if y is a positive integer, for how many different values of y is (144/y)^1/3 a whole number?
a. 1
b. 2
c. 6
d. 15

a) The linearized function is 2x - 1. b) The linearized function is ex. c) The linearized function is 1. d) The linearized function is 5x - 5.

To linearize the given functions around the specified points, we can use the first-order Taylor series expansion. The linearized function will be in the form f(x) ≈ f(a) + f'(a)(x - a), where a is the specified point.

a) f(x) = \(x^1\) + x', around x = 2

To linearize this function, we evaluate the function and its derivative at x = 2:

f(2) = \(2^1\) + 2' = 2 + 1 = 3

f'(x) = 1 + 1 = 2

Therefore, the linearized function is f(x) ≈ 3 + 2(x - 2) = 2x - 1.

b) f(x) = \(e^x\), around x = 1

To linearize this function, we evaluate the function and its derivative at x = 1:

f(1) = \(e^1\) = e

f'(x) = \(e^x\) = e

Therefore, the linearized function is f(x) ≈ e + e(x - 1) = e(1 + x - 1) = ex.

c) f(x) = cos(x), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = cos(0) = 1

f'(x) = -sin(x) = 0 (at x = 0)

Therefore, the linearized function is f(x) ≈ 1 + 0(x - 0) = 1.

d) f(x) = sin(x)(cos(x) - 4), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = sin(0)(cos(0) - 4) = 0

f'(x) = cos(x)(cos(x) - 4) - sin(x)(-sin(x)) = \(cos^2\)(x) - 4cos(x) + \(sin^2\)(x) = 1 - 4cos(x)

Therefore, the linearized function is f(x) ≈ 0 + (1 - 4cos(0))(x - 0) = 5x - 5.

To compare the linearized functions with the actual functions, we can use MATLAB's "taylor" and "plot" commands. Here is an example of how to perform the comparison for the given functions:

% Part (a)

syms x;

f = x^1 + diff(\(x^1\), x)*(x - 2);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (a):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (b)

syms x;

f = exp(x);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (b):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (c)

x_vals = 0:0.1:1;

actual_f = cos(x_vals);

linearized_f = ones(size(x_vals));

disp("Part (c):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

figure;

plot(x_vals, actual_f, 'r', x_vals, linearized_f, 'b');

title("Comparison of Actual and Linearized f(x) for Part (c)");

legend('Actual f(x)', 'Linearized f(x)');

xlabel('x');

ylabel('f(x)');

grid on;

% Part (d)

syms x;

f = sin(x)*(cos(x) - 4);

taylor_f = taylor(f, 'Order', 1);

x_vals = 0:0.1:1;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (d):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

This MATLAB code snippet demonstrates the calculation and comparison of the actual and linearized functions for each part (a, b, c, d). It also plots the actual and linearized functions for part (c) using the "plot" command with the "hold" command to combine the graphs in one plot.

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Answer:

p = 63

Step-by-step explanation:

It is given that the variable v is equal to 7:

v = 7

Plug in 7 for v, and then solve the given equation:

p = 6v + 21

p = 6(7) + 21

Simplify. Remember to follow PEMDAS.
PEMDAS is the order of operation, and stands for:

Parenthesis, Exponents (& Roots), Multiplications, Divisions, Additions, Subtraction.

First, multiply 6 with 7:

p = (6 * 7) + 21

p = 42 + 21

Next, add:

p = 42 + 21

p = 63

63 is your answer for p.

~

Answer:

p = 63

Step-by-step explanation:

p = 6(v) = 21

add in 7 in place of v

p = 6(7) + 21

do 6(7)

p = 42 + 21

add those together

p = 63

Here you go! :)

Answer:

Greater than.

Step-by-step explanation:

3 - 1 = 2, 2 is greater than 1/4 which is equal to 0.25.

Answer:

D

Step-by-step explanation:

Answer:

\(x>-5\)

The solution graph is also attached below. On the solution graph, the value will be:

Step-by-step explanation:

Given the expression

\(-4\left(x\:+\:3\right)\:<\:-2\:-\:2x\)

Expanding

\(-4x-12<-2-2x\)

Add 12 to both sides

\(-4x-12+12<-2-2x+12\)

\(-4x<-2x+10\)

Add 2x to both sides

\(-4x+2x<-2x+10+2x\)

\(-2x<10\)

\(\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\)

\(\left(-2x\right)\left(-1\right)>10\left(-1\right)\)

\(2x>-10\)

Divide both sides by 2

\(\frac{2x}{2}>\frac{-10}{2}\)

\(x>-5\)

The solution graph is also attached below. On the solution graph, the value will be:

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

We have special types of quadrilaterals which are,

1) Rectangle

2) Square

3) Rhombus

4) Parallelogram

5) Trapezium

6) Kite

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

An isosceles trapezoid has left and right sides of equal length that join to the base at equal angles.

Below is the diagram of an Isosceles trapezoid

Answer:

How about:

0, 1, 2, 3, 4..............

lol jk here:

0, 66, 132, 198, 264

Step-by-step explanation:

Guess what it is! ;p

Answer:2

Step-by-step explanation:

If the wait() and signal() semaphore operations are not executed atomically, then mutual exclusion may be violated as a wait operation atomically decrements the value associated with a semaphore.

Semaphores refers to integer variables utilized to solve the critical section problem by using two atomic operations, wait and signal that are used for process synchronization. The wait operation decreases the value of its argument S, if it is positive and if S is negative zero or negative, then no operation occurs. The signal operation increases the value of its argument S. Operation wait() and signal() must be completely atomic or else it violates the mutual exclusion. Mutual exclusion refers to the property of process synchronization which asserts that “no two processes can exist in the critical section at any given point of time”.

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Answer:

[11000, 11600]

Step-by-step explanation:

Give me Brainliest if that helped! :)

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

g(x) = \(2^{x}\) + 4

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here the shift is 4 units up , then

g(x) = \(2^{x}\) + 4

Answer:

the answer is B g(x)=2^x+4

Step-by-step explanation:

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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The car traveled a distance of 30.25 meters while braking.

When a car is brought to a full stop from an initial velocity of 22 m/s with an acceleration of -8 m/s^2, we can use the laws of motion to determine the distance traveled by the car while braking.

The relevant equation to use in this case is:

\(v^2 = u^2 + 2as\)

where v is the final velocity (which is 0, since the car comes to a full stop), u is the initial velocity (which is 22 m/s), a is the acceleration (which is \(-8 m/s^2\), since the car is decelerating), and s is the distance traveled while braking.

Substituting the given values into the equation, we get:

\(0^2 = (22 m/s)^2 + 2(-8 m/s^2)s\)

Simplifying this equation, we get:

\(0 = 484 m^2/s^2 - 16s\)

\(16s = 484 m^2/s^2\)

\(s = (484 m^2/s^2) / 16s = 30.25 m\)

Therefore, the car traveled a distance of 30.25 meters while braking.

This calculation shows that the distance traveled by the car while braking depends on the initial velocity of the car and the rate at which it decelerates. In this case, the car was traveling at a high initial velocity of 22 m/s and decelerated at a rate of -8 m/s^2, which resulted in a braking distance of 30.25 meters. If the initial velocity or the deceleration rate were different, the braking distance would also be different.

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Answer: 6

just beleive me

ok so to find the opposite of something like this you gotta simplify it first

a negative times a negative is a positive

-(-3) = 3

the opposite of 3 is... drumroll please...   -3

Hope this helps,

- Jeron :- )

Answer:

-3

Step-by-step explanation:

-(-3) is just positive 3

The cheapest price for ten (10) rolls would be = £25.50. That is option B.

The wallpapers are those designed paper materials that are used in decoration of a room.

The total number of wall paper that Salima needs to buy= 10 rolls.

A single roll of wallpaper = £9.20

A pack of 3 rolls= £25:50

That is 1 roll = X

make X the subject of formula;

£x = 25.50/3

£x = £8.5

A pack of 5 rolls = £43.05

That is 1 roll = X

make X the subject of formula;

£x = 43.05/3

£x = 14.35

Therefore, the cheapest price that can be used to buy 10 rolls would be = £25.50 because one roll would be = £8.5.

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Answer:

Pack of 3 rolls (total of £85.70

Step-by-step explanation:

25.5+25.5+25.5+9.20= £85.70

If the combination r = 5% and Y = $100 billion is on the Fed rule line, and the combination r = 7% and Y = $100 billion is considered, it would represent a movement up the Fed rule.

The Fed rule represents the relationship between the interest rate (r) and the level of real GDP (Y). As the interest rate increases from 5% to 7% while keeping the level of real GDP constant at $100 billion, it indicates a movement along the Fed rule line in an upward direction.

This implies that as the interest rate increases, the recommended level of real GDP decreases, based on the Fed rule. Therefore, the combination r = 7% and Y = $100 billion represents a movement up the Fed rule.

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Answer:

Step-by-step explanation:

i think i got it wrong so i just deleted what i wrote

no one needs to see that

haha

...

i swear im not that dense sir please

Answer: its 18

Step-by-step explanation: because a rational number is a integer fraction or terminating or repeating decimal.

Geometric sequence

an = a1 r ^(n-1)

____________________

f(n)=1/2*4^n, n≥0

in this case a1= 1/2

r = 4

n= 0 (you just replace n)

f( 0 )=1/2*4^0

f(0) = 1/2 =1/ 2

n f(n)

0 f(0) = 1/ 2 f( 0 )=1/2*4^0

1 f(1) = 2 f( 0 )=1/2*4^2 = 4/2

2 f(2) = 8 f( 0 )=1/2*4^2 = 16/2

3 f(3) = 32 f( 0 )=1/2*4^2 =64/2

4 f(4) = 128 f( 0 )=1/2*4^2 = 256/2

Jennifer Lee argues that the black-white racial divide has evolved into a black-nonblack divide based on the experiences of first- and second-generation Asians and Latinos, where each successive generation shows improved outcomes.

In her interview with Dalton Conley, Jennifer Lee highlights a significant shift in the racial divide in the United States. She notes that the traditional black-white racial binary is no longer sufficient to capture the complexity of racial disparities. Instead, Lee suggests that the black-nonblack divide better reflects the current landscape. Her argument is supported by examining the experiences of first- and second-generation Asians and Latinos. Lee observes that each successive generation within these groups tends to experience improved social and economic outcomes, suggesting that they are able to overcome initial disadvantages. However, this positive pattern of intergenerational progress is not observed among black Americans. Despite efforts to address racial disparities, the gaps between black Americans and all other racial/ethnic groups persist, indicating a unique and persistent disadvantage faced by the black community.

In essence, Jennifer Lee's argument emphasizes that racial disparities in the United States cannot be solely explained by a black-white divide. By considering the experiences of various racial/ethnic groups, particularly the improving outcomes seen among first- and second-generation Asians and Latinos, she highlights the need to recognize the broader black-nonblack divide. This perspective underscores the ongoing challenges faced by black Americans in achieving equitable opportunities and outcomes compared to other racial/ethnic groups in the country.

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In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

This question is a simultaneous equation having a quadratiic equation above and a linear equation below.

substitute the value of y in equation 2 for y in equation 1

recall y = 2x + 10 ( equation 2 )

2x + 10 = x2 - 3x -4 ( since y = 2x + 10 )

Having gotten the two values of x, we see that -2 is in the x position in the options given to us but 7 was ignored. Therefore we shall use x = -2 to find the value of y in equation 2

Recall, y = 2x + 10 ( equation 2 )

thus, y = 2 ( -2 ) + 10 ( since x = -2 )

hence, y = -4 + 10 ( since 2 x -2 = _4 )

so, y = +6

finally, x = -2 and y = 6. the best coordinate is ( -2, 6 )

Answer:

A, D, C, F, B, G

Step-by-step explanation:

The correct order of the given expressions is:

1: (1.93 x 10⁷) - (9.7 x 10⁶)

3: (1.93 x 10⁷) - (0.97 x 10⁷)

6: (1.93 - 0.97) x 10⁷

2: 0.96 x 10⁷

4: 10/10 (0.96 x 10⁷)

7: (1.93 x 10⁷) - 10/10 (9.7 x 10⁶)

8: 9.6 x 10⁶

In mathematics, an expression is a combination of one or more numbers, variables, and mathematical operations that can be evaluated to produce a value or result.

The correct order to perform the subtraction operation is:

Write out the problem: (1.93 x 10⁷) - (9.7 x 10⁶)

Subtract the second number from the first number (ignoring the scientific notation): (1.93 - 0.97) x 10⁷

Simplify the subtraction to get the result in scientific notation: 0.96 x 10⁷. Convert the result to standard scientific notation: 9.6 x 10⁶.

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This means that there is a 50% probability that you run or are on vacation on a randomly chosen day.

To find the probability that you run or are on vacation on a randomly chosen day, we can use the principle of inclusion-exclusion.

The probability that you run on any given day is 40%. The probability that you are on vacation on any given day is not given, but we know that the probability that you run on any given day when you are on vacation is 25%.

We can use these probabilities to set up the following equation:

P(run or vacation) = P(run) + P(vacation) - P(run and vacation)

Substituting the given probabilities, we get:

P(run or vacation) = 40% + P(vacation) - (40% * 25%)

We can simplify this equation to get:

P(run or vacation) = 40% + P(vacation) - 10%

We can rearrange the terms to solve for P(vacation):

P(vacation) = P(run or vacation) - 40% + 10%

Substituting the given probability P(run or vacation) = 40%, we get:

P(vacation) = 40% - 40% + 10% = 10%

Therefore, the probability that you are on vacation on a randomly chosen day is 10%. The probability that you run or are on vacation on a randomly chosen day is the sum of these probabilities:

P(run or vacation) = 40% + 10% = 50%

This means that there is a 50% probability that you run or are on vacation on a randomly chosen day.

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Answer:

the median is the best measure of center and equals 13.

Step-by-step explanation:

To sketch the graph of y = 2 + (1/5)x + 1, we can analyze the linear equation. To sketch the graph of f(x) = -log₈ (x-6), we can analyze the logarithmic function.

For the graph of y = 2 + (1/5)x + 1, the equation represents a linear function. By comparing the equation with the standard form y = mx + b, we can identify the slope, m, which is 1/5, and the y-intercept, b, which is 3. We can plot the y-intercept at (0, 3) and use the slope to find additional points to draw a straight line. Since the coefficient of x is positive, the line will have a positive slope. There are no x-intercepts in this case, and there are no vertical or horizontal asymptotes since the graph is a straight line. The domain is all real numbers, and the range extends from negative infinity to positive infinity.

For the graph of f(x) = -log₈ (x-6), the equation represents a logarithmic function with a base of 8. The argument of the logarithm is shifted by 6 units to the right compared to the standard form y = log₈ (x). We can plot the x-intercept by setting the argument (x - 6) equal to zero, which gives x = 6. This means the graph intersects the x-axis at x = 6. There is a vertical asymptote at x = 6, since the logarithm is undefined for negative values or zero in the argument. The graph approaches the asymptote but does not cross it. The domain of the function is x > 6, since the logarithm is only defined for positive values in the argument. The range is all real numbers since the logarithm can take any real value.

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Answer: See explanation

Step-by-step explanation:

Slope intercept formula: y = mx + b

5 = 10x - 5y

Add 5y to both sides

5y + 5 = 10x

Subtract 5 from both sides

5y = 10x - 5

Divide both sides by 5

y = 2x - 1

The y-intercept is -1

Hope I helped!

The y-intercept of the line 5 = 10x - 5y is b = - 5.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, an equation of line  5 = 10x - 5y.

In slope-intercept form it is 5y = 10x - 5 (y = mx + b).

So, the y-intercept of this line is - 5.

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Answer:

The percent discount is 17.3%.