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The complex number can be written in a trigonometric form as: \(\mathbf{\sqrt{2} (cos (\dfrac{5 \pi}{4})+ i \; sin (\dfrac{5 \pi}{4}))}\)

The conversion of the trigonometric form of a complex number where |z| is the modulus and \(\mathbf{\theta}\) is the angle created on the complex plane.

z = a + bi = |z| (cos (θ) + i sin (θ))

The modulus of a complex number is the distance from the origin on the complex plane.

\(|z| =\sqrt{a^2 + b^2}\)

where;

Let's replace the actual values of a = -1 and b = -1

\(|z| =\sqrt{(-1)^2 + (-1)^2}\)

\(|z| =\sqrt{1 + 1}\)

\(|z| =\sqrt{2}\)

Now, the angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

\(\theta = tan^{-1} (\dfrac{-1}{-1})\)

Since the inverse tangent of \((\dfrac{-1}{-1})\) produces an angle in the third quadrant, the value of the angle is \(\dfrac{5 \pi}{4}\).

\(\theta = \dfrac{5 \pi}{4}\)

substitute the values of \(\theta = \dfrac{5 \pi}{4}\) and  \(|z| =\sqrt{2}\), we have:

\(\mathbf{\sqrt{2} (cos (\dfrac{5 \pi}{4})+ i \; sin (\dfrac{5 \pi}{4}))}\)

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Answer. yess ou add them

Step-by-step explanation:

Yes.

(-9)-(-5)=(-9)+5=-4

Hope it helps!

\(SparklingFlowers\)

Answer:

? = 60.

Step-by-step explanation:

Multiply 3/5 by 20. The answer will yield that 3/5 = 60/100

Answer:

Missing number = 60

Step-by-step explanation:

★ Let the missing number be x.

Forming the equation,

\( \sf \rightarrow \: \frac{3}{5} = \frac{x}{100} \)

Now the value of x will be,

\( \sf \rightarrow \: \frac{3}{5} = \frac{x}{100} \)

\( \sf \rightarrow \: x = \frac{3}{5} \times 100 \)

\( \sf \rightarrow \: x = \frac{300}{5} \)

\( \sf \rightarrow \boxed{ \sf x = 60}\)

Hence, the value of x is 60.

In 13 days they will travel 1904 miles altogether.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Multiplication in action or in progress. The multiplication of 8 and 3 is the same as the sum of 8+8+8, which is a mathematical operation that takes two numbers and returns an answer that is equal to the sum of a column in which one of the numbers is repeated the amount of times of the other number.

Given Data

they travel 238 miles a day for 13 days

1 day = 238 miles

13 days = 238 (13)

13 days = 1904

In 13 days they will travel 1904 miles altogether.

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Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

Answer:

The Equation would be $4 + $3.50x = y

Step-by-step explanation:

Answer: 16 cm

Step-by-step explanation:

Use ratios to solve:

125 m -> 25 cm

80 m -> x cm

Find the value of x:

x = 80*25/125 = 16

Hope this helps!

The length of the building on the scale drawing is 16 centimeters.

To determine the length of the building on the scale drawing in centimeters, we first need to establish the scale factor. Since the actual height of the building is 125 meters and its representation on the scale drawing is 25 centimeters, we can find the scale factor by dividing the height on the scale drawing by the actual height:

Scale factor = (Height on scale drawing) / (Actual height) = 25 cm / 125 m

As there are 100 centimeters in a meter, we need to convert the actual height to centimeters:

125 m * 100 = 12,500 cm

Now, we can recalculate the scale factor:

Scale factor = 25 cm / 12,500 cm = 1/500

This means that every 1 centimeter on the scale drawing represents 500 centimeters (or 5 meters) in reality. Now that we know the scale factor, we can use it to find the length of the building on the scale drawing:

Length on scale drawing = (Actual length) * (Scale factor) = 80 m * (1/500)

First, convert the actual length to centimeters:

80 m * 100 = 8,000 cm

Now, multiply by the scale factor:

Length on scale drawing = 8,000 cm * (1/500) = 16 cm

So, the length of the building on the scale drawing is 16 centimeters.

In summary, we can use the scale factor to convert between the actual measurements and the measurements on the scale drawing.

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Answer:

I think it is C) The line will contain points whose y-coordinate will decrease in value as you move to the right

Step-by-step explanation:

HOPE THIS HELPS

Answer:

it doesn't show what your talking about be more specific.

Step-by-step explanation:                                                                                               explain what your talking about.

This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.

The mathematical field of game theory helps shed light on how it emerges. Game theory is “the study of mathematical models of strategic interaction among rational decision-makers” (according to Wikipedia).

Game theory applies to “games” as varied as economics, politics, chess, and tic-tac-toe. In each case, there are some rules, some “players” or “agents”, and a set of strategies available to them.

Each player has a concept of “utility” – a “currency” they seek to individually maximize through the strategies they play.

The currency of evolution is the concept of fitness.

That is, the chance of being represented in the next generation. Genes and traits which increase the odds of survival to reproductive age are more likely to be passed on to future generations. Therefore, they confer a greater fitness to the individual which "hosts” them.

The evolutionary game theory takes the concepts from game theory and applies them in an evolutionary context.

In the hawk-dove game, at what value of c do doves and hawks have equal payoffs when hawks are extremely rare? The answer is that there is no such value. This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.

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The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

The payment of car washing per hour = $10

The payment for landscaping = $12

Total number of hours worked = 14  hours

Number of hours worked in car washing = x

Number of hours worked in landscaping = y

Then the first equation will be

x + y = 14

x = 14 - y

Total amount he earned = $152

Next equation will be

10x + 12y = 152
Here we have to use substitution method

10(14-y) + 12y = 152

140 - 10y +12y = 152

140 + 2y = 152

2y = 152 - 140

2y = 12

y = 12/2

y = 6 hours

Then

x = 14 - y

x = 14 -6

x = 8  hours

Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

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Answer:

see explanation

Step-by-step explanation:

This polynomial is irreducible, that is cannot be factored.

4x² + 25y² ← is a prime polynomial

Answer:

1, the polynomial itself

Step-by-step explanation:

This is a prime polynomial since the terms have no common factor. The only factors it has are 1 and 4x2+25y2 (the number itself)

Answer:

See below

Step-by-step explanation:

Given there are 56 M&M's:

Remember to use \(np\) to calculate expected value! This will especially be helpful if you are conducting a chi-squared test of independence.

In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

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Answer:

A. or B.

Step-by-step explanation:

I

Answer:

no photo

Step-by-step explanation:

we need a photo to decide if answer is correct or not

The bottom right graph should be correct.

The answer is "NOT" that is  given differential equation is not exact.

To determine whether the given differential equation is exact, we need to check if the partial derivatives of the terms with respect to x and y are equal. Let's calculate these partial derivatives.

The given equation is (2xy^2 - 7)dx + (2x^2y + 6)dy = 0.

The partial derivative of the term with respect to x is:
∂/∂x (2xy^2 - 7) = 2y^2.

The partial derivative of the term with respect to y is:
∂/∂y (2x^2y + 6) = 2x^2.

Since the partial derivatives are not equal (2y^2 ≠ 2x^2), the given differential equation is not exact.

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Answer:

The population of Tokyo is 50 times larger than that of Detroit.

Step-by-step explanation:

The population of Tokyo in 2011 was 3.5 x 10^7 (35,000,000) and the population of Detroit was 7 x 10^5 (700,000).

To calculate how many times larger the population of Tokyo is than that of Detroit, we can divide the population of Tokyo by the population of Detroit:

Population of Tokyo / Population of Detroit = (3.5 x 10^7) / (7 x 10^5)

Simplifying this expression, we get:

Population of Tokyo / Population of Detroit = 50

Therefore, the population of Tokyo is 50 times larger than that of Detroit.

Answer:1533

Step-by-step explanation:

7006-5,479=1533

The length of the wallpaper of 27 inches wide required is  35.56 feet

The problem requires conversion of the dimensions to have similar unit

To convert 80 square feet to square inches. we multiply by 144

80 * 144 = 11520 square inches

area = length * wide

11520 = length * 27

length = 11520 / 27

length = 426.667 feet

to get the length in inches we divide the unit in feet by 12

length = 426.667 inches / 12

length = 35.56 feet

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Derivatives are essential for solving calculus and differential equation problems then the derivative of this function is \($f^{\prime}(x)=k$\)

The rate of change of a function with respect to a variable in Mathematics. Derivatives are essential for solving calculus and differential equation problems.

Given a traditional unbent position, f(x) = kx + d, where k is the pitch and (0, d) is the y-intercept.

a) Consider our position at two distinct points first:

f(x) = kx + d

f(x + h) = k(x + h) + d = kx + kh + d

Evaluate the derivative, then

\($\lim h \rightarrow x \frac{f(x+h)-f(x)}{h}\)

substitute the values in the above equation, we get

\($&=\lim h \rightarrow x \frac{(k x+k h+d)-(k x+d)}{h} \\\)

simplifying the above equation, we get

\($&=\lim h \rightarrow x \frac{k h}{h} \\\)

\(&=\lim h \rightarrow x k \\\)

= k

Therefore, the derivative of this function is \($f^{\prime}(x)=k$\)

b. Since the actual function is linear, its part is all real numbers by definition.

c. Since the product is a constant function, its part is all real digits by meaning.

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The population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.

An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a positive constant called the base, and "x" is a variable that can take on any real value. The base "a" is typically greater than 1, which means the function grows at an increasing rate as "x" increases.

a. The exponential function that relates the total population as a function of t is given by:

P(t) = P₀ × (1 + r)ᵗ

where P₀ is the initial population, r is the annual growth rate (as a decimal), and t is the time in years.

Using the given values, we have:

P₀ = 500,000 (given)

r = 0.05 (5% expressed as a decimal)

Thus, the exponential function is:

P(t) = 500,000 × (1 + 0.05)ᵗ

b. The rate at which the population is increasing in t years is given by the derivative of the population function with respect to time:

dP/dt = P₀ × r × (1 + r)ᵗ

Substituting the given values, we get:

dP/dt = 500,000 × 0.05 × (1 + 0.05)ᵗ

c. To determine the rate at which the population is increasing in 10 years, we simply substitute t = 10 into the expression we derived in part b:

dP/dt = 500,000 × 0.05 × (1 + 0.05)¹⁰

Using a calculator, we get:

dP/dt ≈ 32,263

Therefore, the population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.

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Answer: -19s

Step-by-step explanation:

To construct a 3×3 matrix, not in echelon form, whose columns span ℝ³, we can choose three linearly independent vectors as the columns of the matrix.

To demonstrate that the constructed matrix has the desired property of spanning ℝ³, we can construct a specific example. Let's consider the matrix A:

A = [[1, 0, 0],

[0, 1, 0],

[0, 0, 1]]

In this case, A is a 3×3 matrix with three columns [1, 0, 0], [0, 1, 0], and [0, 0, 1]. Each column represents a standard basis vector in ℝ³.

To show that the columns of A span ℝ³, we need to demonstrate that any vector in ℝ³ can be expressed as a linear combination of the columns of A.

Let's consider an arbitrary vector x = [x₁, x₂, x₃]ᵀ in ℝ³. We can express x as a linear combination of the columns of A:

x = x₁[1, 0, 0] + x₂[0, 1, 0] + x₃[0, 0, 1]

Simplifying this expression, we get:

x = [x₁, x₂, x₃]ᵀ

Thus, we have shown that any vector x in ℝ³ can be expressed as a linear combination of the columns of the matrix A. Therefore, the columns of A span ℝ³.

Note: It is important to emphasize that there are many possible matrices that can be constructed to satisfy the given condition. The example provided here is just one of the many valid choices

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Answer:

∠Z = 155°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

So to find the value of ∠Z we can write the following equation:

65 + 90 = z

155 = z

Answer:

4%

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ,

where

x is the raw score = 100 feet

μ is the population mean = 86 feet

σ is the population standard deviation = 8 feet

Hence,

x > 100 feet

z = (100 - 86)/8

z = 1.75

Probability value from Z-Table:

P(x<100) = 0.95994

P(x>100) = 1 - P(x<100) = 0.040059

Converting to Percentage

= 0.040059 × 100

= 4.0059%

Approximately = 4%

Therefore, the percentage of the pine trees in this forest are taller than 100 feet is 4%

The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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Answer:

66 °

Step-by-step explanation:

Given:

One angle of a right triangle measures 24°.

To Find:

What is the measure of the other acute angle?

Solve:

Note:

Total angles in a triangle 180 degree

Right Triangle ⇒ 90 degree

Let "x" be the measure of the other acute angle

90° + 24° + x = 360°

114° + x = 180°

x = 66°

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