a sample standard deviation and 52 degrees of freedom is 2.03.

To calculate the t value for a 98% confidence level with a sample standard deviation and 52 degrees of freedom, we used the t-distribution table. The t-distribution table has two variables: degree of freedom and confidence level.

The first step was to locate the row in the table that corresponds to the given degrees of freedom (df=52). The next step was to locate the column in the table that corresponds to the given confidence level (98%). the t -value for the given df and CL was located at the intersection of the row and column, which is -2.03. essentially the t-distribution table provides a range of values for the amount of variability that is expected within a given sample.

The t-value is the point within the range that will represent the 98% confidence level for the sample with 52 degrees of freedom. the t-value of -2.03 indicates that the sample has a 9.8% chance of falling within a range of values that is two standard deviations away from the mean.

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

Answer:

It is 4

Step-by-step explanation:

Tim drove at a distance of 511 km in 7 h. His average driving speed in km/h is 73.

By computing Tim's average driving speed, we have to divide the total distance that he traveled by the time it takes him to complete the whole journey. In this respect, Tim drove a total distance of 511 km in 7 hours.

Average driving speed = Total distance/Total time taken

By putting the values in the equation we get :

Average driving speed =\(\frac{ 511 km}{7 h}\)

Now by computing  the average driving speed:

Average driving speed = 73 km

So, Tim's average driving speed was 73 km/h.

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The area of the circle \( r = 4 \sin \theta \) in the first quadrant is 8 square units.

To find the area of the circle \( r = 4 \sin \theta \) in the first quadrant, we need to integrate the equation with respect to theta within the appropriate range.

In the first quadrant, theta ranges from 0 to π/2. We can rewrite the equation as \( r^2 = (4 \sin \theta)^2 \) to eliminate the square root.

Expanding the equation, we get \( r^2 = 16 \sin^2 \theta \).

Using the conversion formula for polar coordinates, the area element in polar coordinates is given by \( dA = \frac{1}{2} r^2 d\theta \).

Substituting the value of \( r^2 \), we have \( dA = 8 \sin^2 \theta d\theta \).

Now, we can integrate the area element from 0 to π/2 to find the total area:

\[ A = \int_0^{\frac{\pi}{2}} 8 \sin^2 \theta \, d\theta \]

Using the trigonometric identity \( \sin^2 \theta = \frac{1 - \cos(2\theta)}{2} \), we can simplify the integral:

\[ A = 8 \int_0^{\frac{\pi}{2}} \frac{1 - \cos(2\theta)}{2} \, d\theta \]

Integrating, we get:

\[ A = 4 \left[ \theta - \frac{\sin(2\theta)}{2} \right]_0^{\frac{\pi}{2}} \]

\[ A = 4 \left( \frac{\pi}{2} - \frac{\sin(\pi)}{2} - 0 + \frac{\sin(0)}{2} \right) \]

\[ A = 4 \left( \frac{\pi}{2} - 0 \right) \]

\[ A = 2\pi \]

Therefore, the area of the circle \( r = 4 \sin \theta \) lying in the first quadrant is 2π square units, which is approximately 6.28 square units when rounded to two decimal places.

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Answer:

the answer is vsco girls are annoying

Step-by-step explanation:

Answer: m=6 I think n=14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Add all the angles together then subtract it by the total angle of the shape by using the method ( n − 2 ) × 180 n being the number of angles. To find x.

Then subtract the value of x by 360 to find the 5 because it is reflex.

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D. The energy used is the same for both segments, the power while running is greater.

Walking and running both require energy, but the distance covered and the time taken are different. In this case, the person covers the same distance of 1 km in both segments.

Therefore, the energy used is the same for both. However, since running involves covering the same distance in less time, the power while running is greater. Power is the rate at which energy is used, and since running takes less time, the power output is higher.

D. The energy used is the same for both segments, the power while running is greater.

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Based on the distance that the yellow jacket flies in 9 seconds, the unit rate in meter per second is 0.5 m/s

The unit rate of the yellow jacket can be found by the formula:

= Distance travelled / Number of seconds

Solving gives:

= 4.5 / 9

= 0.5 meter per second

= 0.5 m/s

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The big O notation for the given code fragment with nested loops is O(n log n), indicating that the runtime grows proportionally to the product of the input size and its logarithm.

The big O notation for the given fragment can be determined by analyzing the nested loops.

The outer loop runs for every power of 2 from 1 to n, which is log₂(n) iterations.

The inner loop runs for n iterations regardless of the value of n.

Therefore, the total number of iterations can be calculated as the product of the iterations of the outer and inner loops, which is O(n log n).

In big O notation, the dominant term is the one that grows fastest as the input size (n) increases. In this case, the log n term dominates over the linear term, so the big O notation for the fragment is O(n log n).

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