what is the inverse of F(x)= x^3+1

The result of the multiplication is 180 [cos(247°) + i sin(247°)].

12 [ cos (103°) i  sin (103°) ] × 15 [ cos (144°) i sin (144°) ]

we multiply the magnitudes and add the angles of the complex numbers. Let the first complex number be z₁ and the second complex number be z₂

z₁ = 12 [cos(103°) + i sin(103°)]

z₂ = 15 [cos(144°) + i sin(144°)]

The product of two complex number can be solved we multiply the magnitudes

|z₁ × z₂| = |z₁| × |z₂| = 12 × 15 = 180

To find the angle, we add the angles

arg(z₁ × z₂) = arg(z₁) + arg(z₂) = 103° + 144° = 247°

Therefore, the result of the multiplication is 180 [cos(247°) + i sin(247°)].

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The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

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The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

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Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

23.9

Step-by-step explanation:

Answer:

<A= 60 degrees

Step-by-step explanation:

Since cosA=0.5, we can take the inverse cos of 0.5 to get 60 degrees.

Hope this helped!

Answer: 35 times 50% is 17.5 so she got a 40% discount because 35 times 40% equals 14

Step-by-step explanation:

You have to do first 35•50% and get your answer and if it’s not the right number then go up or down and I went down 10 and got 14 when I did 35•40%

Answer:

Evan's recipe

Step-by-step explanation:

Given that:

Evan's recipe :

5 cups of milk for every 4 teaspoons of chocolate syrup

Carter's recipe:

3 cups of milk for every 2 teaspoons of chocolate syrup.

Recipe with the stronger tasting chocolate milk:

Take the ratio of cups of milk to teaspoons of chocolate syrup:

Evan's :

5 / 4 = 1.25

Carter's :

3 /2 = 1.5

Evan's recipe has the stronger tasting chocolate milk recipe :

5 milk cup = 4 chocolate spoons

Number of chocolate milks for 3 milk cups = x in Evan's recipe

5 = 4

3 = x

5x = 12

x = 12/5

x = 2.4 teaspoons

This is 2.4 spoons compared Carter's recipe which uses 2 spoons for every 3 milk cups

Using the normal distribution, it is found that:

a) The 10th percentile for incubation times is of: 18.72 days.

b) The incubation times that make up the middle 95​% are of: Between 18.04 and 21.96 days.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the incubation times are presented as follows:

\(\mu = 20, \sigma = 1\)

The 10th percentile for the distribution is X when Z = -1.28, which is the value of Z with a p-value of 0.1, hence:

-1.28 = (X - 20)/1

X - 20 = -1.28

X = -1.28 + 20

Z = 18.72 days.

Considering the symmetry of the normal distribution, the bounds of the middle 95% of values are given as follows:

Hence the lower bound is:

-1.96 = (X - 20)/1

X - 20 = -1.96

X = -1.96 + 20

Z = 18.04 days.

The upper bound is:

1.96 = (X - 20)/1

X - 20 = 1.96

X = 1.96 + 20

Z = 21.96 days.

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Simple interest can be defined as the interest charged on the total amount of principal taken for a particular period of time.

Interest is only charged based on the use of funds. Calculating simple interest is fairly straightforward and is the fastest way to calculate interest.

Total amount of money inverted:

Total interset earne

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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In the given IS-LM model, the equilibrium real output, Y, and the equilibrium value of consumption, C, can be determined using the IS and LM equations. The IS equation relates output to the interest rate, while the LM equation represents the equilibrium condition in the money market. By substituting the given values into the equations, we can find the equilibrium values.

The IS equation is given by: Y = 1,586.27 - 3,145.45i.

The LM equation is given as: i = 0.04.

To find the equilibrium real output, we substitute the value of i from the LM equation into the IS equation:

Y = 1,586.27 - 3,145.45 * 0.04.

Calculating the right side of the equation, we have:

Y = 1,586.27 - 125.82,

Y ≈ 1,460.

Therefore, the equilibrium real output, Y, is approximately 1,460.

To find the equilibrium value of consumption, we substitute the equilibrium real output, Y, into the consumption function:

C = 217 + 0.51Y.

Substituting Y = 1,460, we have:

C = 217 + 0.51 * 1,460.

Calculating the right side of the equation, we find:

C ≈ 984.

Therefore, the equilibrium value of consumption, C, is approximately 984.

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Answer:

67. 50

Step-by-step explanation:

15x4.50= 67.5

To find the rates of change in an isosceles right triangle, we need to relate the area of the triangle, the length of the legs, and the length of the hypotenuse.

By using the related rates equation, we can determine the rates of change for different scenarios. When the legs are 1 m long, the area of the triangle is changing at a specific rate. Similarly, when the hypotenuse is 6 m long, the area of the triangle is changing at another rate. Additionally, we can establish an equation between the length of the legs and the length of the hypotenuse to find the related rates equation.

a. The equation relating the area of an isosceles right triangle, A, and the length of the legs, x, is given by A = (1/2) * x^2. To find the related rates equation, we differentiate both sides with respect to time (t):

dA/dt = (1/2) * 2x * dx/dt

Simplifying:

dA/dt = x * dx/dt

b. When the legs are 1 m long, we substitute x = 1 into the related rates equation:

dA/dt = 1 * dx/dt

Since the rate of change in the length of the legs is given as 5 m/s, we have:

dA/dt = 1 * 5 = 5 m^2/s

Therefore, when the legs are 1 m long, the area of the triangle is changing at a rate of 5 m^2/s.

c. The equation relating the length of the legs, x, to the length of the hypotenuse, h, is given by x^2 + x^2 = h^2. To find the related rates equation, we differentiate both sides with respect to time (t):

2x * dx/dt + 2x * dx/dt = 2h * dh/dt

Simplifying:

2x * dx/dt = 2h * dh/dt

Dividing both sides by 2x:

dx/dt = (h * dh/dt) / x

Therefore, the related rates equation is dx/dt = (h * dh/dt) / x.

Please note that the values for (h * dh/dt) and x would need to be substituted in further calculations based on the specific scenario.

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The height in meters of a lava rock that falls for 5 seconds is; 122.5 m.

We are told that the height is modelled by the equation;

y = ¹/₂gt²

where;

y represents the height.

g is 9.8 m/s²

t represents the falling time of the lava rocks.

Thus, at t = 5, we have;

y(5) = ¹/₂(9.8)(5)²

y(5) = 122.5 m

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Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I did the test

Ozone can be both harmful and beneficial to health, depending on its location in the atmosphere and the levels at which it is present.

In the stratosphere (the layer of the atmosphere that is located about 10-50 kilometers above the Earth's surface), ozone is a beneficial gas that protects life on Earth by absorbing harmful ultraviolet (UV) radiation from the sun. However, at ground level, ozone can be harmful to health, particularly for people with respiratory problems such as asthma.

Exposure to high levels of ozone can irritate the respiratory system and cause coughing, throat irritation, and chest pain. It can also worsen bronchitis, emphysema, and other lung diseases. Ozone can also reduce lung function and inflame the linings of the lungs, leading to more serious health problems.

It is important to note that ground-level ozone is not emitted directly into the air, but is formed when pollutants from sources such as vehicle exhaust, power plants, and industrial facilities react with sunlight and heat.

Therefore, Ozone can be both harmful and beneficial to health.

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Option B, option C, and option E are correct because the equation is Negative 3 less than 4.9 times a number, x, which is the same as 12.8.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

The options are:

A: -3 - 4.9x = 12.8

B: 4.9x - (-3) = 12.8

C: 3+ 4.9x = 12.8

D: (4.9 - 3)x = 12.8

E: 12.8 = 4.9x + 3

We have a statement:

A negative 3 less than 4.9 times a number, x, is the same as 12.8.

We can write in a mathematical form:

4.9x - (-3) = 12.8

or

4.9x + 3 = 12.8

or

12.8 = 4.9x + 3

Thus, option B, option C, and option E are correct because the equation is Negative 3 less than 4.9 times a number, x, which is the same as 12.8.

Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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The function's y-intercept is $60.

The equation y = 1/10x+60 can be used to express the function.

y| y 60 is the range.

The equation for the annual cost in dollars, y, based on x, the quantity of game tokens purchased for an arcade member, is represented by the following statements:

A) The function's y-intercept is $60.

B) The equation y = (1/10)x + 60 can be used to express the function.

C) y ≥ 60 is the range.

Typically, the slope-intercept form of the equation of a line is expressed as;

y = mx + c

Where;

the slope is m.

C is the y-intercept.

The input variable or domain is called x.

The output variable or range is called y.

As of right now, we're informed that a single membership costs $60 annually. This is the cost before any input, in this case, the purchase of game tokens.

It follows that the y-value intercept is $60.

According to what we've been told, members can purchase Game tokens for a discounted price of $1 for every 10 tokens. This implies;

y/x = 1/10

Thus, slope = 1/10

Putting this function's equation in slope intercept form now yields

y = (1/10)x + 60

The quantity of game tokens purchased is now limited to a minimum of 0. Thus;

Therefore, Domain; x ≤ 0

The price cannot be less than $60 since x ≤ 0.

Therefore, Range; y ≥ 60

Complete Question: A video game arcade offers a yearly membership with reduced rates for gameplay. A single membership costs $60 per year. Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens. Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select three answers. The slope of the function is $1.00. The y-intercept of the function is $60. The function can be represented by the equation y = y equals StartFraction 1 Over 10 EndFraction x plus 60.X + 60. The domain is all real numbers. The range is {y| y ≥ 60}.

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Answer:

15/x * 100 %

Step-by-step explanation:

Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)

Answer:

13 tables

Np btw

Answer:

4

Step-by-step explanation:

Answer:

90 minutes

Step-by-step explanation:

it will take twice as long therefore 90 minutes

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:

1cm, 2.4cm, 2.6cm

Step-by-step explanation:

They have to follow the pythagorean theorem a^2+b^2=c^2.

1^2+2.4^2=2.6^2 so it follows the pythagorean theorem so these three squares would form a right triangle.

Using the sides of the squares C, A and E the right triangle can be formed.

The Pythagoras theorem, often known as the Pythagorean theorem, describes the relationship between a right-angled triangle's three sides. The hypotenuse of a triangle's square is equal to the sum of the squares of its other two sides, according to the Pythagoras theorem.

Given that, triangles can be created using the sides of squares.

By applying Pythagoras theorem,

2.6²=2.4²+1²

6.76=5.76+1

6.76=6.76

Therefore, using the sides of the squares C, A and E the right triangle can be formed.

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Answer:

-16, -13, -12, -9, 10, 20

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

-16, -13, -12, -9, 10, 20

Step-by-step explanation: