Let z = equals 38 (cosine (startfraction pi over 8 endfraction) i sine (startfraction pi over 8 endfraction) ) and w = 2 (cosine (startfraction pi over 16 endfraction) i sine (startfraction pi over 16 endfraction) ) . what is the product of zw?

Answer:

Step-by-step explanation:

Solution

Interesting question.

The formula for the sum of the interior angles is

(n - 2)*180 = x

In this case, x = 1260

(n - 2)*180 = 1260                            Divide both sides by 180

(n -2 )* 180/180 = 1260/180

( n - 2) = 7                                         Remove the brackets

n - 2 = 7                                            Add 2 to both sides

n - 2 + 2 = 7 +2                                 The 2s on the left cancel

n = 9

Answer: Nonagon

The polygon with an interior angle sum of 1260° is the nonagon as per the concept of interior angles.

To find the sum of the interior angles of a polygon, we can use the formula:

Sum of interior angles = (n - 2) × 180°

where "n" is the number of sides of the polygon.

To achieve an interior angle sum of 1260°, we would need to consider a polygon with fewer sides.

For example, a nonagon (9 sides) would have an interior angle sum of 1260°:

Sum of interior angles = (9 - 2) × 180°

Sum of interior angles = 7 × 180°

Sum of interior angles = 1260°

So, a nonagon (a polygon with nine sides) has an interior angle sum of 1260°.

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The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ  and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

arc(AB) > arc(CD)      .......(1)

Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D       ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2  and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

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The expression [tex]10^{t^2+2t-3}[/tex] is equivalent to the expression [tex](10^{t+3})^{t-1[/tex]

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression:

[tex]10^{t^2+2t-3}\\\\=10^{t^2+3t-t-3}\\\\=10^{[t(t+3)-1(t+3)]}\\\\=10^{(t-1)(t+3)}[/tex]

The expression [tex]10^{t^2+2t-3}[/tex] is equivalent to the expression [tex](10^{t+3})^{t-1[/tex]

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The solution of the graph can be located at the point of intersection of the two lines. The solution, approximated to the tenths place will be (0.4, 2.8)

The solution of a system of two linear equations can be calculated by determining the point of intersection.

Therefore, the solution = the coordinates of the point of intersection (x-coordinate, y-coordinate).

Given graph shows the system of equations in two lines:

The solution of the graph can be located at the point of intersection of the two lines, the x-coordinate against the y-coordinate.

The integers that the x-coordinate of the point of intersection is in between are 0 and 1.

The y-coordinates of the point of intersection lie between the integers 2 and 3.

The solution, approximated to the tenths place will be (0.4, 2.8)

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The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

This question is incomplete, the complete question is;

Which equation is correct for ∆FON?

Answers:

A.) cos F= 9/18

B.) sin F 9/18

C.) sin F=18/9

D.) cos F=18/9

From the diagram, we have a right angle triangle.

Note that; sinθ = Opposite / Hypotenuse

Therefore, for angle F

sin F = Opposite / Hypotenuse

sin F = 9/18

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

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The radius of the quadrant whose perimeter is 52cm is 14.56cm.

A quadrant is 1/4th of a circle, consisting of two radii, perpendicular to each other.

So, the perimeter of a quadrant consists of two radii and an arc, which is 1/4th the perimeter of a circle.

Therefore, the perimeter of the quadrant = 2r + (1/4)*(2πr) = 2r + (πr/2).

Now, we are given the perimeter of the quadrant = 52cm and are asked to find its radius.

We suppose the radius to be r cm.

Therefore, we can say that:

52 = 2r + (πr/2).

or, 52 = (4r + πr)/2

or, 52*2 = r(4 + π)

or, r = 104/(4 + π) = 14.56.

Therefore, the radius of the quadrant whose perimeter is 52cm is 14.56cm.

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Answer:

262 passengers can have both headphones and blankets .

Step-by-step explanation:

I hope it will help you

The 3-D figure and combination of shapes that Scarlett can use is A. Equilateral triangle prism with two equilateral triangles and three rectangles

This refers to the solid figure or shape that has defined dimensions of length, width, and height.

Therefore, based on the fact that a 3-D figure is made up of six equal squares, option A is the best answer because it contains a total of six squares.

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Answer: a

Step-by-step explanation:

[tex]z_0=-1-2i\\\\z_1=2(-1-2i)+(3-2i)=-2-4i+3-2i=1-6i[/tex]

This eliminates all the options except for a.

Answer:

=======================

Use circumference formula to find the tire circumference:

Find the distance by multiplying the number of revolutions by circumference:

Convert the inches to feet, or yards, considering 12 in = 1 foot and 3 feet = 1 yard:

The coefficient are as follows:

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. 12s + 4t

Variables: s, t

Coefficient: 12, 4

2. 46rs + 10x

Variables: r, s, x

Coefficient: 46, 10

3. 12q + 14x

Variables: q, x

Coefficient: 12, 14

4. 10x + 10y

Variables: x, y

Coefficient: 10, 10

5. 17rs + 32x

Variables: r, s, x

Coefficient: 17, 32

6. 5x + 7y - 12z

Variables: x, y, z

Coefficient: 5, 7, -12

7. 36ab + 70m

Variables: a, b, m

Coefficient: 36, 70

8. 3r + 19a + 10m

Variables: r, a, m

Coefficient: 3, 19, 10

9. 7k + 16m

Variables: k, m

Coefficient: 7, 16

10. 8r + 5s

Variables: r, s

Coefficient: 8, 5

11. 9h + 120m

Variables: h, m

Coefficient: 9, 120

12. 12k + m

Variables: k, m

Coefficient: 12, 1

13. 7g + 15h + w

Variables: g, h, w

Coefficient: 7, 15 , 1

14. 4c - 8d + 12f

Variables: c, d, f

Coefficient: 4, -8, 12

15. 6t + 17r - 35j

Variables: t, r, j

Coefficient: 6, 17, -35

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Answer:

Graph Number 2

Step-by-step explanation:

Use the horizontal line test: If you can draw a horizontal line at any point and it only intersects the line once, then it's a one-to-one function.

The solution of Tx" + (4t - 2)X' + (13t - 4)X = 0, If X(0) = 0 is mathematically given as

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

Generally, the equation for is mathematically given as

[tex]&t x^{\prime \prime}+(4 t-2) x^{\prime}+(13 t-4) x=0, \quad x(0)=0\\\\&\Rightarrow \quad t x^{\prime \prime}+4 t x^{\prime}-2 x^{i}+13 t x-4 x=5\\[/tex]

By taking Laplace to transform,

[tex]&L\left\{t x^{13}\right\}+L\left\{4 t x^{\prime}\right\}-L\left\{2 x^{\prime}\right\}+L\{13 t x\}-L\{4 x\}=0\\\\\\&-25 x(s)-s^{2} x^{1}(5)-4 x(s)-45 x^{\prime}(s)-25 x(s)-13 x^{\prime}(5)-4 x(s)=0\\[/tex]

[tex]&\Rightarrow \quad-\left(5^{2}+45+13\right) x^{4}(5)-4(5+2) x(5)=0\\\\\\&\Rightarrow \quad\left(s^{2}+45+13\right) x^{1}(5)+4(5+2) x(5)=0\\\\\\&\Rightarrow\left(s^{2}+4 s+13\right) x^{\prime}(s)=-4(s+2)^{x}(s)\\\\\\&\Rightarrow \frac{x^{\prime}(s)}{x(s)}=-\frac{4(s+2)}{s^{2}+4 s+13}\\\\\[/tex]

In conclusion, By integrating both sides

The solution is

[tex]&x(s)=\frac{c}{\left(s^{2}+4 s+13\right)^{2}}\\[/tex]

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

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Based on the calculations, the slope of line YZ in simplest form is equal to 2.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since points X, Y, and Z are collinear, we can deduce that the line passes through line Z at 6 units form the origin and 3 units for Y from the origin.

Substituting the parameters into the formula, we have;

[tex]Slope, m = \frac{6\;-\;0}{3\;-\;0}[/tex]

Slope, m = 6/3

Slope, m = 2.

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Answer:

199.5 ft^3

Step-by-step explanation:

to find your answer you simply multiply all the measurements together

19 * 1.5 * 7 is your equation

19 * 1.5 * 7 = 199.5

it is 199.5 ft^3

Answer: the one on the right on the top

Step-by-step explanation:

as x increases by 1, y decreases by 2. this makes a linear function

Answer: the answer is the first option

Step-by-step explanation:

Here are the awnsers

1. D ⅔

2.C 60%

Question : Draw a triangle ABC. Next, create a line through point C that is perpendicular to . Label the intersection between the perpendicular line and as point E. Take a screenshot of the triangle with CE, save it, and insert the image in the space below.

We know that having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional shape. A polygon also includes a triangle.

A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.

The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). The Latin word "perpendicularis," which denotes a plumb line, is where the word "perpendicular" first appeared. Two lines, AB and CD, can be written as AB⊥CD if they are perpendicular to one another. The perpendicular nature of the lines is denoted by the symbol.

Here, we have to draw a triangle. Then we have to draw a line CE which intersects AB at point E.

Image is attached below.

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Answer:

AC Factor: 420

Factors that add up to 41: 20 and 21

Rewritten equation: [tex](35x^2+21x)+(20x+12)[/tex]

Step-by-step explanation:

so a quadratic equation is generally expressed as [tex]ax^2+bx+c[/tex]. So in this polynomial 35=a and c=12. The ac product would thus be (35)(12) which is 420

The factors of the AC product include: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20 , 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Since we're looking for a bigger number which is 41 you would generally want to look near the middle. and you can disregard any factors equal to or above 42. since they wouldn't add to 41. So I'll start at 30. 420/30 = 14 and 30 + 14 = 44 which is pretty close. Alright I'll try 28 instead. 420/28 = 15 and 15+28 = 43 which is also pretty close so I'll try the next factor 420/21 = 20 and 20+21 = 41! so the two factors are 20 and 21

Now using these two factors you can rewrite the equation as

[tex](35x^2+21x)+(20x+12)[/tex] which simplifies to the same quadratic equation

y=35x²+41x+12

Here

So

Now

Factors that add up to 41 are 21 and 20

Now solve

The volume of volume of the rectangular prism is=240cm³ while the surface area of cylinder =225.04cm²

The volume of rectangular prism

= l×w×h

= 10× 6× 4

= 240cm³

The surface area of cylinder,

= 2πrh+2πr²

= 2× 3.14× 2.8 × 10 + 2×3.14×2.8²

= 175.84 + 49.2

= 225.04cm²

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Answer:

Answers are below.

Step-by-step explanation:

1) 60 centimeters

2) Perimeter = 48, Area = 144

3) Circumference = 20π, Area = 100π

4) 180 feet

5) 75 meters

6) 15 yards

Hope this helps!

Answer:

A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

A ∩ B = {3, 1, 2, 4, 5}

Step-by-step explanation:

Given that A = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

B = the set of all Natural numbers

C= the set of all Rational numbers

So set C contains numbers that can be expressed as the ratio of two integers. Since numbers in A can be expressed as follows:

0 = 0/1,  3 = 3/1,  1 = 1/1, 1.3 = 13/10, 2 = 2/1,  4 = 4/1, 5 = 5/1

Then, A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}.

A ∩ B = {3, 1, 2, 4, 5}, since B contains only Natural numbers = {1, 2, 3, ...}.

The function which represents the annual salary for total sales of x dollars, where x is greater than $250000 is 0.025x+29750.

Given basic salary=3000 p.m. , bonus 2.5% of total sales above $250000.

We have to make a function which shows the annual salary for total sales of x dollars where x is greater than $250000.

Function is a relationship between two or more variables which have each y values corresponding to x values.

According to question

Total basic salary of whole year=3000*12=$36000

We have been given total sales be x.

Sales above $250000 is x-250000

Bonus on sales=2.5%(x-250000)

Function f(x)=36000+2.5%(x-250000)

=36000+0.025x-0.025*250000

=36000+0.025x-6250

=0.025x+29750

Hence the function which shows the annual salary for total sales of x dollars is f(x)=0.025x+29750.

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The value of x in the equation 1/2x = -1/2x when 4 is subtracted from both sides is 0(not defined)

Subtraction of fraction

Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction

1/2x = -1/2x

1/2x - 4 = -1/2x - 4

(x-8) / 2 = (-x-8) / 2

(x - 8) / 2 = (-x-8) / 2

2(x - 8) = 2(-x - 8)

2x - 16 = -2x - 16

2x + 2x = -16 + 16

4x = 0

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Answer:c

is the answer

Step-by-step explanation:

The equations for the lines tangent to and normal to the curve at the point (2, 4) are y = 4 · x - 4 and y = (-1/4) · x + 9/2, respectively.

In this question we must use the definitions of linear function, tangent and normal lines and differential calculus to determine the equations needed. The slope of the tangent line (m) is found by implicit differentiation:

2 · x + 2 · y · y' - 3 · (y + x · y') = 0

2 · x + (2 · y - 3 · x) · y' - 3 · y = 0

(2 · y - 3 · x) · y' = 3 · y - 2 · x

y' = (3 · y - 2 · x)/(2 · y - 3 · x)

By (x, y) = (2, 4)

m = (3 · 4 - 2 · 2)/(2 · 4 - 3 · 2)

m = 4

And the slope of the normal line is:

m' = -1/m = -1/4

Lastly, we obtain the intercept for each line:

Tangent line

b = 4 - 4 · 2

b = 4 - 8

b = - 4

The equation of the line tangent to the curve at the point (2, 4) is y = 4 · x - 4.

Normal line

b = 4 - (-1/4) · 2

b = 4 + 1/2

b = 9/2

The equation of the line normal to the curve at the point (2, 4) is y = (-1/4) · x + 9/2.

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Answer:

  647

Step-by-step explanation:

The divisibility rule for 9 can be used to find the unknown number.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The number 3D8 will be divisible by 9 when 3 + D + 8 = <multiple of 9>. Since D is a single digit, we must have ...

  11 +D = 18

  D = 7 . . . . . . . subtract 11

The number 3D8 is 378.

Now we know that the difference is ...

  ABC -3D8 = ABC -378 = 269

  ABC = 269 +378 = 647

ABC represents the number 647.

The correct statement regarding the limit, using asymptotes, is:

The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].

In this problem, we have a limit, which is associated with a horizontal asymptote. The limit is:

[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1}[/tex]

x goes to infinity, hence we consider only the highest exponents.

[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1} = \lim_{x \rightarrow \infty} -\frac{10x^2}{4x^2} = -\frac{10}[4} = -\frac{5}{2}[/tex]

Hence the correct statement is:

The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].

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