Write the trig form of the complex number
18i

(a). All four sides are equal and the angles are right-angled (90 degrees).

(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.

(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.

One of the first areas of mathematics is geometry, along with arithmetic. It is focused on spatial characteristics that relate to the proximity, size, shape, and relative placement of objects.

(a). Two features that make the shape square are all four sides equal and the angles are right-angled (90 degrees).

(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.

(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.

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Let [tex]x[/tex] and [tex]y[/tex] be the amounts of available alloy (AA) and pure magic steel that are used, so we also have

[tex]x + y = 2.7[/tex]

DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of

[tex]0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}[/tex]

[tex]0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}[/tex]

[tex]0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}[/tex]

For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; [tex]x[/tex] kg of it will contain [tex]0.21x[/tex] kg of gold, [tex]0.09x[/tex] kg of silver, and [tex]0.70x[/tex] kg of steel. Each kg of magic steel of course contributes 1 kg of steel; [tex]y[/tex] kg of it will contribute [tex]y[/tex] kg of steel.

Then the dwarves need

• total gold: [tex]0.21x = 0.189[/tex]

• total silver: [tex]0.09x = 0.081[/tex]

• total steel: [tex]0.70x + y = 2.43[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. The first two equations are consistent and give [tex]x = 0.90[/tex], and substituting this into the third we find [tex]y = 1.80[/tex]. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.

Answer:

50<x<60

Step-by-step explanation:

The triangle can only be formed with these two side lengths if the third side is bigger than (Subtract them)

55 - 5

...and smaller than (Add them)

55 + 5

55-5 < x < 55+5

50 < x < 60

The radius of the cylinder should be approximately 2.040 inches long.

The volume required to store the powder is the sum of the volumes of the cylinder and the cone, whose expression is in this case:

204 in³ = (π/3) · r² · (4 in) + π · r² · h

204 in³ = (4/3 + h) · π · r²

204 in³ = (4/3 + 7 · r) · π · r²

204 = (4π/3) · r² + 7π · r³

7π · r³ + (4π/3) · r² - 204 = 0

The positive roots of the cubic equation are:  

r ≈ 2.040 in

The radius of the cylinder should be approximately 2.040 inches long.

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Considering the given rectangle, the coordinates of p are (6,7).

For x, there are two vertices at x = 3 and one at x = 6, hence the x-coordinate of p is x = 6.

For y, there are two vertices at y = 9 and one at y = 7, hence the y-coordinate of p is y = 7.

Then, the coordinates of p are (6,7).

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Debido a restricciones de longitud invitamos cordialmente a leer la explicación de esta pregunta para aprender sobre las cuestiones de las ecuaciones cónicas.

Según la geometría analítica, existen cinco tipos de secciones cónicas: recta, circunferencia, elipse, parábola e hipérbola. Aquí se presentan problemas que emplean este tipo de ecuaciones.

1) La trayectoria de la rana describe la forma de una parábola. Asumimos que el punto máximo de la trayectoria de la rana es de la forma (h, k) = (0, k), entonces tenemos que la ecuación de la parábola es:

y - k = C · x²       (1)

Donde C es la constante del vértice.

Si sabemos que (h, k) = (0, 3) y (x, y) = (9, 0), entonces la ecuación de la parábola es:

C = (0 - 3) / 9²

C = - 1 / 27

La ecuación de la parábola es y - 3 = (- 1 / 27) · x².

2) Se determina el tipo de categoría de cada ecuación:

a) 3 · x - 2 · y + 4 = 0: Recta (a · x + b · y + c = 0)

b) 4 · x + y² - 7 = 0: Parábola ((y² - k) = 4 · p · (x - h))

c) x² + y² = 16: Circunferencia ((x - h)² + (y - k)² = r²)

d) y = x³ - 3 · x + 1: Ecuación cúbica

e) x² + 4 · y² = 4: Elipse (b² · (x - h)² + a² · (y - k)² = a² · b²)

3) Se debe hallar el valor C de la función lineal tal que S = 0.35 por medios algebraicos:

0.35 = 0.03 + 1.805 · C

0.32 = 1.805 · C

C = 0.32 / 1.805

C = 0.177

4) El arco semielíptico tiene una longitud de semieje mayor de 25 pies (paralelo al eje x) y una longitud de semieje menor de 15 pies (paralelo al eje y). Si consideramos que el centro de la elipse está en el origen, entonces tenemos que la ecuación es:

x² / 25² + y² / 15² = 1

y = 15 · √(1 - x² / 25²)

y = 15 · √(1 - 12² / 25²)

y = 13.159 pies

5) a) y b) Ahora graficamos la hipérbola y presentamos las ubicaciones de los focos y las asíntotas correspondientes. a) Las ecuaciones de las asíntotas son y = ± (3 / 2) · x, b) Las ecuaciones de las asíntotas son y = ± (√ 2 / 2) · x.

c) Se puede determinar la naturaleza de cada ecuación por métodos algebraicos:

9 · x² - 4 · y² - 54 · x - 16 · y + 29 = 0

[9 · x² - 2 · 9 · (3 · x) + 81] - [4 · y² - 2 · 8 · (2 · y) + 64] = 116

(3 · x - 9)² - (2 · y - 8)² = 116

9 · (x - 9)² - 4 · (y - 4)² = 116

(x - 9)² /12.889 - (y - 4)² / 29 = 1  - Hipérbola

4 · x² + 2 · y² - 7 · x + y - 5 = 0

[4 · x² - 2 · (7 / 4) · (2 · x) + 49 / 16] + [2 · y² + 2 · (√2 / 2) · (√2 · y) + 1 / 2] = 5

(2 · x - 7 / 4)² + (√2 · y + √2 / 2)² = 5

4 · (x - 7 / 8)² + 2 · (y + 1 / 2)² = 5

(x - 7 / 8)² / 1.25 + (y + 1 / 2)² / 2.5 = 1  - Elipse  

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Answer: c. the mean is greater than the median

Explanation:

To find out the correct answer, we first must know the true meanings and the method of calculation of the terms, "mean", "mode" and "median".

Mean: The mean is a type of average. It is the sum of all the values in a set of data, such as numbers of measurements, divided by the numbers of values on the list.

[tex]\bar{x} = \dfrac{\sum x}{n}[/tex]                                      where, [tex]\bar{x}=[/tex] sample mean
                                                               [tex]\sum x =[/tex] sum of each value in sample
                                                               [tex]n =[/tex] number of values in the sample

Example: in {6, 3, 9, 6, 6, 5, 9, 3} the mean is 5.875 (6+3+9+6+6+5+9+3/8).
                           
                                         

Mode: The mode is the number which appears most often in a set of numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.

Median: The median is the "middle" of a sorted list of numbers in ascending order (small to big). To find the Median, place the numbers in value order and find the middle.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the median is 6. (in 3,3,5,6,6,9,9, the middle number is 6 )

with an even amount of numbers things are slightly different.
In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two. (basically averaging the middle two numbers incase there is an even set of numbers)
Example: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers.

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

In this example the middle numbers are 21 and 23.

To find the value halfway between them, add them together and divide by 2: 21 + 23 = 44, then 44 ÷ 2 = 22

So the Median in this example is 22.
(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)

Now that you understand the terms clearly, let's find out the mean, mode and median from your given set of numbers.
                                           5, 15, 25, 30, 3

Mean: (5+15+25+30+3)/5  is, 15.6
Mode: None since none of the numbers repeated more than once.
Median: 3,5,15,25,30  , so the middle number is 15 .

Since there is no mode, option d. can never be the answer. And clearly, 15.6 is greater than 15 so the answer should be c. the mean is greater than the median.

 ∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
    hope it helped
┗━━━━━━━┛

Answer:

ok

this called f to do

Step-by-step explanation:

1. take a _____

The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.

let

x + y = 54

4x + 3y = 200

From equation (1)

x = 54 - y

4x + 3y = 200

4(54 - y) + 3y = 200

216 - 4y + 3y = 200

216 - y = 200

- y = 200 - 216

-y = -16

y = 16

x + y = 54

x + 16 = 54

x = 54 - 16

x = 38

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73 division 84, 649 would give 8. 64 × 10^-4

In order to determine the value of the division, we have

= [tex]\frac{73}{84649}[/tex]

Using the calculator, put the values in

We would have

= 8. 64 × 10^-4

Thus, 73 division 84, 649 would give 8. 64 × 10^-4

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Answer: [tex]a=\frac{b}{zm-1}[/tex]

Step-by-step explanation:

Let's first multiply both sides by m to get rid of the denominator.

[tex]za=\frac{a+b}{m}\\zam=a+b[/tex]

Now, we have an a on both sides of the equation. It will be easier to solve if there is only one, so let's divide both sides by a.

[tex]\frac{zam}{a}=\frac{a+b}{a}\\zm=\frac{a}{a}+\frac{b}{a}\\zm=1+\frac{b}{a}[/tex]

The 1 on the right can be moved to the left to isolate the fraction.

[tex]zm-1=\frac{b}{a}[/tex]

We want to get a by itself, so let's multiply it on both sides to remove it from the denominator.

[tex]a(zm-1)=b[/tex]

Finally, we can divide zm-1 from both sides to get a by itself.

[tex]a=\frac{b}{zm-1}[/tex]

the probability of getting heads on a two-face coin is simply 1/2.

now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2?   well, AND means "times", namely

[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]

well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.

Answer: Point of intersection (0, -2)

Step-by-step explanation:

Answer:

S =  (0, -2)

Step-by-step explanation:

Convert both standard form equations to slope-intercept form.

-5x+2y=-4 ⇒ y = 5/2(Decimal form: 2.5)x - 2

2x-y=2 ⇒ y = 2x - 2

Given:

⇒ L1 = y = 5/2x - 2

⇒ L2 = y = 2x - 2

The intersection is point:

⇒ S = (0, -2)

Steps:

To find intersection point we need to solve the following system of equations.

STEP 1: Solve for x

5/2x - 2 = 2x - 2

5/2x - 2x = -2 + 2

1/2x = 0

x = 0

STEP 2:  Solve for y by substituting x = 0 into  first equation.

y = 5/2 * 0 - 2 = 0 - 2 = -2

The lateral area of the cone is calculated as: B. 47 in.².

Lateral area = πrl

Given the following:

Slant height (l) = 5 inches

Radius (r) = 3 inches.

π = 3.14

Plug in the values

Lateral area = (3.14)(3)(5)

Lateral area ≈ 47 in.²

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5pi/12 radians

The arc measure is 75, so theta must also be the same. if theta is 75, and 75 in radians is 5pi/12 radians, then the answer is that.

See below for the missing terms of the sequences

The given parameters are:

T4 = 30

T5 = 49

Calculate the third term as follows:

T3 = T5 - T4

T3 = 49 - 30

T3 = 19

Calculate the second term as follows:

T2 = T4 - T3

T2 = 30 - 19

T2 = 11

Calculate the first term as follows:

T1 = T3 - T2

T1 = 19 - 11

T1 = 8

Hence, the first term of the sequence is 8

The given parameters are:

T2 = x

T3 = y

Calculate the first term as follows:

T1 = T3 - T2

T1 = y - x

Calculate the fourth term as follows:

T4 = T2 + T3

T4 = x + y

Calculate the fifth term as follows:

T5 = T3 + T4

T5 = y + x + y

T5 = x + 2y

Hence, the missing terms of the sequence are y - x, x + y and x + 2y

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Answer:

First answer is 1200

Second answer is 900 for each new employee

Step-by-step explanation:

First answer:

2200+1300+800+940+560+x = 7000

5800+x = 7000 subtract 5800 from both sides and you get your answer

x = 1200

Second answer:

x = 900.  Each of the two employees made 900 a month or 1800 a month for both of them.

To find the average we take the total salaries and divide by the number of people to find the average salary.  In this case, we know the average and we know all of the salaries, but two.  We can figure this out.

(7000 + 2x)/8 = 1100  multiple both sides by 8 to clear the fraction/

7000 +2x = 8800  Subtract both sides by 7000

2x = 1800  Divide both sides by 2

x = 900

Using an exponential function, it is found that:

The exponential function for population growth is given as follows:

[tex]P(t) = P(0)e^{kt}[/tex]

In which:

For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:

[tex]P(t) = P(0)e^{kt}[/tex]

[tex]2P(0) = P(0)e^{0.016t}[/tex]

[tex]e^{0.016t} = 2[/tex]

[tex]\ln{e^{0.016t}} = \ln{2}[/tex]

[tex]0.016t = \ln{2}[/tex]

[tex]t = \frac{\ln{2}}{0.016}[/tex]

t = 43 years.

For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.

[tex]P(t) = P(0)e^{kt}[/tex]

[tex]2P(0) = P(0)e^{36k}[/tex]

[tex]e^{36k} = 2[/tex]

[tex]\ln{e^{36k}} = \ln{2}[/tex]

[tex]36k = \ln{2}[/tex]

[tex]k = \frac{\ln{2}}{36}[/tex]

k = 0.019.

For Country B, the growth rate is of 1.9% per year.

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Answer:

[tex]\frac{\sqrt{41}}{4}[/tex]

Step-by-step explanation:

sec(theta) is defined as: [tex]sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}[/tex]

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

So this gives us the equation where a=adjacent side:

[tex]a^2+5^2=\sqrt{41}^2[/tex]

[tex]a^2+25=41[/tex]

Subtract 25 from both sides

[tex]a^2=16[/tex]

Take the square root of both sides

[tex]a=4[/tex]

So now plug this into the definition of sec(theta) and you get: [tex]\frac{\sqrt{41}}{4}[/tex]. This is in most simplified form since 41, has no factors besides 41 and 1.

Using translation concepts, it is found that g(x) is positive on the following interval:

(3, ∞)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Function [tex]g(x) = \sqrt[3]{x - 3}[/tex] is a shift right of 3 units of [tex]f(x) = \sqrt[3]{x}[/tex], which is positive on the interval (0, ∞), hence g(x) is positive on the interval (3, ∞).

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Answer:

a=10%, b=25/100, c=1/2

Step-by-step explanation:

a: If the denominator is exactly 100, then the numerator represents a percentage.

b: when you change a fraction to have a greater denominator, an easy way to figure out how to change the numerator to match it and make the value of the rewritten fraction equal to the old version, is to divide the new value of the denominator by the old value (in this case being 100/4=25), and put the answer where the numerator goes.

c: When simplifying a fraction with a lesser numerator than denominator, find the greatest common factor (a factor is a whole number a number can be divided by without resulting in a negative or a decimal number) and divide both the numerator and denominator by it.

The return on the investment is 3%

The given parameters are:

Buying rate = 7%

Selling rate = 10%

The return on the investment is

ROI = Selling - Buying

So, we have:

ROI = 10% - 7%

Evaluate

ROI = 3%

Hence, the return on the investment is 3%

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Answer: 14.8

Step-by-step explanation: If the number in the hundredths place is less than 5, you must round down. On the contrary, if that number is 5 or greater, you must round up. This applies for rounding to any place not just the tenths place. For example, if you were to round it to the ones place, the answer would be 15.

Answer:

14.8

Step-by-step explanation:

The hundredth is smaller than 5, therefore you have to round down.

hope it helps

Answer:

obtuse

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

In the above problem, it's given that one of the angles of the triangle exceeds 90° [ that is : 97° ]

[tex] \qquad \large \sf {Conclusion} : [/tex]

hence, it's an obtuse angled triangle

Answer:

Step-by-step explanation:

area=length×width

=(2x+3)(3x-5)

Area=6x²-10x+9x-15

=6x²-x-15

Using derivatives, the equation of the tangent line is: y + 2= -(x + 2)

The equation is:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the derivative at point [tex](x_0, y_0)[/tex].

The function is:

[tex]x^2 + y^2 = 8[/tex].

Applying implicit differentiation, the derivative is:

[tex]2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0[/tex]

[tex]2ym = -2x[/tex]

[tex]m = -\frac{x}{y}[/tex]

We have that x = y = -2, hence m = -1 and the equation is:

y + 2= -(x + 2)

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Answer:

1.6 < x < 9.6

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

5.6 - 4 < x < 5.6 + 4

1.6 < x < 9.6

Answer:

A minimum of 21250 packets per day.

Step-by-step explanation:

If Monday produced 15,000 packets, and Tuesday was closed they produced 15,000 packets in 2 days.

The factory is open 6 days a week.

They need 100,000 packets.

They have 15,000 packets.

6 subtract 2 is 4.

100,000 subtract 15,000 is 85,000.

They need 85,000 packets in 4 days.

That is a minimum of 21250 packets per day.

Applying the Pythagorean theorem, the missing side of the triangle is: C. √193 km.

To find the missing side (x) in the right triangle, based on the Pythagorean theorem, we would have the following equation:

x = √(12² + 7²)

x = √(144 + 49)

x = √193

The missing side of the triangle is: C. √193 km

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Answer:

C.)  193√ km

Step-by-step explanation:

I got it right on founders edtell

The limit of

[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex].

In Mathematics, a limit exists described as a value that a function approaches the output for the provided input values. Limits exist necessary in calculus and mathematical analysis and exist utilized to determine integrals, derivatives, and continuity.

Given:

[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)$$[/tex]

Substitute the value x = 0, then we get

[tex]$=\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}$$[/tex]

Simplify the above equation, we get

[tex]$\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}= 1$[/tex]

Therefore, the limit of

[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex]

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