a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 20 cm to 10 cm in 30 minutes. at what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 9 cm?

To find the surface area of the volume generated when the curve y = x^2 revolves around the y-axis from x = 0 to x = 2, we will use the surface area formula for revolution:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from x = 0 to x = 2.

First, find the derivative dy/dx:
y = x^2
dy/dx = 2x

Now, plug in the derivative and simplify the expression inside the integral:
sqrt(1 + (2x)^2) = sqrt(1 + 4x^2)

Now, set up the integral with the surface area formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + 4x^2)] dx from x = 0 to x = 2.

Next, we will approximate the integral using a calculator:
Approximate Integral ≈ 9.8433

Finally, multiply by 2 * pi:
Surface Area ≈ 2 * pi * 9.8433 ≈ 61.9362

So, the surface area of the volume generated when the curve revolves around the y-axis is approximately 61.9362 (rounded to four decimal places).

Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.

Maggie is 15 years older than Bobby. We have to determine Bobby's age.

Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.

1) In 3 years, Maggie's age will be 50% greater than Bobby's age.

The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.

According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.

So, (x + 15) + 3 = (1.5)(x + 3)

Simplifying the above equation, we get

x + 18 = 1.5x + 4

Now, we will solve for

x.x - 1.5x = -14-0.5x = -14x = 28

Therefore, Bobby is 28 years old now.

2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.

Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.

So, x + 25 = (x + 10) + 15x = 15

Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.

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The area of the rectangular section in the garden is Area = (x₂ - x₁) x (y₂ - y₁)

Now, let's look at the rectangular section of the garden represented by the coordinate plane. We are told that the section is represented by Rectangle JKLM. The four corners of this rectangle can be represented by their respective coordinates:

Point J: (x₁, y₁)

Point K: (x₂, y₁)

Point L: (x₂, y₂)

Point M: (x₁, y₂)

To find the area of this rectangle, we need to use the formula:

Area = length x width

The length of the rectangle is the distance between points J and K, which is given by:

Length = x₂ - x₁

The width of the rectangle is the distance between points J and M, which is given by:

Width = y₂ - y₁

Therefore, the area of the rectangle is:

Area = (x₂ - x₁) x (y₂ - y₁)

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Complete Question:

Gina is growing lettuce in a section of a garden. She represents this section with Rectangle JKLM. Each unit in the coordinate plane represents 1 foot.

What is the area of the section where lettuce grows?

The domain for n in the arithmetic sequence is the one in the first option:

all integers where n ≥1

We have a arithmetic sequence defined by the general formula:

aₙ  = 4 - 3*(n - 1)

And we want to find the domain for the possible values of n that we can use in that formula.

Remember that the terms of a sequence are defined as:

a₁, a₂, a₃,...

So the values of n are positive whole numbers, in this case the first one is n = 1.

a₁ = 4 + 3*(1 - 1)

a₁ = 4

And then we can keep using any positive integer, then the correct option is:

all integers where n ≥1

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Answer:

$27.50

Step-by-step explanation:

If the sales tax rate is 10%, then Ariana will pay 10% of the price of the cowboy hat as tax.

To calculate the amount of tax Ariana will pay:

First, we need to calculate the amount of the tax by multiplying the price of the cowboy hat by the sales tax rate: 0.10 x $25 = $2.50

So, the amount of tax that Ariana will pay is $2.50.

Therefore, Ariana will pay $2.50 in tax when she buys the cowboy hat priced at $25. Her total cost will be $25 + $2.50 = $27.50.

Answer:

2.50$

Step-by-step explanation:

Hope that helps ✌

the answer is A: 63 square units

Answer:

A (Im not entirely sure if this is correct)

Step-by-step explanation:

how I got this answer is: I found the area of the two triangles which was 12.5 (because the area of a triangle is 1/2(b*h) and the base is 3 and the height is 7 then you divide that by two) and I added them up to get 21. Then you would multiply 3 by two because a triangle is half of a rectangle and you would do b*h for a rectangle area and then multiply that by 7 ot get 42 and you would add taht to 21 to get 63

Answer:

Step-by-step explanation:

(g * h)(24)

gh*24

24gh

The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.

In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:

(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:

6⁽⁷⁻⁶⁾ = 6¹ = 6.

Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.

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The plant is growing 0.89 feet per month.

To calculate how much a plant grows per month, you need to first convert the measurements into one unit of measurement.

Since the plant is growing 2/3 of a foot every 3/4 of a month,

we can first convert the fractions of a foot and a month into decimal equivalents.

2/3 of a foot is 0.67 feet, and 3/4 of a month is 0.75 months.

We can then calculate the amount of growth per month by dividing the amount of growth per 3/4 of a month by the amount of time that is 3/4 of a month (0.75).

The equation is 0.67 feet / 0.75 months = 0.89 feet per month.

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Answer:

1440000

Step-by-step explanation:

Since for every mile, there are 12 people, we have 120000 miles. If we multiply 12 by 120000, we get 1440000.

The required sides of kite are √61, √61, √221 and √221 units.

According to the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle equals the total of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two sides. Pythagoras theory triangles are another name for these triangles.

In ΔAOD

AD = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units

In ΔAOB

AB = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units

In ΔBOC

BC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units

In ΔDOC

DC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units

Thus, required sides of kite are √61, √61, √221 and √221 units.

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The coordinates for the dilated triangle is obtained as A'(-1, 8), B'(-7, 6), and C'(-7, -4).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The coordinates point of the triangle is given as -

A (-1,6)

B (-4,5)

C (-4,0)

To dilate triangle ABC by a scale factor of 2 about the point (-1, 4), we can follow these steps -

Translate the triangle so that the center of dilation is at the origin.

We can do this by subtracting (-1, 4) from each vertex -

A' = (-1, 6) - (-1, 4) = (0, 2)

B' = (-4, 5) - (-1, 4) = (-3, 1)

C' = (-4, 0) - (-1, 4) = (-3, -4)

Dilate the translated triangle by multiplying the coordinates of each vertex by the scale factor of 2 -

A'' = 2(0, 2) = (0, 4)

B'' = 2(-3, 1) = (-6, 2)

C'' = 2(-3, -4) = (-6, -8)

Translate the dilated triangle back to its original position by adding (-1, 4) to each vertex -

A'B'C' = A'' + (-1, 4) = (-1, 8)

B'' + (-1, 4) = (-7, 6)

C'' + (-1, 4) = (-7, -4)

Therefore, the coordinates of the dilated triangle A'B'C' are (-1, 8), (-7, 6), and (-7, -4).

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Step-by-step explanation:

[tex]{ \tt{h(x) = {x}^{2} + 4x - 7 }}[/tex]

Substitute for x as -2;

[tex]{ \tt{h( - 2) = {( - 2)}^{2} + 4( - 2) - 7}} \\ \\ { \tt{h( - 2) = 4 - 8 - 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt{h( - 2) = - 11}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:-9

Step-by-step explanation:

h(-2)=h(x)

it symbolize that x=-2;

so, we'll replace every x with -2:

-2^2+3*(-2)-7=4-6-7=-9

Answer:

$510,000

Step-by-step explanation:

Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.

Remember, 4 or less, round down. 5 or more, round up.

Since the hundreds digit is 4, we do not need to round.

We only need to change the rest of the digits to 0.

So, our answer would be $510,000.

The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.

We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:

x = (9 mi/h) * (0.25 h) = 2.25 mi

y = (8 mi/h) * (0.25 h) = 2 mi

The distance between the two people is given by:

[tex]d = sqrt(x^2 + y^2)[/tex]

Taking the derivative with respect to time t, we get:

[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]

Substituting the values we found earlier, we get:

[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]

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Answer: 40/7 or 5.7

Step-by-step explanation:

using angle bisector theorem we get,

x/5 = 8/7

Upon substituting our given values in above equation, we will get:

x/5 X 5 = 8/7 X 5

x = 40/7 or 5.7

Answer:

3.3

Step-by-step explanation:

Angle bisector theorem: In a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

       [tex]\dfrac{x}{8-x}=\dfrac{5}{7}[/tex]

Cross multiply,

    x *7 = 5*(8 - x)

        7x = 40 - 5x

   7x + 5x = 40

        12x   = 40

             [tex]x = \dfrac{40}{12}\\\\x = 3.3[/tex]

The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.

When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).

The y value of the y-intercept point is denoted by the symbol b in the formula.

The general form of a linear equation is y-y1=m(x-x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

So, in the given situation:
The point-slope form is: y = mx + b

Then y is y and b is the x value and m is the slope.

Now, insert values as follows:

y = mx + b

140 = -14x + 10

Graph the equation as follows:

(Refer to the graph attached below)

Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.

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Probability of

=0.0403.

The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.

The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.

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The correct option is the second one, your supervisor did not divide by the total number of bags.

Here we can see a table with the size of each bag (in grams) and the number of sold bags.

Now, remember that for a set of N numbers {x₁, ..., xₙ} the mean is:

M = (x₁ + x₂ + ...)/N

So the denominator is the amount of elements in the set.

Then here in the denominator we should see the total number of bags sold, which is:

25 + 32 + 40 + 18 = 115

That number should be in the denominator instead of the sum of the masses.

Then the correct option is the second one.

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The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.

The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.

cos θ = 7/18

= arccos(7, 18, 7)

A 1.1181 radian angle

We can use the conversion factor /180 to convert radians to degrees.

θ = 1.1181 × 180/π

64.12 degrees.

As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.

Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.

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The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).

To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:

y - (-5) = -3(x - 2)

Simplifying this expression, we get:

y + 5 = -3x + 6

y = -3x + 1

Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.

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Complete Question:

Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.

A.) y = −3x − 13

B.) y = −3x + 11

C.) y = −3x + 13

D.) y = −3x + 1

Answer:

The answer is y = -3x + 1

We have 6 red and 1 blue marble thus the probability of drawing blue marble = 1/7

To understand probability as a concept, pay attention to the steps below.

Step 1. Multiply the individual probabilities to obtain the chance of numerous separate events.

Step 2. As there are two separate events in this scenario, double the probabilities of each.

Step 3. Add the individual probabilities to obtain the chance of several events that are mutually exclusive.

In this bag of 7 marbles, there is 1 blue one. Assume that each is marked with a number. Choosing blue-1 has a 1/7 chance of happening. (Why? As there are 7 marbles that may be chosen, each with an equal probability, and since those 7 occurrences are mutually exclusive, the 7 probabilities total up to 1.)

The probability of choosing blue-2 is similarly 1/7; the same goes for blue-3,..., and blue-8. To determine the likelihood of picking a blue, add those up (and blue).

Step 4. Do the same for red next.

Thus the probability of drawing blue marble =  1/7

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The length of the base of a parallelogram is 30 feet and the height is 40 feet.

Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.

We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.

Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.

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I think the best way to do this is by splitting up the trapezoid into two shapes since it is not a regular trapezoid. We can make a split to form a small right triangle on the left and a regular trapezoid on the right.

Small right triangle on the left:

4 inch side length and 6 inch hypotenuse with the Pythagorean theorem will give us the missing side.

missing side = square root of 6^2-4^2 = [tex]2\sqrt{5}[/tex]

Then the area is [tex]\frac{1}{2}*4*2\sqrt{5}=4\sqrt{5}[/tex]

Regular trapezoid on the right:

Area will be [tex]\frac{6+(17-2\sqrt{5})}{2}*4=46-4\sqrt{5}[/tex]

Summing up the two areas to get the total we have [tex]4\sqrt{5}+46-4\sqrt{5}=46[/tex] in^2.

Answer: 126in

Step-by-step explanation:

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5+10=24

g5ghykn

The equation that represents the total area of the pool and deck is: A(x) = 2x² + 24x + 64.

In algebra, a binomial is a polynomial that consists of two terms connected by either an addition or a subtraction operator. A binomial can be written in the form (ax + b) or (ax - b), where "a" and "b" are constants and "x" is a variable.

Binomials are used in a variety of algebraic operations, such as factoring, expanding, and solving equations. They also appear in binomial probability distributions and binomial theorem.

Let's start by drawing a diagram to visualize the problem:

___________      

|                       |    4 ft

|   _________|_________

|   |                   |                    |

|   |                   |                    |

|  |                    |                    |   2x

|  |                    |                    |

|  |_________|_________ |

|                       |    4 ft

|__________ |

      2w

The rectangular pool is twice as wide as it is long, so we can let the length be x, and the width be 2x.

The deck around the pool is 4 feet wide on each side, so the total width of the pool and deck is (2x + 8), and the total length is (x + 8).

Therefore, the total area of the pool and deck can be represented as:

(2x + 8)(x + 8)

Expanding the expression, we get:

2x² + 24x + 64

So the equation that represents the total area of the pool and deck is:

A(x) = 2x² + 24x + 64

where A(x) is the area of the pool and deck, and x is the length of the pool.

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Answer:

14

Step-by-step explanation:

all you have to do to find difference is subtract the small number from the bigger number, 18 - 4 = 14

Answer:

14

Step-by-step explanation:

The difference of 18 and 4

18 - 4

14

Answer: 1287

Step-by-step explanation: