a rectangle has a fixed area of 100 units^2 and its length l is increasing at 2 unit/sec. find the length l at the instant the width is decreasing at .5 units/sec. ap calc related rates

The equation of the line with slope [tex]1[/tex] and y-intercept is [tex]7[/tex] i.e. [tex]y=x+7[/tex]

The slope-intercept form is

[tex]y=mx+c[/tex]

Here, m is the slope and c is the y-intercept

y=x+7

The equation of the line is [tex]y=x+7\\[/tex]

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Answer: I pretty sure its 9 feet

Step-by-step explanation:

Sorry if Im wrong

The expected area of a random square which has a side length that is uniform random variable is 1/3.

A family of symmetric probability distributions includes the continuous uniform distribution and rectangular distribution. The distribution describes an experiment with a random result that falls within predetermined bounds.

 The parameters, a and b, which represent the minimum and maximum values, define the bounds. The interval may be closed (for example, [a, b]) or open (for example, (a, b)). common abbreviation for the distribution is U (a, b), where U stands for uniform distribution. 

The length of the interval is defined by the difference between the bounds; intervals with the same length on the distribution's support are equally likely.

Let, side of the square = X

we know that the area of a square = side × side

                                                          =  X  ×  X

                                                          =  X^{2}

now, by using Continuous uniform distribution,

E[ X^{2} ] =  [tex]\int\limits^1_0 X^{2} \, dx[/tex]    

                =  [tex][\frac{1^{3} }{3} - \frac{0^{3} }{3} ][/tex]

                =  [tex]\frac{1}{3}[/tex]

Hence , the expected area of the square is [tex]\frac{1}{3}[/tex].

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The table that shows a function that is decreasing only over the interval (–1, ∞) is circled on the image given at the end of the answer.

The behavior of a function is classified as either increasing, decreasing or constant, as follows:

In this problem, we want a function that is decreasing only over the interval (–1, ∞), hence:

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What is externality?

A cost or benefit connected to the creation or consumption of a good or service is known as an externality. Externalities have an impact on parties that are not involved in a product's production or consumption.

1) Positive externality says:

An advantage of creating or using a product is known as a positive externality. For instance, because people learn and develop skills for careers and their lives, education is a beneficial externality of school.

The example follows all the rules of positive externality, so for that it is an positive externality.

2) Through market mechanisms, governmental regulation, self-governing organizations, or a combination of these institutions, externalities can be internalized. We advise taking the institutional approach since it will cost the company the least overall (the sum of technology, management, and transaction costs).

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Answer:

31.992 dollars

Step-by-step explanation:

39.99 times 80%

=31.992

Bonnie bought more jolly because the weight of her 2 bags is more than that of Linsey.

The pound or pound-mass is a unit of mass used in British imperial and United States customary systems of measurement.

If each Linsey's bag of jolly weighs 18 ounces then 3 bags would weigh 18 x 3 = 54 ounces

If each Bonnie's bag of jolly weighs 2 pounds then the 2 bags would weigh 2 x 2 = 4 pounds.

converting 4 pounds to ounces at the rate of 16 ounces per pound we have 16 x 4 = 64 ounces

So Bonnie bought more jolly than Linsey as the weight of the bags of Bonnie is heavier than that of Linsey.

In conclusion Bonnie bought more than Linsey as the weight of bags of Bonnie outweighs Linsey's

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Answer:

Could you please explain your question with proper English?

Step-by-step explanation:

Thank you.

Answer:

0

Step-by-step explanation:

The formula to find slope is:

plug in both set of parenthesis into the equation

m = 5-5 / -1 - 2

Solve numerator (top) and denominator (bottom)

m = 0 / -3

Solve, 0 divided by -3

=0

The system of inequalities that are graphed are:

y < (1/2)x + 4

y > 2x - 1

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Two coordinates from the graph of the green line.

(0, 4) and (2, 5)

The equation of the line.

y = mx + c

m = (5 - 4) / (2 - 0) = 1/2

m= 1/2

(0, 4) = (x, y)

4 = (1/2) x 0 + c

c = 4

y = (1/2)x + 4

Two coordinates from the graph of the Blue line.

(1, 1) and (2, 3).

The equation of the line.

y = mx + c

m = (3 - 1)/(2 - 1) = 2/1 = 2

m = 2

(1, 1) = (x, y)

1 = 2 + c

c = 1 - 2

c = -1

y = 2x - 1

Now,

The system of  linear inequalities that are graphed on the given graph are:

y < (1/2)x + 4

y > 2x - 1

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A word is put between to and the verb while splitting an  infinitive. In terms of grammar, splitting an infinitive is acceptable.

In other cases, it might even be more logical to do so. An infinitive is a verb's to form, such as "to go" or "to be."

When it is said that infinitives should never be split, it means an adverb should never come before the verb in the sentence "to confidently proceed."

As we know  split infinitive is one in which the word "to" and the verb in the base (infinitive) form of the verb are separated by one or more words.

Adverbs are the words that split infinitives the most frequently.

Example,

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The standard size of the rectangle's area is x² + 12x + 35

Given:

a diagram that depicts the polynomial that denotes a rectangle's length and width.

The rectangle's area is equal to its length x width.

Given that length is equal to x + 7 and width is equal to x + 5, the area is equal to length plus width.

Add the numbers in brackets: Area = x2 + 5x + 7x + 35

Area = x2 + 12x + 35

A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. We are surrounded by numerous rectangular objects. The length and width of a rectangular shape are the two dimensions that define it. The rectangle's length and width are its longer and shorter sides, respectively. We will learn about the properties of the rectangle shape in this chapter.

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Full Question = Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.

x+7 x+5

For the Polynomials to be closed under closure property for the operation of addition if the addition operation produces another polynomial.

Closure property states that when a set of numbers is closed beneath any arithmetic operation such as subtraction, addition, division, and multiplication and is performed on any two numbers of the set with the reply being another number from the set itself. When including polynomials, the factors and their exponents don't alter. As it were their coefficients will possibly alter. This ensures that the sum has factors and exponents which are as of now classified as having a place in polynomials. Polynomials are closed beneath the addition.

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The approximate number of price increases needed to maximize profit is 2.5

From the question, we have the following parameters that can be used in our computation:

x = number of price increases

y = Profit

Also from the question, we have

Begins at (0, 50)

Increases to (2.5, 81.25)

Decrease through (6.531, 0)

This means that

Maximum = (2.5, 81.25)

Recall that

x = number of price increases

So, we have

x = 2.5

Hence, the number of price increases is 2.5

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As per the given correlation, the appropriate null and alternative hypothesis for calculating number of goggles is

H0 : No linear relation

H1 : there is a relation

What is meant by correlation?

In math, correlation is referred as a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

And it is a common tool for describing simple relationships without making a statement about cause and effect.

Based on the given question, a group of scientist randomly selected 20 piknits from the sea-floor and measured their respective weights in grams.

And we also know that, they wanted to know if the weight of the piknits can be used to predict the number of gogles.

Here from the given information, the null hypothesis : H0 : There is no linear relationship between the weight of piknits and the number of goggles

And the Alternative hypothesis : Ha: There is a linear relationship between the weight of piknits and the number of gogles

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Answer: B they are parallel

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Lines that are both perpendicular to a given line are parallel.

Answer: c = -14 over 3 (c = -14/3)

Step-by-step explanation:

1. Distribute: 5c + 4 = 2(c - 5) --> 5c + 4 = 2c - 10

2. Subtract 4 From Both Sides: 5c + 4 = 2c - 10 --> 5c + 4 - 4 = 2c - 10 - 4

3. Simplify: 5c = 2c - 14

4. Subtract 2c From both sides: 5c = 2c - 14 --> 5c - 2c = 2c - 14 - 2c

5. Simplify: 3c = 14

6. Divide Both Sides By The Same Factor: 3c divided by 3 = -14 divided by 3

7. Simplify: c = -14 over 3

To prove that the triangles are similar by the SSS similarity theorem, we use MN corresponds to QR, also ∠S ≅ ∠O

Two triangles are comparable if the measurements of their corresponding sides are proportionate. Additionally, if the measurements of two sides in one triangle are proportional to the measurements of the corresponding sides in another triangle and the included angles are congruent, the triangles are similar.

Similar figures

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides is in the same proportion.

From the image, MN corresponds to QR, also ∠S ≅ ∠O

To prove that the triangles are similar by the SSS similarity theorem, we use MN corresponds to QR, also ∠S ≅ ∠O

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Answer: The answer is A: Brazil

explanation: Brazil already gets imports from Argentina IRL

It is discovered that the (1) graph represents a function whose inverse is also a function using the concept of an inverse function.

The set of ordered pairs is the graph of a function f in mathematics, where these pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph.

Since there is only one value of x in the first graph for any value of y, the inverse is also a function, making this the right answer.

The inverse is not a function in the second graph since, for instance, y = 0 when x = -1 and when x = 1.

For instance, in the third graph, the inverse is not a function because y = -3 when x = 0 and x = 2.

For instance, in the fourth graph, y = 1 for two different values of x, proving that the inverse is not a function.

Therefore, it is discovered that the (1) graph represents a function whose inverse is also a function using the concept of an inverse function.

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Correct question:

Which graph shows a function whose inverse is also a function?

The equation that Amy can use to find how many games of Balloon Bouncer, g, she played is; g = (35 - 2a)/3

We are told that Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score.

Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

Thus, the expression for the number of balloon bouncer games played at the arcade is :

2a + 3g = 35

Let :

Glimmer arcade, a = $2 per game

Balloon bouncer, g = $3 per game

Total game tokens = 35

Her spending could be represented using the expression :

2a + 3g = 35  

g = number of balloon bouncer games played

Thus, making g the subject of the formula we have;

g = (35 - 2a)/3

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Answer:

3g + 2 = 35 is the answer.

She played 11 games.

Step-by-step explanation:

8 feets will the bottom of the ladder slip.

What is pythagora's theorem?

In ΔABC

AC² = AB² - BC² (∴Pythagoras theorem)

AC = √25² - 7²

AC = √625 - 49

AC = √576

AC = 24 feet

As after sliping length of ladder remains same ⇒ DE = 25 feet and feet 4 feet.

Let say x be the length of how much the ladder slips.

New height = DC = AC - AD = 20 feet

EC = (x + 7 ) feet

In ΔDEC,

DE² = DC² + EC²  (∴Pythagoras theorem)

25² = 20² + (x + 7)²

(x + 7)² = 225

x + 7 = 15

(∵ x+7)>0, We can't take negative value)

x = 8 feet

Hence, 8 feets will the bottom of the ladder slip.

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Answer:

Step-by-step explanation:

To find the missing numbers, we must simplify the second half of the original proportion/fraction. Let's use number 2 as an example. First, we need to find out which number we are using to simplify. To do this, we divide 21 by 7. This gives us 3. Now, we divide 12 by 3 to get y, or 4. This strategy can be applied to all the problems.

The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy is [tex]e^{\frac{5x^2}{2} }[/tex] .

The slope of the curve is 5xy.

Therefore:

dy/dx =  5xy

dy/y = (5x)dx

Then,

The integrate both sides giving us

ln(y) = (15x²)/2 + C

Since, the curve passes through (0,1) .

Therefore, x=0 and y=1 for solving 2

ln(1) = 0/2 + C

0 = 0 + C

⇒ C = 0

We now,

substitute C back in and isolate y

ln(y) = (15x²)/2

⇒ y = e(15x²) / 2

Therefore, The answer is y = [tex]e^{\frac{5x^2}{2} }[/tex]

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The zeros of the function, along with their multiplicities and effects, are given as follows:

The zeros of the function are given by the zeros of the linear factors.

The linear factors are given as follows:

Then the zeros are given as follows:

Then the multiplicities are given by the exponents, and the effects are defined according to the multiplicities, as follows:

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Two ways in which the combination can be represented = 720 , 46656

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

According to the given information

Whether you can repeat numbers or not will determine which of two possibilities

First Way

If you cannot repeat the digits  

Then

You might perform 6 ! or 6x5x4x3x2x1 = 720

This is so that the initial digit, which can have up to six numbers, can never be repeated. As a result, one digit cannot be repeated, therefore

6 - 1 = 5. The third digit is the same, but since you've already used two of the six digits, you can only have 4.

The alternative

If you're able to repeat :

either [tex]6^{6}[/tex] or 6x6x6x6x6

= 46,656

This is due to the fact that each digit has six possible values.

Two ways in which the combination can be represented = 720 , 46656

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120120 Different number of arrangements can be made.

7 identical stuffed dogs

4 identical stuffed cats

3 identical stuffed teddy bears

Total number of objects a toy store managers want

to display = 14.

We know formula to arrange n objects in which p are identical:

There are n!/p! ways to arrange n objects in a row, and p of those ways are exactly the same.

Similarly for this problem we can say:

Different number of arrangements possible.

Here in this question value of n =14 total number of objects.

Total number of arrangements possible for 14 objects is 14! but some objects are duplicate that may be counted more than ones so we have to divide them.

number of arrangements = 14!/ (7!*4!*3!).

by solving this we get

number of arrangements = 120120.

So we can say 120120 Different number of arrangements can be made.

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If the radius of the base of a cone is decreasing at rate of 2 cm/minute and the height is kept constant at 9 cm, the rate of change of the volume at radius 13 cm is 489.4 cm³/minute

To calculate the rate of change, we need to take the derivative of the variables with respect to time.

The volume of a cone is given by:

V = 1/3 . πr²h

Where:

r = radius of the base

h = height

Since the height of the cone is held constant, then the derivative with respect to time is:

dV/dt = 1/3 h. 2πr dr/dt

Parameters given:

dr/dt = 2 cm/minute

h = 9 cm

r = 13 cm

Hence,

dV/dt = 1/3 x 9 x 2π x 13 x 2

dV/dt = 489.4 cm³/minute

Hence, at radius 13 cm, the rate of change of the volume is 489.4 cm³/minute

It looks like there was typos in your question, most probably your question was:

The radius of the base of a cone is decreasing at a rate of 2 centimeters per minute. The height of the cone is fixed at 9 centimeters. At a certain instant, the radius is 13 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?

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Answer:

The last graph that is a straight line represents y as a function of x

Step-by-step explanation:

In order for a graph to be considered a function, it can't intercept the same value twice. To test this, use the vertical line test to see if the graph hits the line twice. If it does, then it is not a function. But if the line hits the graph only once, then it is a function.