What is the area of the given triangle?

The period of the given function is T = 2π

The period T of a function f(x) is such that:

f(x + T) = f(x).

In this case, our function is:

f(θ) = e^{iθ}

Remember that this can be written as:

f(θ) = cos(θ) + i*sin(θ)

So yes, this is in did a periodic function.

Then the period of the function f(θ) is the same as the period of the cosine and sine functions, which we know is T = 2π.

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The period of the considered function f(θ) = e^{iθ} is found to be P = 2π (assuming 'i' refers to 'iota' and 'e' refers to the base of the natural logarithm)

For any real value θ, we have:

[tex]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/tex]

where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.

Functions which repeats their values after a fixed interval, are called periodic function.

For a function [tex]y = f(x)[/tex], it is called periodic with period 'T' if we have:

[tex]y = f(x) = f(x + T) \: \forall x \in D(f)[/tex]

where D(F) is the domain of the function f.

Suppose that, the period of the function [tex]f(\theta) = e^{i \theta}[/tex] be P, then we get:
[tex]f(\theta + P) = f(\theta)\\\\e^{i(\theta)} = e^{i(\theta + P)}\\\\\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex]

When two complex numbers are equal, then their real parts are equal and their imaginary parts are equal.

That means,

[tex]\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex] implies that:

[tex]\cos(\theta) = \cos(\theta + P)\\\sin(\theta) = \sin(\theta + P)[/tex]

Also, we know that the period of sine and cosine function is [tex]2\pi[/tex]

Thus, we get:

[tex]P = 2\pi[/tex]

Thus, the period of the function [tex]f(\theta) = e^{i \theta}[/tex]  is P = 2π

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Answer:

x = 9/10

Step-by-step explanation:

This problem features a ratio: 4x/3 = 6/5

By cross multiplying you get that 4x*5 = 3*6 or 20x = 18. By dividing both sides by 20, you get that x = 18/20, and when simplified, 9/10.

Answer: 48

Step-by-step explanation:

3x16=48

3 gallons=48 cups

There are 48 cups in 3 gallons.

To start your conversion, you need to know how many cups are in one gallon.

There are 2 cups in 1 pint, and 2 pints in 1 cup.

Answer: 13.5 in

Step-by-step explanation:

The formula for the volume of a cone is: V = π*r^2*(h/3).

Therefore, when the given numbers are plugged in, it becomes:

1144.53 = (3.14)(9^2)(h/3).

Solving this for h, we get the answer of 13.5 in

Answer:

100.53m² area of carpet is left after putting the table in place.

Answer:

find the product of (4m-n)and(3m-2n)

Answer:

1

Step-by-step explanation:

the number of circles which can pass through three given non-collinear points is exactly one.

the reason is that the center of such a circle must be on the (perpendicular) bisectors of the lines between each pair of these points.

these bisectors intersect at one unique point which is the center of the circle and the distance of any point from the center is the radius. So given three non collinear points fixes the center and the radius thereby giving us one unique circle.

the same way we find the circumscribing circle of a triangle, which is exactly the same situation.

Hey there!

Formula:

a = √p(diagonal)^2 + q(diagonal)^2 / 2

a = √p + q / 2

SOLVING FOR CURRENT EQUATION

a = √10^2 + 12^2 / 2

a = √10 * 10 + 12 * 12 / 2

a = √100 + 144 / 2

a = √244 / 2

a = √61

a ≈ 7.81

Thus, your answer is: √61

Or as you put….

5^2 + 6^2 = c^2

5 * 5 + 6 * 6 = c^2

25 + 36 = c^2

√61 or -√61 = c^2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Subtract to find how much was spent on coffee:

90 - 47.65 = 42.35

Divide what was spent by the price per pound:

42.35 / 8.47 = 5

They bought 5 pounds of coffee

The Area of the shaded portion = area of 5 shaded squares = 80 in.².

Area of a square = s², where the edge length is s.

Edge length of each small square = 12/3 = 4 in.

Area of the shaded portion = area of 5 shaded squares = 5(s²)

s = 4 in.

Area of the shaded portion = 5(4²)

Area of the shaded portion = 80 in.²

Therefore, the Area of the shaded portion = area of 5 shaded squares = 80 in.².

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Answer:

[tex]23n + 64[/tex]

Step-by-step explanation:

Hope this helps

Check the picture below.

Answer:

Top question) 12

Bottom question) 16

Step-by-step explanation:

top) you can fit 6 in the bottom of a 3x2 box if the smaller boxes are only 1 cubic foot and since it's also 2 feet high you can also fit another 6 which in total equals 12.

bottom) you can fit 8, 1 cubic foot boxes, in a larger box thats 4x2 and since it's also two feet tall you can fit another 8 in making 16 fitting in the larger box

Hope this helps! pls mark brainliest

Reflecting the archaeological dig implies that the dig is flipped

The vertices of the second outlined rectangle after completing both reflections are (-5,-2),(-5,-9),(-10,-9) and (-10,-2)

The coordinates of the rectangle are given as:

(5,2) , (5,9) , (10,9) , (10,2)

When reflected across the x and the y axes, the transformation rule is:

[tex](x,y) \to (-x,-y)[/tex]

So, the new coordinates are:

(-5,-2),(-5,-9),(-10,-9),(-10,-2)

This means that:

The vertices of the second outlined rectangle after completing both reflections are (-5,-2),(-5,-9),(-10,-9) and (-10,-2)

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First, you know that Jackson (let call her J) scored 42 more points than L (Leslie).  What we don't know is how many points L scored so we can use a variable that will be 'x'.

So the equation will be J=42+x.

We also know that the total points is 1,144.

To find out what x is we first subtract 1,144-42.  We then get 1,102.

We are now left with 2x and 1,102 so we divide 1,102 by 2 and get 551.

551=x so now we can plug that in.

J = 551 + 42

Jackson scored 593 points and Leslie scored 551 points

(You can use bar modeling to do solve this problem.  An example of bar modeling is shown below.  

The concentration of ions in the solution of lemon juice whose pH value is 2.32 is 4.79×10⁻³ M.

The pH value shows that how much a solution is acidic or basic. The range of the pH value lies between the 0-14.

The pH value can be calculated with the following formula.

[tex]\rm pH=log[H^{+}][/tex]

Here, [H⁺] is the molar hydrogen ion concentration.

The pH of lemon juice at 298 K is found to be 2. 32. Put this value of pH in the above formula as,

[tex]\rm 2.32=log[H^{+}]\\\ [H^{+}]=4.79\times10^{-3} \rm \; M[/tex]

Hence, the concentration of ions in the solution of lemon juice whose pH value is 2.32 is 4.79×10⁻³ M.

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Answer:

B ✔️

Step-by-step explanation:

The Prism has a larger surface area than the pyramid.

Area is the amount of space occupied by a two dimensional shape or object.

Surface area of Prism = 2 * base area + 4(base length)(height)

Surface area of Prism = 2(6 * 6) + 4(6)(4) = 168 in²

Surface area of pyramid = (base area) + 2(base length)(slant height)

Surface area of pyramid = (6 * 6) + 2(6)(5) = 96 in²

The Prism has a larger surface area than the pyramid.

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Answer:

  6 cm

Step-by-step explanation:

A diameter of a circle is a line segment that connects one side of the circle to the other, passing through the center.

The distance from the center to any point on the circle is the radius. So, a diameter is the sum of a radius to one side of the circle and a radius to the other side of the circle. (The circle center is the midpoint of the diamter.)

The diameter is twice the radius:

  d = 2 × (3 cm) = 6 cm

The dial's diameter is 6 cm.

Answer:

Question (a)

Given equation:

[tex]8^{2x} = 32^{x+3}[/tex]

8 can be written as [tex]2^3[/tex]

32 can be written as [tex]2^5[/tex]

Therefore, we can rewrite the equation with base 2:

[tex]\implies (2^3)^{2x} = (2^5)^{x+3}[/tex]

------------------------------------------------------------------------------

Question (b)

To solve:

[tex](2^3)^{2x} = (2^5)^{x+3}[/tex]

Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] :

[tex]\implies 2^{3 \cdot 2x} = 2^{5(x+3)}[/tex]

[tex]\implies 2^{6x} = 2^{5x+15}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex] :

[tex]\implies 6x = 5x+15[/tex]

Subtract [tex]5x[/tex] from both sides:

[tex]\implies x = 15[/tex]

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation

A.96=6+576

B.576=96+6

C. 96=6×576

D. 576=96×6

Answer:

11mi² = 28489869m²

Step-by-step explanation:

m² = mi² / 0.00000038610

The solutions to the system of the equations graphed below are where the graphs intersect:

In this case, the two graphs intersect at (0,6) and (-3, -3)

So the solutions are (0,6) and (-3,-3)

Hope that helps!

The solution to the system of the equations below is: (0,6) and (-3,-3)

The solutions are where the two graphs of the equations intersect

Answer:

139

Step-by-step explanation:

A = Pe^rt

A = 600$

P = 300$

R = 0.005

T = ?

600 = 300e^(0.005)(t)

t = 138.63

Answer:

approximately V =  201 m^{3}

Step-by-step explanation:

Volume of a right circular is π[tex]r^{2} h[/tex]

R = radius of 4m

H = height of 4m

pi = approximatly 3.14

[tex]V = 3.14*4^{2}*4[/tex]

[tex]V = 3.14*16*4[/tex]

[tex]V = 3.14*64[/tex]

approximately [tex]V = 201 m^{3}[/tex]

Hope this helps :)

(If this was not the corrrect answer please give me more information)

Answer:

x = 102.5°

Step-by-step explanation:

these two angles are adjacent and supplementary which means their sum must be equal to 180 degrees

create this equation to find 'x':

x + x-25 = 180

combine 'like' terms:

2x - 25 = 180

add 25 to each side:

2x = 205

x = 205/2 or 102.5°

Answer:

there is no picture,you need to add a pic

Answer:

y-intersept is where the line crosses the y axis

on this one it is

(0,-3)

Hope This Helps!!!

Answer:

(0,-3)

Step-by-step explanation:

The y-intercept is where the equation of the line intersects the y-axis. In this case, by looking at the graph, we see that the y-intercept is (0,-3).

Hope this helps!!

Answer:

y = -x + 1

example:

(-2, 3)

y = -(-2) + 1

y = 2 + 1

y = 3

Answer:

y = -x + 1

Step-by-step explanation:

slope = (y2-y1)/(x2-x1) = (-2-3)/(3-(-2)) = -5/5 = -1

y-int: y=mx+b --> plug in a point --> 3 = (-1)(-2)+b --> b=1

y = -x + 1

Answer:

  11.5 m

Step-by-step explanation:

The problem can be solved using a trig relation that relates the side opposite the angle to the side adjacent to the angle. That relation is ...

  Tan = Opposite/Adjacent

The lengths of the adjacent sides of the triangle can be found by rearranging this formula:

  Adjacent = Opposite/Tan

__

The "opposite" side of the triangle is the height of the tree, which we can represent using h. The problem statement tells us of a relation between adjacent side lengths and angles:

  h/tan(25°) -h/tan(50°) = 15 . . . . . moving 15 meters changes the angle

  h(1/tan(25°) -1/tan(50°)) = 15

  h = 15·tan(25°)·tan(50°)/(tan(50°) -tan(25°)) = 15(0.55572/0.72545)

  h ≈ 11.4907 . . . . meters

The height of the tree is about 11.5 meters.

graphed below:

[tex]\sf f(x)=3x^2-6x+5[/tex]

Answer:

Given function:    [tex]f(x)=3x^2-6x+5[/tex]

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  

(where [tex](h, k)[/tex] is the vertex)

Expand vertex form:

[tex]y=ax^2-2ahx+ah^2+k[/tex]

Compare coefficients of given function with expanded vertex form

Comparing coefficient of [tex]x^2[/tex]:

[tex]3=a[/tex]

Comparing coefficient of [tex]x[/tex]:

[tex]\ \ \ \ \ -6=-2ah\\\implies-6=-2 \cdot 3h\\\implies -6=-6h\\\implies h=1[/tex]

Comparing  constant:

[tex]\ \ \ \ \ \ 5=ah^2+k\\\implies5=3(1)^2+k \\\implies 5=3+k\\\implies k=2[/tex]

Therefore, the vertex is (1, 2)

As the leading coefficient is positive, the parabola will open upwards.

Additional plot points:

[tex]f(0)=3(0)^2-6(0)+5=5[/tex]

[tex]f(2)=3(2)^2-6(2)+5=5[/tex]

(0, 5) and (2, 5)