How do you solve a recurrence relation using the master method?

Meaning of infinitive generally represents the action or some purpose of the given word. For example: They will lock the front gate to prevent the house from theft.

Explanation:

Meaning of infinitive :

Example of infinitive representing action is:

They will lock the front gate to prevent the house from theft.

To prevent represent the action.

Example: To swim in the deep lake may be dangerous for a person.

Example : i like to read in Sanskrit.

Example : I can't wait to eat.

Therefore,  infinitive meaning generally represents the action or some purpose of the given word. For example: They will lock the front gate to prevent the house from theft.

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1. False

2. True

3. True

4.  A register is not part of RAM.

1. False. The largest unsigned value is 2ⁿ⁻¹.

2ⁿ⁻¹ is the maximum value an unsigned value can take where n is the number of bits allocated for it.

2. In terms of 2's complement a signed number is equal to the value of the number but with the opposite sign. True.

For a signed number in 2's complement, we first convert the number to binary. Then we invert all the bits and add 1 to the result.

This gives us the 2's complement representation of the number. The result will have the same magnitude as the original number, but the opposite sign.

3. True. If the sum of two digits exceeds the radix, then we need to carry over to the next place value.

For example, if we are using base 10 (decimal), then we can only add two digits together if the sum is less than or equal to 9. If the sum is greater than 9, we need to carry over to the next place value.

Similarly, if we are using base 2 (binary), then we can only add two digits together if the sum is less than or equal to 1.

If the sum is greater than 1, we need to carry over to the next place value.

4. A register is not part of RAM. Registers are small, high-speed storage locations that are located within the processor itself.

RAM, on the other hand, is external to the processor and is used for temporary storage of data and instructions.

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Poisson distribution is the measure to summarize the information contained in a probability distribution in a single parameter.

Poisson distribution gives the probability of an event occurring a certain number of times (k) within a specified time period.

It is denoted by λ , which is the mean number of events.

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The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

$112.50

Step-by-step explanation:

150x.75=112.5

Answer:

its 112.50

Step-by-step explanation:

i got it right

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

C

Step-by-step explanation:

Answer: -15

Step-by-step explanation:

Let the unknown number be 'x'

Using the statement we can form the equation:

4 + x = -11

Now, solve the above equation to get :

4 + x = -11

x = -11 -4

x = -15

The number is -15. To check our answer, substitute for x :

4 + (-15) = -11

4 - 15 = -11

The above equation is correct. Therefore, the number is -15.

Answer: 194

Step-by-step explanation:

From the volumes, we deduce that the side lengths of the cubes are 1 cm, 2 cm, 3 cm, and 5 cm. We position the cubes as follows:

[asy]

unitsize(0.5 cm);

draw((0,0)--(5*dir(-30))--(5*dir(-30) + 5*dir(30))--(10*dir(-30))--(5*dir(-30) + 5*dir(-90))--(5*dir(-90))--(0,0));

draw((5*dir(-30))--(5*dir(-30) + 5*dir(-90)));

draw((0,0)--(0,2)--((0,2) + 2*dir(-30))--(2*dir(-30)));

draw((0,2)--((0,2) + 2*dir(30))--((0,2) + 2*dir(30) + 2*dir(-30))--(2*dir(30)));

draw((2*dir(-30))--(2*dir(-30) + dir(30))--(2*dir(-30) + dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,2)));

draw((2*dir(-30) + dir(30))--(3*dir(-30) + dir(30))--(3*dir(-30) + dir(30) + (0,1))--(2*dir(-30) + dir(30) + (0,1)));

draw((3*dir(-30) + dir(30) + (0,1))--(3*dir(-30) + 2*dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,1)));

draw((2*dir(30) + (0,2))--(2*dir(30) + (0,3))--(2*dir(30) + 3*dir(-30) + (0,3))--(2*dir(30) + 3*dir(-30))--(dir(30) + 3*dir(-30)));

draw((2*dir(30) + (0,3))--(5*dir(30) + (0,3))--(5*dir(30) + 3*dir(-30) + (0,3))--(5*dir(30) + 3*dir(-30))--(5*dir(30) + 5*dir(-30)));

draw((3*dir(-30) + 2*dir(30))--(3*dir(-30) + 5*dir(30)));

draw((3*dir(-30) + 2*dir(30) + (0,3))--(3*dir(-30) + 5*dir(30) + (0,3)));

[/asy]

The surface area of a cube with side length $s$ is $6s^2$, so the total surface area of the cubes is $6 \cdot 1^2 + 6 \cdot 2^2 + 6 \cdot 3^2 + 6 \cdot 5^2 = 234$.

Note that every pair of cubes touches, and furthermore, they have maximum contact. (This is why this solid has the smallest possible area.) The area of contact of the 1-cube and the 2-cube is 1 square centimeter, so we must subtract this twice from 234 (because this portion of the area from both the 1-cube and 2-cube is not seen anymore).

Doing this for every pair of cubes, we find that the surface area of this solid is $234 - 2 \cdot 1^2 - 2 \cdot 1^2 - 2 \cdot 1^2 - 2 \cdot 2^2 - 2 \cdot 2^2 - 2 \cdot 3^2 = \boxed{194}$.

Answer:

370mm

Step-by-step explanation:

15mm×30mm=450mm

8mm×10mm

450mm-80mm =370mm

Based on the information given, the explanatory variable will be the SAT prep program and the response variable is the student's scores.

The information given is that the researcher conducts an experiment to investigate whether an SAT prep program would improve students' scores on the SAT.

The explanatory variable is the factor that is manipulated by the researcher. The response variable is the result of the experiment.

In this case, the explanatory variable is the SAT prep program and the response variable is the student's scores.

In this case, the treatment will be the 120 students that took part in the research. They're the ones that are exposed to manipulation by the researcher.

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Answer:

\(33 {ft}^{2} \)

Step-by-step explanation:

SA = 4(Area of ) + Area of ⬜

= 4(bh/2) + l*b

\(4(3 {ft}\times 4ft) \div 2 + (3ft \times 3ft)\)

\(4 \times (12 {ft}^{2}) \div 2 + 9 {ft}^{2} \)

\(24 {ft}^{2} + 9{ft}^{2} \)

\(33 {ft}^{2} \)

The relationship between the radius and volume of a cylinder with a height of 4 feet is nonlinear because the volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, the height is fixed at 4 feet. As we change the radius, the volume changes in a nonlinear manner.

The volume increases much faster as the radius increases. This can be seen from the exponential nature of the formula, as the radius is squared. Therefore, even a small increase in the radius results in a substantial increase in the volume, making the relationship between radius and volume nonlinear.

In contrast, if the height were to be proportional to the radius, then the relationship between radius and volume would be linear. This is because the volume would be proportional to the product of the radius and height, which is a linear relationship.

Therefore, the nonlinear relationship between radius and volume, in this case, is due to the exponential nature of the formula for the volume of a cylinder and the fixed height of 4 feet.

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--The given question is incomplete; the complete question is

"This function represents the relationship between the radius of cylinders with a height of 4 feet and their volumes. Why is this relationship between radius and volume nonlinear?"--

Answer:

Px = $4

Step-by-step explanation:

Given that:

En el mercado de satisfacción X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 - Px y 1,000 productores idénticos de X satisfactorio, cada uno con una función de oferta dada por Qsx = 20 Px

El precio de equilibrio y la cantidad de equilibrio se pueden determinar de la siguiente manera;

Qdx = 10000(12-Px)

Qdx = 120000 - 10000Px

Qsx = 1000(20 Px)

Qsx = 20000 Px

El punto de equilibrio para completar el enunciado, cuando Qdx = Qsx es:

Qdx = Qsx

120000 - 10000 Px =   20000 Px

120000 =  20000 Px + 10000 Px

120000 =  30000 Px

Px = \(\mathbf{ \dfrac{120000}{30000}}\)

Px = $4

Answer:

10.717

Step-by-step explanation:

15.31×0.7 = 10.717

The function (f-g)(x) is in standard form -3x²+ 3x -14.

A quadratic function is  of the form f(x) = ax2 bx c, where a, b, and c are numbers for which a is not  zero. The graph of a quadratic function is a curve called a parabola. Parabolas can open up or down and vary in "width" or "steepness", but they all have the same U shape.  

To find (f-g)(x), we must subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

We already know that f(x) = x-9 and g(x) = 3x² - 2x + 5, so we can substitute them into the equation above:

(f-g) (x) = (x-9) - (3x² - 2x + 5)

Now we can simplify by dividing the negative sign by the second term:

(f-g)(x) = x - 9 - 3x² + 2x - 5

Combining like terms, we get:

(f-g)(x) = -3x² + 3x -14

Therefore, the function (f-g)(x) is -3x² + 3x - 14 in standard form.

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A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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Answer:

x=102⁰

Step-by-step explanation:

180⁰-47⁰-31⁰=180⁰-78⁰=102⁰

Answer:

The minimum is 87

Step-by-step explanation:

The minimum is the lowest number that you can see. 87 is the minimum because it is the lowest of all numbers listed

Answer:

87

Step-by-step explanation:

Put them in order

87, 89, 94, 98, 99, 103, 109, 112, 115

Minimum = The least

The least = 87

Using the slope concept, it is found that the shelf should have a measure of 0 degrees relative to the floor.

In this problem, the shelf and the floor are parallel, hence they have the same slope, meaning that the difference of their angles is of 0 degrees, thus, the shelf should have a measure of 0 degrees relative to the floor.

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Solution:

Given:

Account 2 details:

Assume a year is 365 days;

Using the compound interest formula to get the amount;

Hence, substituting the values;

Therefore, the balance in account 2 will be $9633.55

The solution is: the approximate surface area of the cone is 103.6 in², which is closest to option (B).

To find the exact surface area of the cone, we need to know the slant height of the cone. Since we are not given the slant height, we can use the Pythagorean theorem to find it:

Slant height² = h² + r²

Slant height² = 4² + 3²

Slant height² = 16 + 9

Slant height² = 25

Slant height = 5

Now that we know the slant height, we can use the formula for the surface area of a cone:

Surface area = πr² + πr×s

where s is the slant height

Surface area = π(3²) + π(3)(5)

Surface area = 9π + 15π

Surface area = 24π

Therefore, the exact surface area of the cone is 24π square units.

The surface area of a cone is given by:

Surface area = πr² + πr×s

where r is the radius of the circular base and s is the slant height.

We are given that the diameter of the circular base is 6 inches, so the radius is 3 inches. We are also given that the slant height is 8 inches. Using these values, we can calculate the surface area of the cone:

Surface area = π(3²) + π(3)(8)

Surface area = 9π + 24π

Surface area = 33π

We can approximate π as 3.14, so:

Surface area ≈ 33(3.14)

Surface area ≈ 103.62

Therefore, the approximate surface area of the cone is 103.6 in², which is closest to option (B).

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complete question:

PLEASE ANSWER THESE QUESTIONS THROUGHLY FOR BRAINLIEST!!

1.)

In this figure, h = 4, and r = 3.

What is the exact surface area of the cone?

(picture inserted below!!!!)

2.)

The diameter of a cone's circular base measures 6 inches, and the slant height of the cone is 8 inches.

What is the approximate surface area of the cone?

94.2 in²

103.6 in²

131.9 in²

257.5 in²

3.)

The slant height of a cone measures 15 centimeters. The height of the cone measures 12 centimeters.

What is the exact surface area of the cone?

4.)

The radius of the circular base of a cone measures 1.6 inches, and its slant height measures 2.5 inches.

What is the approximate lateral area of the cone?

Use π≈3.14.

round to the nearest tenth.

5.) The area of the circular base of a cone is 9π cm², and the slant height of the cone is four times the radius of the cone.

What is the approximate lateral area of the cone?

Use π≈3.14.

round to the nearest whole number.

Answer: Melinda’s loan will be equal to the value of the car after 10 months.

Step-by-step explanation:

Hi, to answer this question we have to equal both equations:

Melinda’s loan will be equal to the value of the car

y = y

10,000 – 250x = 8,000 – 50x

Solving for x:

10,000-8,000 = -50x+250x

2,000 = 200x

2,000/200 =x

10 = x

Melinda’s loan will be equal to the value of the car after 10 months.

Feel free to ask for more if needed or if you did not understand something.

Answer:

it is 2

Step-by-step explanation:

i think it is

Answer:

Perimeter  = 9x+4x+18x+16

Perimeter = 31x+16

Give Brainliest please :)

By the principle of mathematical induction, we conclude that n! > n^3 for all positive integers n ≥ 3.

By the principle of mathematical induction, we have proven that an = ((3 + √2)^n + (3 - √2)^n) / 2 for all positive integers n = 1, 2, 3, ....

(a) To find the smallest possible positive integer N such that N! > N^3, we can test values starting from N = 1 and incrementing until the inequality is satisfied. Let's do the calculations:

For N = 1: 1! = 1, 1^3 = 1. The inequality is not satisfied.

For N = 2: 2! = 2, 2^3 = 8. The inequality is not satisfied.

For N = 3: 3! = 6, 3^3 = 27. The inequality is satisfied.

Therefore, the smallest possible positive integer N such that N! > N^3 is N = 3.

Now, let's prove by mathematical induction that n! > n^3 for all positive integers n ≥ N = 3.

Base case: For n = 3, we have 3! = 6 > 3^3 = 27. The inequality holds.

Inductive step: Assume that the inequality holds for some positive integer k ≥ 3, i.e., k! > k^3.

We need to show that (k+1)! > (k+1)^3.

(k+1)! = (k+1) * k! [By the definition of factorial]

> (k+1) * k^3 [By the inductive assumption, k! > k^3]

= k^3 + 3k^2 + 3k + 1

Now, let's compare this expression with (k+1)^3:

(k+1)^3 = k^3 + 3k^2 + 3k + 1

Since the expression (k+1)! > (k+1)^3 is true, we have shown that if the inequality holds for some positive integer k, then it also holds for k+1.

(b) To prove by mathematical induction that an = ((3 + √2)^n + (3 - √2)^n) / 2 for n = 1, 2, 3, ..., we follow the steps of induction:

Base cases:

For n = 1: a1 = 3 = ((3 + √2)^1 + (3 - √2)^1) / 2. The equation holds.

For n = 2: a2 = 11 = ((3 + √2)^2 + (3 - √2)^2) / 2. The equation holds.

Inductive step:

Assume that the equation holds for some positive integer k, i.e., ak = ((3 + √2)^k + (3 - √2)^k) / 2.

Now, we need to prove that it also holds for k+1, i.e., ak+1 = ((3 + √2)^(k+1) + (3 - √2)^(k+1)) / 2.

Using the given recurrence relation, we have:

ak+2 = 6ak+1 - 7ak.

Substituting the expressions for ak and ak-1 from the induction assumption, we get:

((3 + √2)^(k+1) + (3 - √2)^(k+1)) / 2 = 6 * ((3 + √2)^k + (3 - √2)^k) / 2 - 7 * ((3 + √2)^(k-1) + (3 - √2)^(k-1)) / 2.

Simplifying both sides, we can show that the equation holds for k+1.

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The response rate of the survey has also been low, which can lead to a sample that is not representative of the civilian population.

The National Health and Nutrition Examination Survey (NHANES) is a series of surveys conducted by the Centers for Disease Control and Prevention (CDC) to assess the health and nutrition of adults and children in the United States. The NHANES series has been influential in the development of the CDC Growth Charts in 2000, as it provides data on the growth and development of the U.S. population. However, the design of the survey is not perfect and could use some revision. The response rate of the survey has also been low, which can lead to a sample that is not representative of the civilian population. Therefore, it is important to take into account the design of the survey and the response rate when interpreting the results of the NHANES series.

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Answer:

2

Step-by-step explanation:

i^2 = -1

i^4 = 1

i^20 repeats the cycle 5 times, making i^20 = 1

Answer:

the answer is D) i

Step-by-step explanation: i got it wrong to the bozo who said 1 and it says the answer is i

The explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\). B.

The explicit rule for the geometric sequence 3, 12, 48,... need to determine the common ratio, r.

We can do this by dividing any term by the previous term:

r = 12/3

= 48/12

= 4

Now that we know the common ratio can use the formula for the nth term of a geometric sequence:

\(a_n\) = \(a_1 \times r^{(n-1)\)

where:

\(a_n\) is the nth term

\(a_1\) is the first term (3 in this case)

r is the common ratio (4 in this case)

n is the term number

Substituting these values into the formula, we get:

\(a_n\) = \(3 \times 4^{(n-1)\)

So, the explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\)

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