Challenge Find the volume of the solid where the cone and half sphere are hollow. Use 3.14 for .

A = 2π ∫[-2, 2] (9 - x^2) √(1 + 4x^2) dx. Evaluating this integral will yield the symbolic answer for the area of the resulting surface.

To find the area of the surface generated by rotating the curve y = 9 - x^2, -2 ≤ x ≤ 2, about the x-axis, we can use the formula for surface area of revolution. The surface area is given by the integral:

A = 2π ∫[a,b] y√(1+(dy/dx)^2) dx

In this case, we have y = 9 - x^2. To calculate dy/dx, we differentiate y with respect to x:

dy/dx = -2x

Substituting the values into the surface area formula, we have:

A = 2π ∫[-2,2] (9 - x^2)√(1+(-2x)^2) dx

Simplifying the expression under the square root, we get:

A = 2π ∫[-2,2] (9 - x^2)√(1+4x^2) dx

Evaluating this integral will provide the symbolic representation of the area of the resulting surface generated by rotating the curve y = 9 - x^2 about the x-axis. Please note that the calculation and evaluation of this integral may require advanced mathematical techniques, such as integration by parts or trigonometric substitutions, depending on the complexity of the resulting expression.

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Answer:

15 km

Step-by-step explanation:

Given the table:

\(\begin{center}\begin{tabular}{ c c}Position(Km) & Time(sec) \\ 5 & 0 \\ 8 & 2 \\ 10 & 4 \\ 16 & 6 \\ 20 & 8 \\ 20 & 10 \\\end{tabular}\end{center}\\\)

To find:

The distance traveled by the car.

Solution:

Here, we are given the position of the car after an interval of 2 seconds.

We are not given the distance traveled.

If the distance traveled would have been given, then distance traveled by car = Sum of all the values = 5 + 8 + 10 + 16 + 20 + 20 = 79 km

Then the answer would have been 79 km.

As, we are given the position here, so the distance traveled will be equal to final position minus the initial position.

Distance traveled in 10 seconds = Position at 10 seconds - Position at 0 seconds = 20 - 5 = 15 km

Answer:

x = 30°

Step-by-step explanation:

All three angles of a triangle must add up to 180°.

53 + 97 + x = 180

150 + x = 180

x = 30

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Tossing two coins in a  sample space has four possible outcomes. (T,H,) (T,T), (H,H), (H,T).

All possible outcomes form the sampling space of a randomized experiment. A subset of the sample space are events associated with randomized experiments.

Given that, Ava tossed the coin her twice. T represents a coin that lands heads up, H represents a coin that lands heads up.

If the first coin is tails, the second coin is either tails or heads. So you have two options. (T,H) (T,T) (T,T)

If the first coin is heads, the second coin is either heads or tails. So you have two options. (H,H) (H,T) (H,T)

Tossing two coins in a pattern room has four possible outcomes.

(T,H,) (T,T), (H,H), (H,T)

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To calculate the Loan to Value (LTV) ratio, we divide the loan amount by the purchase price of the property and express the result as a percentage. LTV = 80%

Given: Purchase price of the building: $8,000,000 Loan amount: $6,400,000 LTV = (Loan amount / Purchase price) * 100 LTV = ($6,400,000 / $8,000,000) * 100 LTV = 0.8 * 100 LTV = 80%

Therefore, the Loan to Value (LTV) ratio in this scenario is 80%. This means that the bank has provided a loan equivalent to 80% of the purchase price of the building.

The remaining 20% of the purchase price, which is $1,600,000 in this case, would be the down payment or equity contribution made by the borrower. Correct answer is 80%

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The area of the rectangle is 64.8 square .inch

A rectangle is a polygon with four sides , opposite sides are parallel and equal.

It is given that

A rectangle is divided into exactly 20 congruent squares

If they are lined up the Length is 36 inches

Therefore the length of each square or the side of the square = 36/20

= 1.8 inch

The area of the rectangle will be

20* Side of square * Side of square

=20*1.8*1.8

= 64.8 square inch

The area of the rectangle is 64.8 square .inch

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Emmy's actual score in the exam is 64.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given,

class average =  76

standard deviation = 8

Z- score = -1.50

The formula of Z-score is -

z = (x-μ)/σ

Where x is the actual score,

μ is the mean,

σ is the standard deviation.

Now putting the values in the formula we get,

-1.50 = (x- 76) / 8

⇒ on solving, we get x = 64

So the actual score of Emmy = 64

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The mean is the best measure οf center, and it equals 7.3.

Given that a line plot displays the number of roses purchased per day at a grocery store.

We need to find the mean,

So,

Mean = 6+6+7+7+8+8+8+9+9+10+1 / 11 = 7.3

Hence, the mean is the best measure οf center, and it equals 7.3.

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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Answer:

slope

Step-by-step explanation:

The slope is the rise divided by the run

Answer: The slope.

Step-by-step explanation: That's what I think.

Answer:

54

Step-by-step explanation:

162/3=54

Answer:

the sequence begins as {4, 7, ... }

Step-by-step explanation:

a(n) = 3n + 1

The first term is a(1) = 3(1) + 1 = 4, and

the second term is a(s) = 3(2) + 1 = 7

So the sequence begins as {4, 7, ... }

Answer:

f= -g/3

Step-by-step explanation:

C is the correct answer.

The minimum height of the rear-view mirror should be approximately 0.121 meters in order for the driver to be able to see the entire height of the rear window without moving her head.

To determine the minimum height of the rear-view mirror, we can use similar triangles.

Let h be the minimum height of the rear-view mirror.

According to the given information, the distance from the driver's eyes to the mirror (0.440 m) is to the distance from the mirror to the rear window (1.42 m) as the height of the mirror (h) is to the height of the rear window (0.390 m).

This can be expressed as a proportion:

0.440 m / 1.42 m = h / 0.390 m

To find the value of h, we can solve for it using cross-multiplication:

h = (0.440 m / 1.42 m) * 0.390 m

h ≈ 0.121 m

Therefore, the minimum height of the rear-view mirror should be approximately 0.121 meters in order for the driver to be able to see the entire height of the rear window without moving her head.

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Answer:

34

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2.5,-0.15,0.50,5/8

The answer to this question is none of the given options (A, B, C, D, or E).To find the maximum perimeter of a square that can fit inside a circle of radius 5 cm, we need to consider that the diameter of the circle is equal to the diagonal of the square.

This means that the side of the square will be equal to the radius of the circle multiplied by the square root of 2 (since the diagonal of a square is the side length times the square root of 2).

So, the side length of the square will be 5 cm x √2 = 7.07 cm. And since a square has four sides of equal length, the perimeter of the square will be 4 x 7.07 cm = 28.28 cm.

However, this perimeter is greater than the circumference of the circle with radius 5 cm, which is 2 x π x 5 cm = 31.42 cm. This means that the square cannot fit entirely inside the circle.

Therefore, the answer to this question is none of the given options (A, B, C, D, or E).

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Answer:

About $137.79

Step-by-step explanation:

Hope this helps!

Answer:

6,000,000

Step-by-step explanation:

the amount of 0's you add is one less than the exponent listed (for example, the exponent here is 6, so add 5 0's)

To find a recursive Nevill's method when interpolating a table using a polynomial at x = 4.1, we can use the following steps:

Step 1: Set up the given data in a table with two columns, one for f(x) and the other for x.

f(x)             x

36               1.16164956

3.80201036       4.0

0.30663842       4.2

0.35916618       -123926000.4

Step 2: Begin by finding the first-order differences in the f(x) column. Subtract each successive value from the previous value.

Δf(x)            x

-32.19798964     1.16164956

-3.49537194      4.0

-0.05247276      4.2

Step 3: Repeat the process of finding differences until we reach a single value in the Δf(x) column. Continue subtracting each successive value from the previous one.

Δ^2f(x)          x

29.7026177       1.16164956

3.44289918       4.0

Step 4: Repeat Step 3 until we obtain a single value.

Δ^3f(x)          x

-26.25971852     1.16164956

Step 5: Calculate the divided differences using the values obtained in the previous steps.

Divided Differences:

Df(x)             x

36                1.16164956

-32.19798964     4.0

29.7026177       4.2

-26.25971852     -123926000.4

Step 6: Apply the recursive Nevill's method to find the interpolated value at x = 4.1 using the divided differences.

f(4.1) = 36 + (-32.19798964)(4.1 - 1.16164956) + (29.7026177)(4.1 - 1.16164956)(4.1 - 4.0) + (-26.25971852)(4.1 - 1.16164956)(4.1 - 4.0)(4.1 - 4.2)

Solving the above expression will give the interpolated value at x = 4.1.

Q2: To construct an approximation polynomial using the Hermite method, we follow these steps:

Step 1: Set up the given data in a table with three columns: f(x), f'(x), and x.

f(x)             f'(x)              x

2.572152         7.615964          1.2

3.602102         13.97514          1.3

5.797884         34.61546          1.4

14.101442        199.500           1.5

Step 2: Calculate the divided differences for the f(x) and f'(x) columns separately.

Divided Differences for f(x):

Df(x)            \(D^2\)f(x)           \(D^3\)f(x)

2.572152         0.51595           0.25838

Divided Differences for f'(x):

Df'(x)           \(D^2\)f'(x)

7.615964         2.852176

Step 3: Apply the Hermite interpolation formula to construct the approximation polynomial.

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Answer:

Step-by-step    

The metric system, with its decimal nature, is a highly efficient and convenient measurement system for making calculations. Compared to other measurement systems, it allows for faster and easier computations, which is a significant advantage. Moreover, using the metric system provides increased accuracy, which is essential in various fields where precision is critical. Overall, the metric system is a reliable and practical option for anyone who needs to make accurate and efficient calculations.

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Step-by-step explanation:

Yo tengo de descargar la imagen pudes aserle screenshot?

A

Step-by-step explanation:

formula is base times height /2

so 8*3*5/2= 4*3*10 = 120yd^3

Answer:

6 pepper fruits

Step-by-step explanation:

Given the following :

Fraction of pepper in terms of tomato = 2/3

Number of fruits on pepper plant = 9

Therefore number of pepper fruits on pepper plant:

2/3 * number of tomato fruits

2/3 * 9

(2 * 3) = 6

6 pepper fruits.

Answer:

x = 24

y = 19

Step-by-step explanation:

From the picture attached,

m(∠CAB) = (5y - 23)° [Vertically opposite angles]

By applying triangle sum theorem in ΔABC,

(5y - 23)° + (2x + 13)° + 47° = 180°

2x + 5y = 143 -----(1)

(3x)° = (5y - 23)° [Corresponding angles]

3x - 5y = -23 -----(2)

By adding equation (1) and (2)

(2x + 5y) + (3x - 5y) = 143 - 23

5x = 120

x = 24

From equation (2)

3(24) - 5y = -23

72 - 5y = -23

5y = 95

y = 19

The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ y ≤ - 5/6x + 2/3

Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.

Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

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Let us consider the breadth(B) of the rectangle to be x.

So now,

Length of Rectangle(L) = 2x-3

Perimeter of Rectangle = 2 (Length + Breadth) = 2(L+B)

So according to the question,

Perimeter = 2(L+B) = 24 feet

                     L + B   = 12 feet

                     2x - 3 + x = 12 feet

                     3x - 3 = 12 feet

                        3x = 12+3

                         x = 15/3

                          x = 5 feet = Breadth

So ,                   Length = 2x - 3 = 2x5 - 3 = 10 - 3 = 7 feet

Hence the length of the Rectangle is 7 feet.

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To calculate SAM and SOM, you need to follow the following steps:

1. SAM (Simple Arithmetic Mean): SAM is calculated by adding up all the values in a set of data and then dividing that sum by the number of values in the dataset.

Formula: SAM = (x1 + x2 + ... + xn)/n

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SAM would be (2+4+6+8+10)/5 = 30/5 = 6

2. SOM (Simple Geometric Mean): SOM is calculated by multiplying all the values in a set of data and then taking the nth root of that product, where n is the number of values in the dataset.

Formula: SOM = (x1 * x2 * ... * xn)^(1/n)

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SOM would be (2*4*6*8*10)^(1/5) = 3840^(1/5) = 5.16

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