the top of a 13 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. how fast is the bottom of the ladder sliding along the ground away from the wall when the bottom of the ladder is 12 feet away from the base of the wall?

To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0), we can use the formula:

dy/dx = (dy/dtheta) / (dx/dtheta) = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))

where r' = dr/dtheta.

First, we need to find r' by taking the derivative of r with respect to theta:

r' = dr/dtheta = -7 sin(theta)

Then, we can plug in the given values to find the slope at (16, 0):

dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]

= [(-7 sin(0) sin(0) + (9 + 7 cos(0)) cos(0))] / [(-7 sin(0) cos(0)) - (9 + 7 cos(0)) sin(0))]

= (9 + 7) / (-9) = -2

Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0) is -2.

To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi), we can use the same formula as above:

dy/dx = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))

First, we need to find r' by taking the derivative of r with respect to theta:

r' = dr/dtheta = -7 sin(theta)

Then, we can plug in the given values to find the slope at (2, pi):

dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]

= [(-7 sin(pi) sin(2) + (9 + 7 cos(pi)) cos(2))] / [(-7 sin(pi) cos(2)) - (9 + 7 cos(pi)) sin(2))]

= (-2) / (7)

Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi) is -2/7.

The polar curve r = 9 + 7 cos(theta) intersects the origin when r = 0, which occurs when cos(theta) = -9/7, which is not possible since the range of cosine function is [-1, 1]. Therefore, the curve does not intersect the origin.

Since the curve does not intersect the origin, the answer is "The curve does not intersect the origin" for the equation of the tangent line in polar coordinates.

y + 1 = -3 (x - 2) an equation of the line in point-slope form with the given slope and the point it passes through, slope=(2,-1)

An indication as to how sharp a line is its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The ratio of the increase in elevation between two places to the run in elevation between those same two points is referred to as the slope.

Slope-related equations The "change in y" over the "change in x" of a line is referred to as the slope. By dividing (y₂ - y₁) over (x₂ - x₁) and choosing two locations on the line (x₁, y₁) and (x₂, y₂), you can get the slope.

The point-slope formula states: (y₂- y₁) = m (x₂ - x₁)

where, m = slope and (x₁, y₁) is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

[y₂- (-1)] = -3 (x₂ - 2)

y + 1 = -3 (x - 2)

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The complete question is as follows:

How do you write the equation in point slope form given (2,-1), m= -3?

We can solve the problem using the We can solve the problem using the time value of money formula, which relates present value, future value, time, and interest rate. Let i and j be the two interest rates, then:$100 + \frac{$108.15}{(1+i)^2} = \frac{$208}{(1+j)}$.

Simplifying and rearranging, we get:

$\frac{1}{(1+j)} = \frac{1}{(1+i)^2} + \frac{108.15}{100(1+i)^2}$

To find the absolute difference between i and j, we can use trial and error or a numerical method such as Newton-Raphson. Using trial and error, we can start with i = j = 0.05 (5%) and calculate the left and right-hand sides of the equation. If they are not equal, we can adjust one of the rates and try again until we get a match.

After several iterations, we find that i = 0.05 and j = 0.06 (6%) satisfy the equation. The absolute difference between the two rates is |i - j| = |0.05 - 0.06| = 0.01 (1%). Therefore, the absolute difference between the two rates is 1%.

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Answer:

aas

Step-by-step explanation:

it's marked two angles and one side, which is angle angle side, the posulate aas.

Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

In plan A,

    Plans for saving = $500

  Amount of saving each week = $20

∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)

                                                                       = 25

In plan B,

    Plans for saving = $500

   Amount of saving each week = $30

∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)

                                                                       = 17

In plan C,

    Plans for saving = $500

   Amount of saving each week = $40

∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)

                                                                       = 13

In plan D,

    Plans for saving = $500

   Amount of saving each week = $50

∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)

                                                                       = 10

So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

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The real interest rate, using the approximation formula, is 0.01 or 1%. This means that after considering the expected inflation rate, the purchasing power of the money grows at a rate of 1%.

The real interest rate can be calculated using the approximation formula: real interest rate = nominal interest rate - expected inflation rate.

We have:

Nominal interest rate (i) = 0.04

Expected inflation rate (+1) = 0.03

Using the formula, we can substitute the given values:

Real interest rate = 0.04 - 0.03

Calculating the difference:

Real interest rate = 0.01

Therefore, the real interest rate, using the approximation formula, is 0.01 or 1%.

The nominal interest rate represents the rate at which money grows in a bank account or investment without considering inflation. On the other hand, the real interest rate takes into account the effects of inflation, allowing us to understand the true purchasing power of the money.

To calculate the real interest rate, we subtract the expected inflation rate from the nominal interest rate. In this case, the nominal interest rate is 0.04 (4%), and the expected inflation rate is 0.03 (3%).

Substituting the values into the formula, we get:

Real interest rate = 0.04 - 0.03

Real interest rate = 0.01 or 1%

Therefore, the real interest rate, in this scenario, is 0.01 or 1%. This means that after accounting for inflation, the purchasing power of the money grows at a rate of 1%.

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The approach to probability that assumes that the events are equally likely is d. classical probability.

Classical probability, also known as a priori or theoretical probability, is based on the assumption that all possible outcomes of an experiment or event are equally likely. In this approach, probability is determined by the ratio of favorable outcomes to the total number of equally likely outcomes.

For example, when rolling a fair six-sided die, the classical probability of rolling a specific number, such as a 3, is 1 out of 6 because there is one favorable outcome (rolling a 3) out of six equally likely outcomes (rolling any number from 1 to 6).

Classical probability is often used in situations where the outcomes are known and the sample space is well-defined. However, in practice, events may not always have equally likely outcomes, and other approaches such as empirical or subjective probability may be more appropriate.

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The surface area of the rectangular prism is 462 square feet.

Length, L = 10 ft

Width, W = 6 ft

Height, H = 7 ft

SA= 2(LW + LH + WH)

= 2(10×7 + 10×6 + 6×7)

= 2(70+60+42)

= 2(172)

= 344 square feet

Surface area of the missing prism:

Length, L = 5 ft

Width, W = 2 ft

Height, H = 7 ft

SA= 2(LW + LH + WH)

= 2(5×2 + 5×7 + 2×7)

= 2(10 + 35 + 14)

= 2(59)

= 118 square feet

Therefore, the surface area of the figure

= 344 square feet + 118 square feet

= 462 square feet

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The plan that is most useful for demonstrating a new technology or service or to reach a market that is widely spread out is a proof-of-concept website

The statement about the market section of the classic business plan that is not true is that some people prefer to relocate the competition and competitive advantage section from the market section to the industry section.

A critical risk to the success of your business plan is Overlooked competition.

The pitch deck categories that is sometimes given in the form of a user's experience is Problem slide.

There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is to get the listener to Make a micro-commitment

A good marketing strategy is most likely to focus on the longer-term competitive plan.

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There are 48 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

Explanation: We are given that a standard deck of 52 cards. (a) The first card is an Ace and (b) the second card is not a Queen. In a standard deck of 52 cards, there are four aces. If the first card drawn is an ace, then there are 51 cards left in the deck and 12 cards that are queens. Hence, there are 51 − 12 = 39 cards that are not queens. So, we can say that, There are 4 aces × 39 cards that are not queens = 156 ways to choose two different cards from a standard 52-card deck such that the first card is an Ace and the second card is not a Queen.

However, we have to remove the case where both cards are aces and the second card is a queen. So, we subtract 1 from the previous answer to get, 156 − 1 = 155 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

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Answer:

35

Step-by-step explanation:

f(x)=5x^3-2x^2+3

f(2)=5x2^3-2x2^2+3

=5x8-2x4+3

=40-8+3

=40-5

=35

Answer:

35

Step-by-step explanation:

F(x) = 5x^3 -2x^2 + 3

Let x=2

F(2) = 5(2)^3 -2(2)^2 + 3

       = 5*8 -2(4) +3

       = 40 -8+3

       = 32+3

      = 35

Answer:

Itis 11

Step-by-step explanation:

0.22 times 50=11

By answering the presented question, we may conclude that  area of the circle is  = 113.1 mm².

A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

area of a circle A = πr²,

A = π(6 mm)² = π(36 mm²) ≈ 113.1 mm²

area = 113.1 mm².

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We know that 7x - 1 must equal 125 because of Alternate interior angles. Now, let's solve for x.

Therefore, we can conclude that x = 18.

Hoped this helped.

\(BrainiacUser1357\)

\(\\ \tt\Rrightarrow 7x-1=125\)

\(\\ \tt\Rrightarrow 7x=125+1\)

\(\\ \tt\Rrightarrow 7x=126\)

\(\\ \tt\Rrightarrow x=126/7\)

\(\\ \tt\Rrightarrow x=18\)

Answer:

Step-by-step explanation:

p(x)=7x+20

p=7x/x + 20/x

answer   p=7+20/x

I hope its helpful.

Answer:

Hay 3,875 litros de jugo multifrutal.  

Step-by-step explanation:

(Se asume que el problema fue propuesto en un país distinto a los Estados Unidos, razón por la cual se emplea las reglas del Sistema Internacional.)

La capacidad de jugo multifrutal en el bidón se obtiene con la mezcla de cada jugo frutal y se logra mediante la suma de cada capacidad. A partir del enunciado, tenemos que la capacidad del jugo multifrutal es:

\(V = \frac{3}{4}\,L + 1\,\frac{1}{2}\,L + \frac{1}{8}\,L + 1\,\frac{1}{2}\,L\)

\(V = \frac{3}{4}\,L + 1\,L + \frac{1}{2}\,L + \frac{1}{8}\,L + 1\,L + \frac{1}{2}\,L\)

\(V = 3,875\,L\)

Hay 3,875 litros de jugo multifrutal.  

pretty sure that the answer is 2 cuz

Answer:

Greater than

Step-by-step explanation:

The quotient of 3 and 1/4 would be 3/(1/4).

You could then multiply by the inverse of 1/4 to simplify the expression. This would give you \(3*\frac{4}{1}\) or just 3 times 4. 3 * 4 = 12.

Since 12 is greater than 3, the quotient of 4 and 1/4 is greater than 3.

Answer:

So the answer is 30%

Step-by-step explanation:

1. For 50 = 15 increase euros

2. For 100 = 15/50 x 100 = 30 increase in euros

3. 30/100 = 30%

OR....

1. Ten percent of 50 is 5.

2. 5x3= 15(increase in euros)

3. 10 percent three times which is equal to 30%.

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:88

Step-by-step explanation: cause it say 88 students in class then it say how many students per class its 88 i think

Answer:

22

Step-by-step explanation: divided 88 by 4

Answer:

0.5 or 1/2...........................

Using the division, 12 times will Pogo fetch the frisbee in 444 minutes.

In the given question we have to find how many times will Pogo fetch the frisbee in 4 minutes.

As given that the double number line shows that in 2 minutes, Pogo the dog can fetch a frisbee 6 times.

As given that in 2 minutes Pogo the dog fetch a frisbee = 6 times

So in 1 minutes Pogo the dog fetch a frisbee = 6/2 times

In 1 minutes Pogo the dog fetch a frisbee = 3 times

We have to find in 4 minutes how many frisbee Pogo the dog fetch

In 4 minutes Pogo the dog fetch a frisbee = 3*4 times

In 4 minutes Pogo the dog fetch a frisbee = 12 times

Hence, 12 times will Pogo fetch the frisbee in 444 minutes.

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The right answer is;

The double number line shows that in 2 minutes, Pogo the dog can fetch a frisbee 6 times.

Based on the ratio shown in the double number line, how many times will Pogo fetch the frisbee in 4 minutes?

Step-by-step explanation:

1.)i always eat salad

2.)you ate rice

3.)She has a lot of children

4.)He drank tea

5.)i still drink wine

6.)you are students of the French language

(thanks, sorry and hope I helped)

Answer:

6 \(units^{2}\)

Step-by-step explanation:

The first point is not labeled.  I assumed that it is point A.

Answer:

To plot the points on a graph paper, you need to draw the x and y axes first. Then, plot the points (-2, 3), (-2, 0), (2, 0), and (2, 6) on the graph paper by counting the number of units from the origin (0, 0) in the x and y directions. Once you have plotted the points, join them consecutively to form triangle ABC.

To find the area of triangle ABC, you can use the formula:

Area = 1/2 * base * height

where the base is the length of BC and the height is the perpendicular distance from A to BC. To find the length of BC, you can use the distance formula:

BC = sqrt[(2 - (-2))^2 + (0 - 0)^2] = 4

To find the height, you need to draw a perpendicular line from A to BC and find its length. Since A is located at (-2, 3) and the line BC is horizontal, the perpendicular line from A to BC is vertical and passes through the point (-2, 0). Therefore, the height is equal to the distance between (-2, 3) and (-2, 0), which is 3 units.

Substituting the values into the area formula, we get:

Area = 1/2 * 4 * 3 = 6 square units

Therefore, the area of triangle ABC is 6 square units.

Answer:

12

Step-by-step explanation:

Answer:

To calculate the surface area and volume of a cylinder, we can use the following formulas:

a) Surface Area of a Cylinder:

The surface area of a cylinder consists of two circles (top and bottom) and the curved surface area.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

Where:

SA = Surface Area

r = Radius of the base (half the diameter)

h = Height of the cylinder

Given that the diameter is 16 yards, the radius is half of that, so r = 8 yards. The height is 20 yards.

Substituting the values into the formula, we get:

SA = 2π(8)² + 2π(8)(20)

= 2π(64) + 2π(160)

= 128π + 320π

= 448π

So, the surface area of the cylinder is 448π square yards.

b) Volume of a Cylinder:

The formula for the volume of a cylinder is:

V = πr²h

Using the same values for the radius (r = 8 yards) and height (h = 20 yards), we can calculate the volume:

V = π(8)²(20)

= 64π(20)

= 1280π

The volume of the cylinder is 1280π cubic yards.