Find the derivative of the function. g(t) = phi cos(3t) - 2 /t^2

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Answer:

18π + 90

Step-by-step explanation:

The perimeter is the sum of quarter of the circumference and 2r , that is

P = 2πr + (45 + 45)

  = 2 × π × 36 × \(\frac{1}{4}\) + 90

  = 2 × π × 9 + 90

  = 18π + 90

Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,

    determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.

The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.

Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9

The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.

When a ball falls from height, it gains potential energy.

Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height

PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules

Initial kinetic energy (KE) = PE of Basketball

KE of Basketball = 18.4 J

Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.

Using the coefficient of restitution (e) we can find the velocity of the balls after collision

   v1 - v2 = -e(u1 - u2)

Initial momentum (P) = Final momentum (P)

before the collision  P = m1u1 + m2u2

after collision  P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P

                           = (0.625 kg * v1) + (0.0585 kg * v2)

        Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)

     Here, m1 = mass of basketball

                     = 0.625 kg,

                m2 = mass of tennis ball

                      = 0.0585 kg,

  u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)

Also given that the time taken by the balls to meet is 0.15 seconds

Let h be the height to which the tennis ball bounces after the collision.

When the tennis ball bounces to height h, it gains potential energy.

KE + PE = Total energy

             = Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h

              = (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²

              = (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²

              = (1/2) * u2² - g * h

Substituting the values of u1, u2, m1, m2, e, t and g, we get:

v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1

   = 1.96 m/sv2

    = (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2

    = 5.5 m/s

Here, u1 = u2 = 0.

Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J

                = -0.286 J - 0.572 h0.572 h

                = -12.83 J / 2h

                = -12.83 J / (2 * 0.572)

                = 11.2 m

Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.

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Answer:

Adding another row of dots that are 1 bigger than the last row

Answer:

Step-by-step explanation:

To find the diameter Y of the circle we must first find the radius of the circle

Area of a circle = πr²

where

r is the radius

From the question

Area = 400cm²

Substitute the value into the above formula and solve for the radius

That's

400 = πr²

Divide both sides by π

We have

\( {r}^{2} = \frac{400}{\pi} \)

Find the square root of both sides

\(r = \sqrt{ \frac{400}{\pi} } \)

radius = 11.28 cm

Since we have the radius we can use it to find the diameter Y using the formula

diameter = radius × 2

radius = 11.28

Y = 11. 28 × 2

We have the final answer as

Hope this helps you

Answer:

2 \(\frac{1}{3}\)

Step-by-step explanation:

The absolute value of a number is the value of x (the number) without a negative, 2 and a third is already positive, so that is the answer :D

Hope this helps, good luck! :)

The total surface area of the cylinder with a height of 5 cm and radius of 2 cm is 28π cm^2.

The total surface area of a cylinder can be calculated using the formula: 2πrh + 2πr^2, where r is the radius and h is the height of the cylinder.

Given that the height (h) of the cylinder is 5 cm and the radius (r) is 2 cm, we can substitute these values into the formula:

Total Surface Area = 2πrh + 2πr^2

= 2π(2)(5) + 2π(2)^2

= 20π + 8π

= 28π cm^2

Therefore, the total surface area of the cylinder with a height of 5 cm and radius of 2 cm is 28π cm^2.

The correct option is:

a. 28π cm^2

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Answer:

The INTEGER function returns an integer representation of a number or character string in the form of an integer constant.

Step-by-step explanation:

The total spending figures indicate that Joe's demand for pizza is elastic as his total spending decreases when the price decreases, suggesting he is responsive to price changes.

a. The demand curve for Joe's pizza can be plotted by using the equation Q = 30 - 2P, where Q represents the quantity of pizza consumed and P represents the price per slice.

On the graph, the vertical axis represents the price (P), and the horizontal axis represents the quantity (Q). The vertical intercept occurs when Q is 0, which corresponds to P = 15. The horizontal intercept occurs when P is 0, which corresponds to Q = 30.

b. The total spending on pizza at P = 5 is $100, and the total spending at P = 4 is $88. This information indicates that Joe's total spending decreases as the price of pizza decreases.

Based on this, we can infer that Joe's elasticity of demand for pizza between P = 5 and P = 4 is elastic. When the price decreases from $5 to $4, the total spending decreases, indicating that the demand is responsive to price changes.

c. When P = 9, we can substitute this value into the demand function to calculate the corresponding quantity: Q = 30 - 2(9) = 30 - 18 = 12. To calculate Joe's consumer surplus, we need to find the area of the triangle formed by the demand curve and the price line.

The consumer surplus is given by (1/2) ˣ  (9 - P) ˣ  Q = (1/2) ˣ (9 - 9) ˣ  12 = 0.d. If the price of pizza rises to $15 per slice, we can again substitute this value into the demand function to find the corresponding quantity: Q = 30 - 2(15) = 30 - 30 = 0.

Joe's consumer surplus at this new price would be zero since he is not consuming any pizza at that price, resulting in no surplus.

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Answer:

C. 14%

Step-by-step explanation:

We know that Dallas's wage increased from $9 to $10.25.

Let's say the percent increase is x. Then we write the expression:

9 + x * 9 = 10.25

Divide by 9 from both sides:

1 + x = 10.25 / 9 ≈ 1.14

Subtract 1 from both sides:

x = 1.14 - 1 = 0.14

Since x is a percent, that means x = k/100, where k is an integer. So we have:

x = k/100 = 0.14

Multiply both sides by 100:

k = 0.14 * 100 = 14%

The answer is thus C.

~ an aesthetics lover

Answer:

Step-by-step explanation:

\(Original\:price = \$9\\New\:price =\$10.25\\\\Increase = 10.25-9\\Increase = 1.25\\\\Increase \: \% = \frac{Increase}{Original \:price} \:\times 100\\\\= \frac{1.25}{9} \times 100\\\\= \frac{125}{9}\\ \\= 13.888\\= 14\%\)

The factored expression will be 8(a+5).

Given is an expression 8a+40, we need to find the factor the expression using the distributive property.

So,

8a+40

= 8 × a + 8 × 5

= 8(a+5)

Hence the factored expression will be 8(a+5).

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Answer:

352

Step-by-step explanation:

220 ÷ 100 = 2.2

2.2 x 60 = 132

132 + 220 = 352

I hope this helps, have a good day and stay safe! if this is right can i get a brainiest? :3

Answer:

$42.88

Step-by-step explanation:

Let's create a proportion using the following setup:

cost/pounds=cost/pounds

We know that it costs $20.42 for a 10 pound turkey.

$20.42/10 pounds= cost/pounds

We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.

$20.42/ 10 pounds= $x/ 21 pounds

20.42/10=x/21

We want to find x, by getting x by itself.

x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.

21*(20.42/10)=(x/21)*21

21* 20.42/10=x

21*2.042=x

42.882=x

Round to the nearest cent, or hundredth.

42.88=x

x= $42.88

A 21 pound turkey costs $42.88

The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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Answer:

18/3 cannot be written as an integer

In the context of data or matrices, sparsity refers to the proportion of zero elements compared to the total number of elements. The sparsity level indicates how sparse or dense the data or matrix is.

A sparsity factor of 0.95 means that 95% of the elements in the data or matrix are zeros, while a sparsity factor of 0.5 means that 50% of the elements are zeros.

The difference between a 0.95 sparsity factor and a 0.5 sparsity factor lies in the density of the data or matrix. A higher sparsity factor indicates a more sparse data structure, with a larger proportion of zero elements. On the other hand, a lower sparsity factor suggests a denser data structure, with a smaller proportion of zero elements.

The choice of sparsity factor depends on the specific characteristics and requirements of the data or matrix. Sparse data structures are often beneficial in certain applications where memory efficiency and computational speed are crucial, as they can significantly reduce storage requirements and computation time for operations involving zero elements.

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The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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Given:

The sum of three numbers is 212 .

The ratio of the first to the second is 13:16 and that of the second to the third is 2:3.

To find:

The unknown numbers.

Solution:

We have,

First : Second = 13:16

Second: Third = 2:3

We need to combine these ratios, to get a single ratio for all three numbers.

Second: Third = 2×8:3×8 = 16:24

Now,

First: Second: Third = 13:16:24

Let the first, second and third numbers are 13x, 16x and 24x respectively.

\(13x+16x+24x=212\)

\(53x=212\)

\(x=\dfrac{212}{53}\)

\(x=4\)

So, the numbers are,

\(First=13x\)

\(First=13(4)\)

\(First=52\)

Similarly,

\(Second=16x\)

\(Second=16(4)\)

\(Second=64\)

And,

\(Third=24x\)

\(Third=24(4)\)

\(Third=96\)

Therefore, the three unknown numbers are 52, 64, 96.

The intersection of M and N has 3 final states, and the union of M and N has 7 final states.

Suppose that we have two DFAs with 7 and 6 states, respectively, and 3 and 4 final states, respectively. How many final states will the intersection of these two DFAs have? Justify your answer briefly.If we have two DFAs, M and N, then the intersection of these two DFAs is another DFA, P, such that P = (Q, Σ, δ, q0, F) where Q is the set of states, Σ is the input alphabet, δ is the transition function, q0 is the initial state, and F is the set of final states. Now we can find the intersection of M and N by combining the states of M and N, and the final states of P are the states that are both in M and N.Therefore, the number of final states of the intersection of two DFAs is the minimum of the number of final states in each DFA. In this case, M has 3 final states and N has 4 final states, so the intersection of M and N has 3 final states.

Suppose that we have two DFAs with 7 and 6 states, respectively, and 3 and 4 final states, respectively. How many final states will the union of these two DFAs have? Justify your answer briefly.If we have two DFAs, M and N, then the union of these two DFAs is another DFA, P, such that P = (Q, Σ, δ, q0, F) where Q is the set of states, Σ is the input alphabet, δ is the transition function, q0 is the initial state, and F is the set of final states. Now we can find the union of M and N by combining the states of M and N, and the final states of P are the states that are in either M or N. Therefore, the number of final states of the union of two DFAs is the sum of the number of final states in each DFA. In this case, M has 3 final states and N has 4 final states, so the union of M and N has 7 final states.Therefore, the intersection of M and N has 3 final states, and the union of M and N has 7 final states.

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The diagonals of a quadrilateral are perpendicular and one pair of opposite sides is parallel.

A quadrilateral is a shape with four straight sides. The trapezoid is a quadrilateral with only one pair of parallel sides.

An isosceles trapezoid is a trapezoid with two of the sides having the same length.

It can be proven that a quadrilateral is either a rectangle or an isosceles trapezoid by the following statement:

The diagonals of a quadrilateral are perpendicular and one pair of opposite sides is parallel.

If a quadrilateral has perpendicular diagonals and one pair of opposite sides that are parallel, then it can be either a rectangle or an isosceles trapezoid.

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Answer:

C

Step-by-step explanation:

Using the trig. identity

sin²x + cos²x = 1 ⇒ cosx = ± \(\sqrt{1-sin^2x}\)

Here sinθ = \(\frac{1}{2}\) , thus

cosθ = ± \(\sqrt{1-(\frac{1}{2})^2 }\) = ± \(\sqrt{1-\frac{1}{4} }\) = ± \(\sqrt{\frac{3}{4} }\) = ± \(\frac{\sqrt{3} }{2}\)

Since 0 ≤ θ > 90 then cosθ > 0 , thus

cosθ = \(\frac{\sqrt{3} }{2}\) → C

The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

Here, 6k + 10.5 = 3k + 12

         6k - 3k = 12 - 10.5

         3k = 1.5

          k = 1.5/3

          k = 1/2

Thus, The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

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The measurement 779,000 mi has three significant digits and they are: 7, 7, and 9.

To determine the number of significant digits in a measurement, we follow these rules:

1. Non-zero digits are always significant. In this case, the digits 7, 7, and 9 are non-zero, so they are all significant.

2. Zeros between non-zero digits are also significant. There are no zeros between the non-zero digits in this measurement.

3. Leading zeros, or zeros to the left of the first non-zero digit, are not significant. In this case, there are no leading zeros.

4. Trailing zeros, or zeros to the right of the last non-zero digit, may or may not be significant.

In this measurement, the zeros at the end are not significant because they only serve to indicate the magnitude of the number.

Therefore, the measurement 779,000 mi has three significant digits: 7, 7, and 9.

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The two triangles n = (75 + 3) / 5 = 18. The measure of angle q is 18 degrees.

1. First, find the value of n by using the equation 5(n - 3) = 75 + 3

2. Next, add 75 and 3 together and divide by 5. This gives us a value of 18 for n.

3. Finally, use the equation 5(n - 3) to determine the measure of angle q in triangle qrs. This equals 5(18 - 3) = 5(15) = 75 degrees.

The two triangles qrs and xyz are similar, meaning they have the same angle measures. In order to find the measure of angle q in triangle qrs, we must first find the value of n. The measure of angle x in triangle xyz is 75 degrees and the measure of angle q in triangle qrs is equal to 5(n - 3) degrees. We can use this equation to solve for the value of n. To do this, we add 75 and 3, then divide by 5. This gives us a value of 18 for n. Therefore, the measure of angle q in triangle qrs is 18 degrees.

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Answer:

[2 , ∞)  

Step-by-step explanation:

y = sqrt( x-2)

The domain is the values that x can take

Since we have a square root

Domain: [2 , ∞)  since the square root must be greater than or equal to zero

The range is the values that y can take

The square root starts at 0 and increases

Range [0,∞)

The inverse swaps the domain and range

Range: [2 , ∞)  

Domain [0,∞)

Answer: it’s A on here but check which is A on your test

Step-by-step explanation:

The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

2 1/14

Step-by-step explanation:

First, we will equalize the denominators of the fractions.

(1/7) × 2 = 2/14

Then we can solve this equation.

2 2/14 - 1/14 = 2 1/14

Answer:

25

Step-by-step explanation:

d=2r

2r=25+25=50

d=50

Radius =25

Answer:

25 yds

Step-by-step explanation:

2*radius=diameter

radius=d/2

r=50/2

r=25yds