Problem 7. (1 point) Suppose you are given a solid whose base is the circle x2 + y2 = 36 and the cross sections perpendicular to the x- axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level X = 3.

It will take 15 months for the number of basic subscriptions to match the number of deluxe subscriptions.

Let's denote the number of months passed by "m".

In m months, the number of basic subscriptions will be 288 - 5m (since 5 basic subscriptions are decreasing each month), and the number of deluxe subscriptions will be 93 + 8m (since 8 deluxe subscriptions are increasing each month).

We want to find out when the number of basic subscriptions will match the number of deluxe subscriptions, so we can set the two expressions equal to each other:

288 - 5m = 93 + 8m

We can then solve for m:

288 - 93 = 8m + 5m

195 = 13m

m = 15

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The angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.

Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the angle θ lies.

Recall that there are four quadrants in a Cartesian coordinate system: Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.

Since cos(θ) > 0, the angle θ must be in a quadrant where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.

Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.

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Therefore, the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high is approximately 28.7 feet.

In order to find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high, we will use the angle of elevation and the tangent function.

1. Given the lowest angle of elevation of the sun in winter is 20 degrees, we will use this angle in our calculations.

2. Set up a right triangle with the fence as the vertical side (opposite side), the distance x as the horizontal side (adjacent side), and the angle of elevation (20 degrees) at the point where the fence meets the ground.

3. Use the tangent function to find the distance x:

tan(angle) = opposite side / adjacent side

4. Plug in the values we have:

tan(20) = 10.5 / x

5. Solve for x:

x = 10.5 / tan(20)

6. Calculate the value of x:

x ≈ 28.7 feet

Therefore, the distance x is approximately 28.7 feet.

Note: The question is incomplete. The complete question probably is: In one area, the lowest angle of elevation of the sun in winter is 20 degrees. Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.

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The correct answer is D. 29.50.

To find the wingspan of the actual airplane, we will use the given scale factor and the wingspan of the model airplane.
Given information:
Model airplane wingspan = 11.8 inches
Scale factor = 1 inch to 2.5 feet

Step 1: Convert the model wingspan to feet using the scale factor.
1 inch on the model represents 2.5 feet on the actual airplane. To convert 11.8 inches to feet, multiply by the scale factor.
Step 2: Calculate the actual wingspan.
Actual wingspan = Model wingspan * Scale factor
Actual wingspan = 11.8 inches * 2.5 feet/inch

Step 3: Perform the multiplication.
Actual wingspan = 29.5 feet
So, the wingspan of the actual airplane is 29.5 feet.

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The difference in the means is two times the MAD.

To find the difference between the means as a multiple of the MAD, follow these steps:

Difference of the means = |mean of A - mean of B|

Multiplying the result by 1/MAD will give us the difference of the means as a multiple of the MAD.
1. Determine the difference between the means of the two data sets: Mean of data set A is 42, and the mean of data set B is 47.
  Difference = 47 - 42 = 5.

2. Divide the difference of the means by the MAD: The MAD of both data sets is 2.5.
  Multiple = Difference / MAD = 5 / 2.5 = 2.

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Answer: 31

Step-by-step explanation:

We know that the perimeter is equal to 2W + 2L.

       178 cm = 2W + 2L

We also know that the length is 4 cm less than twice the width.

       L = 2W - 4

We will create a system of equations. Then we will solve with substitution.

       178 cm = 2W + 2L

       L = 2W - 4

       178 cm = 2W + 2L

       178 cm = 2W + 2(2W - 4 cm)

       178 cm = 2W + 4W - 8 cm

       178 cm = 6W - 8 cm

       186 cm = 6W

               W = 31

Answer:

31 cm

Step-by-step explanation:

First, we choose two variables.

Let W = width.

Let L = length.

The perimeter of a rectangle is:

perimeter = 2(L + W)

Now we translate the statements of the problem into two equations.

"the perimeter is 178 cm"

2(L + W) = 178

Divide both sides by 2:

L + W = 89

"the length of a rectangle is 4 cm less than the twice of the width"

L = 2W - 4

We have a system of equations:

L + W = 89

L = 2W - 4

Rewrite the first equation:

L + W = 89

Since the second equation is already solved for L, we can easily use the substitution method.

Substitute 2W - 4 for L in the equation above.

2W - 4 + W = 89

Combine like terms on the left side.

3W - 4 = 89

Add 4 to both sides.

3W = 93

Divide both sides by 3.

W = 31

Answer: The width is 31 cm

Check:

The length is 4 cm less than twice the width. 2 × 31 cm - 4 cm = 58 cm

The length is 58 cm, and the width is 31 cm. Calculate the perimeter.

P = 2(L + W) = 2(58 cm + 31 cm) = 2(89 cm) = 178 cm

The perimeter is 178 cm as the problem states, so the answer, width = 31 cm, is correct.

To verify that F is a conservative vector field, we need to check if its curl is zero.

First, let's find the curl of F:

curl F = (∂Q/∂x - ∂P/∂y)k

where P = xy^2 + 1 and Q = x^2y - 2y

∂Q/∂x = 2xy and ∂P/∂y = 2xy

So,

curl F = (2xy - 2xy)k = 0

Since the curl is zero, we can conclude that F is a conservative vector field.

To find a function f such that F = ∇f, we need to integrate the components of F with respect to their respective variables:

∂f/∂x = xy^2 + 1

f = (1/2)x^2y^2 + x + g(y)

Taking the partial derivative of f with respect to y, we get:

∂f/∂y = x^2 + g'(y) = x^2y - 2y

Integrating this with respect to y, we get:

g(y) = -y^2

So,

f = (1/2)x^2y^2 + x - y^2

Therefore,

F = ∇f = (∂f/∂x)i + (∂f/∂y)j

= (xy^2 + 1)i + (x^2y - 2y)j

Finally, using the conservative property of F, we can use the line integral to find the work done by F along the given curve C:

W = ∫C F · dr

= ∫C (∂f/∂x)dx + (∂f/∂y)dy

= f(r(ostsi)) - f(r(0))

= (1/2)(ostsi)^2(ostsi)^2 + ostsi - (ostsi)^2 - (-1)

= 1/2(ostsi)^4 + ostsi + 1

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A sample size of 77 is needed for a scientist studying premature babies to estimate the mean birth weight of babies born during a week of gestation within 0.5 pounds with 95% confidence, assuming a population standard deviation of 2 pounds.

To determine the minimum sample size needed for the scientist to be confident that her estimate is within a certain margin of error of the true mean birth weight of babies born during the week, we can use the formula

n = (zα/2 * σ / E)²

where

n = sample size

zα/2 = critical value for the desired level of confidence (e.g. 1.96 for 95% confidence)

σ = population standard deviation

E = margin of error (i.e. the maximum amount by which the estimate can differ from the true mean)

Substituting the given values, we have

n = (1.96 * σ / E)²

To determine E, we need to use the fact that the margin of error is equal to the critical value times the standard error, where the standard error is given by

SE = σ / √(n)

Substituting the given values, we have

SE = σ / √(n) = 2 / √(n)

Thus, we have

E = zα/2 * SE = 1.96 * 2 / √(n) = 3.92 / √(n)

Substituting this expression for E into the formula for n, we have

n = (1.96 * σ / (3.92 / √(n)))²

Simplifying, we get

n = (1.96 * σ * √(n) / 3.92)²

n = (0.5 * σ * √(n))²

n = (0.25 * σ² * n)

n = (zα/2)² * σ² / E²

Substituting the given values, we have

n = (1.96)² * 4 / (0.5)² = 76.96

Rounding up to the nearest whole number, we get

n = 77

Therefore, the minimum sample size needed for the scientist to be confident that her estimate is within 0.5 pounds of the true mean birth weight of babies born during the week is 77.

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50% is the percentage the snake is longer if the new measurement is 111 inches and the previous one was 74 inches.

The growth percent refers to the percent of the growth in the length of the snake. It is calculated by the growth divided by the original length multiplied by 100.

Growth rate = [tex]\frac{L-l}{l}*[/tex] 100

where L is the new length

l is the original length

L = 111 inches

l = 74 inches

Growth = 111 - 74

= 37 inches

Growth percent = [tex]\frac{37}{74}[/tex] * 100

= 50%

The growth rate of Abigail's pet snake comes out to be 50%

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The number of people who did not like pop songs is 175.

Given data :

In a survey, the ratio of people who liked pop songs and rap songs is 7: 9.

The number of people who liked both songs = 60.

The number of people who liked only rap songs =  30.

The number of people who liked none of the songs = 40

First of all, we will find the number of people who only like pop songs. We are given a ratio of 7:9 for the people who liked pop songs and rap songs. Let us assume that the number of people who liked pop songs is x and those who liked rap songs is y. According to the ratio given,

[tex]\frac{x}{y} = \frac{7}{9}[/tex]   .....(1)

As we know the number of people who only liked rap songs are 30. Therefore, y - x = 30

x = y - 30

We will substitute the value of x in equation 1.

[tex]\frac{y - 30}{y} = \frac{7}{9}[/tex]

9y - 270 = 7y

2y = 270

y = 135

Now, x = 135 -30

x = 105

Total number of people in survey = x + y + 40

105 + 135 + 40 = 280

Out of 280, the number of people who liked pop songs is 105. So, the number of those who did not like pop songs is ( 280 - 105) = 175.

Therefore, the number of people who did not like pop songs are 175.

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the roots of the function are[tex]x = 1[/tex] and  [tex]x = 3.[/tex] These are also the x-intercepts of the parabola.

This polynomial is a quadratic function and can be graphed as a parabola. a polynomial of degree two.

[tex]f(x) = x^2 - 4x + 3[/tex]

The coefficient of the x^2 term is positive, which means that the parabola opens upwards. The vertex of the parabola is at (2, -1) and the y-intercept is at (0, 3).

The roots of the function can be found by setting f(x) = 0 and solving for x:

[tex]x^2 - 4x + 3 = 0[/tex]

[tex](x - 3)(x - 1) = 0[/tex]

[tex]x = 1, 3[/tex]

Therefore, the roots of the function are[tex]x = 1[/tex] and  [tex]x = 3.[/tex] These are also the x-intercepts of the parabola.

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The total count of inches that a Kameron cover is 301.44 inches, under the condition that we have to  use 3.14 as an approximation of π.

The circumference formula of a circle is
C=πd

Here
C =  refers to circumference
d = refers to diameter.
Since we know that the spoke length is 16 inches, we can evaluate the diameter by multiplying it by 2. Hence, the diameter of the wheel is 32 inches.

Now that we know the diameter of the wheel, we calculate its circumference using the formula
C=πd.
Staging in this formula
d=32 inches
π=3.14

C = πd
= 3.14 x 32
= 100.48 inches

So Kameron covers 100.48 inches of ground in one full rotation of the unicycle wheel.
Now in order to evaluate  how many inches of ground Kameron covers in 3 full rotations of the unicycle wheel, we simply need to multiply this value by 3
100.48 x 3
= 301.44 inches

Thus, Kameron covers approximately 301.44 inches of ground in 3 full rotations of the unicycle wheel.

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Correspondence is a relation of connection as it establishes a link between two sets of elements, often by relating each element in one set to a specific element in the other set.

Correspondence refers to the exchange of communication or information between two or more parties. It is a relation of connection because it involves establishing a link or connection between the sender and the receiver of the message.

For example, when two people exchange letters or emails, they establish a correspondence that connects them and allows them to communicate. Similarly, in business, correspondence can refer to the exchange of official documents such as letters, memos, and reports, which establish a connection between different departments or organizations. Overall, correspondence is an important aspect of communication that helps to establish and maintain relationships between individuals and groups.

For example, in mathematics, a correspondence can be seen when matching the elements of one set to another, such as associating students with their grades. In this case, the connection is created by linking each student to their respective grade, illustrating the concept of correspondence.

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Answer:

Since Q is a center of gravity, we can apply these formulas

The probability of a hurricane hitting the U.S. coast and being a category 1 hurricane is 0.403, or 40.3%.

The National Oceanic and Atmospheric Administration (NOAA) is a federal agency that is responsible for monitoring and predicting changes in the Earth's environment, including the atmosphere and oceans. One of their main responsibilities is to track and study hurricanes that affect the United States.

According to their data, there have been a total of 290 hurricanes that have hit the U.S. coast between 1851 and 2013. These hurricanes are categorized based on their wind speeds, with categories ranging from 1 to 5.

To create a probability distribution for this data, we need to calculate the probability of each category of hurricane occurring. We can do this by dividing the number of hurricanes in each category by the total number of hurricanes.

Category 1 hurricanes: 117/290 = 0.403
Category 2 hurricanes: 76/290 = 0.262
Category 3 hurricanes: 76/290 = 0.262
Category 4 hurricanes: 18/290 = 0.062
Category 5 hurricanes: 3/290 = 0.010

Therefore, the probability of a hurricane hitting the U.S. coast and being a category 1 hurricane is 0.403, or 40.3%. This means that out of all the hurricanes that have hit the U.S. coast, about 40% of them were category 1 hurricanes. It is important to note that this probability distribution is based on historical data and may not accurately predict the likelihood of future hurricanes.

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The average walking rate for Path A is 2.5 mph, path B's is 2 mph and path C's is 3 mph.

Average walking rate = distance/time

for path A = 0.5/12 = 0.0416 mpm

To convert miles per meter into miles per hour it we will multiply the equation by 60 because 1 hour has 60 min

so, for path A = 0.0416 × 60 = 2.5 mph

Similarly , for path B = (1.5/45) × 60 = 2 mph

For path C = (0.75/15)×60 = 3 mph

Table to show the average walking rate

Path     Distance(mi)     Time(min)      Walking rate (mph)

  A              0.5                   12                    2.5

  B              1.5                    45                    2

  C              0.75                 15                     3

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The expected cell count for free music downloads in a sample of 200 bottles from a beverage company's prize promotion is 30, based on the company's claimed probabilities of winning.

To find the expected cell count for music downloads in this study, we first need to calculate the total expected counts for each category of the prize promotion.

Given that the company claims that 5% of the bottle-tops will win a free beverage and 15% will win a free music download, the expected counts for each category in a sample of 200 bottles are

Expected count for free beverages = 0.05 * 200 = 10

Expected count for free music downloads = 0.15 * 200 = 30

Expected count for non-winners = 0.80 * 200 = 160

The expected count for music downloads is 30, which is calculated by multiplying the probability of winning a free music download (0.15) by the sample size (200). Therefore, the expected cell count for music downloads in this study is 30.

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On the basis of given data & Using combining-functions, We can say that

a).The function P(x) which represents the price of a ticket can we given by where x represents the number of 0.75 price decreases= ($15 - 0.75x)

b). the function T(x) which represents number of tickets sold on a day

=(180 + 10x)

c). the revenue would be if the magician decides to sell the tickets for

$12 =  $ 2640

The process of composition, in which the result of one function becomes the input of another, allows us to create complex functions from basic ones. A complicated function may occasionally need to be broken down into two or more simpler ones, using the opposite method.

Given that:

Current price of ticket = $15

Average tickets sold per day = 180

Price decrease each time = $0.75

Number of price decreases = x

Total Price decrease = 0.75x

Increase in number of tickets with price decrease each time = 10

Total increase in number of tickets with x times price decrease = 10x

a). Function to represent total price of tickets

P(x) = current price - total price decrease  

      = ($15 - 0.75x)

Function to represent number of tickets T(x)

= average number of tickets+ total increase in tickets

= (180 + 10x)

b)Function to represent total revenue R(x) = total tickets x total price

                                                                      = T(x) . P(x)

                                                                      = (180 + 10x) ($15 - 0.75x)

c)Given that total price of tickets=$12

                                            P(x)=$12

                             ($15 - 0.75x) = $12

                                      - 0.75x  =  $12 - $15

                                       - 0.75x  =  - $3

                                              x = 3 ÷ 0.75

                                              x = 4 times

The number of times price decreased=4

Total tickets sold T(x) =(180 + 10x)

                                  =(180 + 10(4))

                                  =180+40

                                   =220 tickets

Total revenue= T(x) . P(x)

                    = 220 x 12

                    =$2640

Total revenue earned on 220 tickets at $12 is $ 2640

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There were initially 8 people on Team One.

Let's assume the number of people on Team Two to be "x". According to the given condition, the number of people on Team One is one-quarter of Team Two. Therefore, the number of people on Team One is x/4.

Now, 12 people are transferred from Team Two to Team One. So, the new number of people on Team Two is x-12, and the new number of people on Team One is x/4+12.

As per the given condition, the new number of people on each team is equal. So, we can write the following equation:

x/4+12 = x-12

Solving this equation, we get:

3x/4 = 24

x = 32

So, the initial number of people on Team One is x/4, which is:

32/4 = 8

Therefore, there were initially 8 people on Team One.

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In triangle EOD, angle EOD = 14 degrees, angle DOE = 76 degrees, and angle DEO = 90 degrees. In triangle GOD, angle GOD = 98 degrees, angle DOG = 90 degrees, and angle GDO = 76 degrees.

Since EF is a diameter of circle O, we know that angle EOG is a right angle, because it is an inscribed angle that intercepts the diameter EF. Therefore, angle EOG = 90 degrees.

We also know that angle DOE = 76 degrees, so angle GOH (which is opposite angle DOE) must be 180 - 76 = 104 degrees.

Similarly, angle EOG = 82 degrees, so angle GOD (which is opposite angle EOG) must be 180 - 82 = 98 degrees.

Now, we can use the fact that angles in a triangle add up to 180 degrees to find angle DOG:

angle DOG = 180 - angle GOD - angle GOH

= 180 - 98 - 104

= -22

This result doesn't make sense, because angles can't be negative. However, we made a mistake when calculating angle GOH earlier. Since D and G are opposite sides of EF, they must be collinear.

Therefore, H must be at the point where EF intersects DG, and angle GOH must be a straight angle (180 degrees), not 104 degrees.

With this correction, we have:

angle GOH = 180 degrees

angle GOD = 98 degrees

angle DOG = 180 - angle GOD - angle GOH

= 180 - 98 - 180

= -98

Again, this result doesn't make sense because angles can't be negative. We made another mistake when calculating angle DOG.

Since EF is a diameter of circle O, angles DOG and DEG must be right angles. Therefore, we have:

angle DOG = 90 degrees

angle DEG = 90 degrees

Finally, we can use the fact that angles on a straight line add up to 180 degrees to find angle EOD:

angle EOD = 180 - angle DOG - angle DOE

= 180 - 90 - 76

= 14

Therefore, the angles in triangle EOD are:

angle EOD = 14 degrees

angle DOE = 76 degrees

angle DEO = 90 degrees

And the angles in triangle GOD are:

angle GOD = 98 degrees

angle DOG = 90 degrees

angle GDO = 180 - angle GOD - angle DOG

= 180 - 98 - 90

= -8

Once again, we have a negative angle, which doesn't make sense.

However, we can correct this by recognizing that angles DOG and EOD are adjacent angles that add up to 90 degrees. Therefore, we have:

angle GDO = 90 degrees - angle EOD

= 90 - 14

= 76 degrees

Therefore, the angles in triangle GOD are:

angle GOD = 98 degrees

angle DOG = 90 degrees

angle GDO = 76 degrees

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The result of subtracting 5 from 3 1/3 is -2 2/3.

To subtract 5 from 3 1/3, we need to first convert the mixed number to an improper fraction. This can be done by multiplying the whole number (3) by the denominator of the fraction (3), and adding the numerator (1) to get 10/3. Therefore, 3 1/3 is equivalent to 10/3.

Next, we can subtract 5 from 10/3 by finding a common denominator of 3, which gives 15/3 - 10/3 = 5/3. This is the result in improper fraction form.

To convert back to a mixed number, we can divide the numerator (5) by the denominator (3), which gives a quotient of 1 and a remainder of 2. Therefore, the answer is -2 2/3.

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Answer:

Step-by-step explanation:

You want the median of the Blue box plot and the IQR of the Pink box plot shown in the figure.

A box plot has 5 vertical lines. From left to right, they are ...

Based on the above, we can see the median is the middle line inside the box of the box plot.

The median of the blue plot is 5.2.

The "Interquartile range" is the difference between the 3rd quartile and the 1st quartile. That is, it is the difference between the two ends of the box, the length of the box.

The IQR of the pink plot is 6.4 -5.6 = 0.8.

__

Additional comment

This is basically an exercise in understanding the terms associated with a box plot, and reading a graph. The only calculation involved is figuring out the missing graph coordinates and finding the difference of the coordinates at the ends of the pink plot.

The length of leg of given triangle is s 13√(2) units.

A 45-45-90 triangle is a special right triangle in which the two legs are congruent and the angles opposite the legs are both 45 degrees. The hypotenuse is the longest side of the triangle and is located opposite the right angle.

In this problem, we are given that the hypotenuse length of a 45-45-90 triangle is 26 units. Our goal is to find the length of one of the legs of the triangle. Let us denote the length of one of the legs as x.

By the Pythagorean theorem, we know that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In a 45-45-90 triangle, the two legs are congruent, so we can set up the following equation:

x² + x² = 26²

Simplifying the left-hand side of the equation, we get:

2x² = 676

Dividing both sides by 2, we get:

x² = 338

Taking the square root of both sides, we get:

x = √(338)

Since we are asked to give the answer in simplified radical form, we can write:

x = √(2 × 169) = √(2) × √(169) = 13√(2)

Therefore, the length of one of the legs of the 45-45-90 triangle with a hypotenuse length of 26 units is 13√(2) units.

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Answer:

$4139.93

Step-by-step explanation:

Formula for amount accrued at compound interest annually is given by

A = P( 1+ r)ⁿ

where
P = principal
r = interest rate expressed as a decimal
n = number of years

Given P = 3900, r = 1/100 = 0.01, n = 6 we get

A = 3900(1 + 0.01)⁶ = 3900(1.01)⁶ = 4139.93

So the amount accrued after 6 years = $4139.93

Brandon rode his bike 8.35 miles further than Randy.

To find out how much further Brandon rode his bike last month than Randy, you'll need to subtract Randy's miles from Brandon's miles using the given values.

Step 1: Identify the miles ridden by both Brandon and Randy.
- Brandon rode 56.28 miles.
- Randy rode 47.93 miles.

Step 2: Subtract Randy's miles from Brandon's miles.
- 56.28 miles (Brandon's miles) - 47.93 miles (Randy's miles) = 8.35 miles.

So, last month, Brandon rode his bike more than Randy.

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It would take 15 years of investing $200 at 8% interest to reach a value of $248.

To solve for t, we can rearrange the formula:

a = p + prt

a - p = prt

t = (a - p) / (pr)

To solve for how long $200 must be invested at 8% interest to reach a value of $248, we can plug in the given values into the formula and solve for t:

a = 248

p = 200

r = 0.08

t = (a - p) / (pr)

t = (248 - 200) / (200 * 0.08)

t = 15

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Sure, I'd be happy to help you with that. Based on the information provided, we know that HA Leonardo received three books for his birthday and two of them cost a total of 760. To find out the cost of the third book, we need to subtract the cost of the two books from the total amount paid, which is 1125.

To do this, we can use a simple equation:

Total cost of three books - Total cost of two books = Cost of third book

So, we can plug in the values we know:

1125 - 760 = Cost of third book

Solving for the cost of the third book:

365 = Cost of third book

Therefore, the third book cost 365.

In summary, HA Leonardo received three books for his birthday and two of them cost 760. The total amount paid was 1125, so the cost of the third book was 365.

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The volume, in cubic feet, of the right rectangular prism is 9 cubic feet

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

A right rectangular prism has a length of 2 feet, a width of 3 feet, and a height of 1 2/4 feet

Using the above as a guide, we have the following:

Volume = Length * Width * height

Substitute the known values in the above equation, so, we have the following representation

Volume = 2 * 3 * (1 2/4)

Evaluate

Volume = 9

Hence, the volume is 9 cubic feet

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The area of the spill is increasing at a rate of approximately 94.25 square meters per minute at the end of an hour.

Using the formula for the rate of change of the area, we can calculate the rate at which the area is increasing at the end of an hour:

dA/dt = 2πr(dr/dt) = 2π(30 meters)(0.5 meters per minute) ≈ 94.25 square meters per minute

Area is a mathematical concept that refers to the amount of space contained within a two-dimensional shape or surface. It is typically measured in square units, such as square meters or square feet. The formula for calculating the area of a shape depends on its geometry. For example, the area of a rectangle is calculated by multiplying the length and width, while the area of a circle is calculated by multiplying pi (approximately equal to 3.14) by the square of its radius.

Area is used in a variety of fields, including mathematics, physics, engineering, and architecture. In mathematics, the study of area is a fundamental part of geometry, and is used to solve problems related to shapes and their properties. In physics, the concept of area is used to calculate quantities such as force, pressure, and energy.

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Answer:

  (c)  y < -x +1

Step-by-step explanation:

You want the inequality that matches the graph.

The boundary line of the shaded area has a negative slope: it falls one unit for each unit to the right, so the slope is ...

  m = rise/run = -1/1 = -1

The line crosses the y-axis at y = 1, so the y-intercept is b = 1.

The equation of the boundary line is ...

  y = mx + b

  y = -x +1

The boundary line is dashed, so its values are not part of the solution set. The shading is below the line, so only y-values less than those on the line are included.

The inequality is ...

  y < -x +1 . . . . . choice C

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