this function represents the relationship between the radius of cylinders with a height of feet and their volume. why is this relationship between radius and volume nonlinear?

The last step in evaluating the expression r is D) 120-48.

BODMAS is an acrοnym used tο remember the οrder οf οperatiοns in mathematics. It stands fοr Brackets, Order (expοnents), Divisiοn and Multiplicatiοn (left-tο-right), and Additiοn and Subtractiοn (left-tο-right).

Tο evaluate the expressiοn, yοu need tο fοllοw the οrder οf οperatiοns, which is Parentheses, Expοnents, Multiplicatiοn and Divisiοn, and finally Additiοn and Subtractiοn (PEMDAS).

(9+4-1) X 10'- 3 X2 (4x2)

First, simplify the parentheses:

(9+4-1) X 10'- 3 X 2 (4x2) = (12) X 10' - 3 X 2 (8)

Next, evaluate the expοnents:

(12) X 10' - 3 X 2 (8) = (12) X 1 - 3 X 2 (8)

Then, perfοrm the multiplicatiοn and divisiοn οperatiοns:

(12) X 1 - 3 X 2 (8) = 12 - 3 X 16

Finally, perfοrm the additiοn and subtractiοn οperatiοns:

12 - 3 X 16 = 12 - 48 = -36

Therefοre, the answer is D) 120-48.

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The transmission speed of the circuit cannot be calculated without knowing the number of channels. The formula requires the number of channels in addition to the number of samples per second and the number of bits per sample.

We can use the following formula to calculate the transmission speed of the circuit.

Bandwidth = (Number of samples per second) × (Number of bits per sample)

Transmission speed = Bandwidth × Number of channels.

The given number of bits per sample is 16 and the number of samples taken each second is 8000.

Transmission speed = Bandwidth × Number of channels

Transmission speed = (Number of samples per second) × (Number of bits per sample) × Number of channels

The transmission speed on the circuit is calculated by multiplying the number of samples per second by the number of bits per sample and the number of channels.

However, the number of channels is not provided. So, we cannot calculate the transmission speed of the circuit.

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Answer:

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 .................................(1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ..............................................(2)

Or

Q = N + 3 .............................................(3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 .............................................(4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ................................................(5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ..........................................(6)

Solving (5) and (6) simultaneously

From (5): D = N - 3

From (6): D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12..........................................(7)

Using (7) in (6)

2(12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ........................................................(8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15.......................................(9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15

The ratio of their circumference =200.96cm² : 308.16 cm² and the ratio of the area = 50.24cm: 75.36cm.

The formula that can be used to calculate the area of a circle = πr².

π= 3.14

r= 8cm

area= 3.14×8²

= 3.14× 64= 200.96cm²

For the second circle ;

area = 3.14 × 12²

= 2.14 × 144

= 308.16 cm²

The circumference of the first circle = 2πr

= 2×3.14×8

= 50.24cm

The circumference of the second circle;

= 2×3.14×12

= 75.36cm.

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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:

126°

Step-by-step explanation:

1. We know that 54 degrees and its adjacent are a linear pair, meaning that they add up to 180 degrees. To find the measure of the adjacent angle, we subtract 54 from 180.

2. Now, we know that adjacent of 54 is 126. Also, we know that \(l\) ║ \(m\) ║ n, and x and 126 degrees are corresponding angles. Corresponding angles are congruent within angle measures, so x = 126 degrees.

Given the expression

Use the facts that

So, the expression can be simplified as:

Answer:

ahah yea and its 10 by the way

Answer:

heyyyyy :)    its 10

Step-by-step explanation:

The system defined by the impulse response h(n) = 28(n+3) + 28n + 28(n-3) can be represented as h(n) = 28δ(n+3) + 28δ(n) + 28δ(n-3), where δ(n) denotes the unit impulse function.

In terms of causality, we can determine whether the system is causal by examining the impulse response. If the impulse response h(n) is non-zero only for n ≥ 0, then the system is causal. In this case, since the impulse response h(n) is non-zero for n = -3, 0, and 3, the system is not causal.

To determine the stability of the system, we need to examine the summation of the absolute values of the impulse response. If the summation is finite, the system is stable. In this case, we can calculate the summation as ∑|h(n)| = 28 + 28 + 28 = 84, which is finite. Therefore, the system is stable.

However, since the impulse response is given in the time domain and not in a closed-form expression, it is not possible to directly determine the frequency response without further manipulation or additional information.

Given the absence of specific frequency domain information or a closed-form expression for the frequency response, it is not possible to accurately represent the module and phase of the system H(e^ω) without further calculations or additional details about the system.

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Answer: a is the correct answer

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Card B = 8,666 bottles collected

Card C = 300,000 and 200

Step-by-step explanation:

Card B = 1,238 * 7 is 8,666

7 days in a week

Card C = 270,240 to the nearest hundred thousand is 300,000

240 to the nearest hundred is 200

Answer:

25 = 1/2(3 + 7)h

5 feets

Step-by-step explanation:

Given that:

Window shaped in the form of a trapezium :

The length of its bases :

Top of window base = 3 feets

Bottom of window base = 7 feets long

Area of Windom = 25 feets²

Recall :

Area of a trapezium is given by :

Area, A = 1/2(a + b)h

a and b are the bases

h = height

Inputting the Given values into the equation :

25 = 1/2(3 + 7)h

Hence, the height of the window can be Obtian using the expression

25 = 1/2(3 + 7)h

25 = 1/2(10)h

25 = 5h

h = 25 /5

h = 5 feets

It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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The simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

To simplify the expression 8x - 2x - x^2, we can combine like terms by adding or subtracting coefficients.

8x - 2x - x^2

First, let's combine the x terms:

(8x - 2x) - x^2

This simplifies to:

6x - x^2

Therefore, the simplified form of the expression 8x - 2x - x^2 is 6x - x^2.

Now, let's simplify the expression 2x^2 - 3x - 2:

The expression is already in simplified form, and no further simplification is possible.

Therefore, the simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

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The value of x of the given right angle triangle is: x = 8.57

Pythagoras Theorem is defined as the way in which we can determine the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of; a² + b² = c²

Thus, from the given image, we have:

x² + 13² = (x + 7)²

x² + 13² = x² + 14x + 49

169 = 14x + 49

14x = 120

x = 120/14

x = 8.57

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Answer:

2.000 45

Step-by-step explanation:

you're welcome

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x and y are 166/12 and 56/18.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

2x + 3y = 37 ______(1)

4x - 2y = 18 _______(2)

From (1) we get,

2x = 37 - 3y

x = (37 - 3y)/2 ______(3)

Putting (3) in (2) we get,

4 [ (37 - 3y)/2 ] - 2y = 18

2(37 - 3y) - 2y = 18

74 - 6y - 2y = 18

74 - 8y = 18

74 - 18 = 8y

56 = 18y

y = 56 / 18 _____(4)

Now,

Putting (4) in (3) we get,

x = [37 - 3 x 56/18] / 2

x = (37 - 56/6)/2

x = (222 - 56) / 12

x = 166/12

Thus,

The value of x and y are 166/12 and 56/18.

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Answer:

Step-by-step explanation:

a) 60 / 30 = 2

b) 700/70 = 10

c) (90 * 20)/ 60

= 9*2 / 6

= 3.

Answer:

5

Step-by-step explanation:

the ladder reaches about 18.75 feet up the side of the house.

we can use the Pythagorean theorem which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). In this case, the ladder is the hypotenuse, and the distance from the house to the base of the ladder is one leg.
So, if we let x be the distance up the side of the house that the ladder reaches, then we can write:
\(x^{2}\) + \(7^{2}\) = \(20^{2}\)
Simplifying this equation, we get:
\(x^{2}\) + 49 = 400
Subtracting 49 from both sides, we get:
\(x^{2}\) = 351
Taking the square root of both sides, we get:
x ≈ 18.75 feet

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Answer:

19.1

Step-by-step explanation:

Answer:

Kelvin will save (1/2) × $1,842 = $921.

The inequality can be written as g * 37.5 >= 120.

What is linear inequality?

A linear inequality is a mathematical statement that describes a relationship between two or more variables that form a half-plane when graphed. The equation of a linear inequality is in the form of "ax + by < c" or "ax + by > c" or "ax + by <= c" or "ax + by >= c", where x and y are variables, and a, b and c are constants.

An inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother's house is:

g >= 120/37.5

This inequality states that the number of gallons, g, must be greater than or equal to the number of miles Darla needs to drive, 120, divided by the number of miles per gallon her car gets, 37.5. This is because Darla wants to ensure that she has enough gasoline to make the trip, and she may not want to risk running out of gas on the way.

Another way to write this inequality is

g * 37.5 >= 120

This inequality represents the same meaning as before, we multiply g by the number of miles per gallon the car gets, 37.5 and it should be greater than or equal to the distance she needs to travel which is 120 miles.

Hence, the inequality can be written as g * 37.5 >= 120.

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Andrew can buy maximum 3 meals this weekend.

From given question,

Andrew must spend less than 53$ on meals during the weekend.

He has already spent 21$ on meals costing 8$ average.

Let x, the number of meals

So, we get an inequality,

8x + 21 < 53

We need to find the number of meals he can buy this weekend.

From above inequality,

⇒ 8x + 21 < 53

⇒ 8x < 53 - 21

⇒ 8x < 32

⇒ x < 4

This means, from 1 to 3 meals.

Therefore, Andrew can buy maximum 3 meals this weekend.

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Answer:

1

Step-by-step explanation:

First, Distribute

Then, add 3 to both sides

Then, Divide 15 from both sides

1=Z