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Answer:

y = 1sin(3x)

Step-by-step explanation:

y = A sin( (2π/ω)x )

A is amplitude = 1

ω is period = 2π/3

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

y = 1sin( 2π / (2π/3) x)

y = 1sin(3x)

The equation for the graph with a sinusoidal wave, given an amplitude of 1, a period of 2π/3, and a phase shift of 0, is y = sin((2π/3)x).

The equation for a sinusoidal wave can be written as:

y = A * sin(ωx + φ)

In this case, we are given the values of amplitude (A = 1), period (ω = 2π/3), and phase shift (φ = 0).

The amplitude (A) represents the maximum displacement or height of the wave from the center line. In this case, it is 1.

The period (ω) represents the length of one complete cycle of the wave. The period is the reciprocal of the frequency, and in this case, it is 2π/3.

The phase shift (φ) represents any horizontal displacement of the wave. In this case, the phase shift is 0, indicating that the wave starts at its equilibrium position.

Using these values, the equation for the given graph would be:

y = 1 * sin((2π/3)x + 0)

Simplifying it further:

y = sin((2π/3)x)

To learn more about equation click on,

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Given the expression below:

[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } }[/tex]

Use the following property:

[tex] \large \boxed{ {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }[/tex]

Therefore:

[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } = \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } } \\ \large{ \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } = \frac{ \sqrt{7 \times 7 \times 7} }{ \sqrt{7} } \longrightarrow \frac{7 \sqrt{7} }{ \sqrt{7} } } \\ \large{ \frac{7 \cancel{ \sqrt{7} }}{ \cancel{ \sqrt{7} }} = 7}[/tex]

Note that a¹ = a. Therefore, 7¹ = 7.

Answer

Answer:H = 3 + 0.5x

Step-by-step explanation:

This would be H = 3 + 0.5x

Answer:

11 unit

Step-by-step explanation:

Applying,

s = √[(y₂-y₁)²+(x₂-x₁)²]...................... Equation 1

Where s = length of the side formed.

From the question,

Given: x₁ = -2, x₂ = 9, y₁ = 5, y₂ = 5

Substitute these values into equation 1

s = √[(9+2)²+(5-5)²]

s = √(11²)

s = 11 unit.

Hence the length of the side formed by the vertices is 11 unit

Answer:

Step-by-step explanation:

Area of rectangle:

Given:

The area is:

A = (2x - 7)(3x² + 4x) =

   2x(3x² + 4x) - 7(3x² + 4x) =

   6x³ + 8x² - 21x² - 28x =

   6x³ - 13x² - 28x

Answer:

Area of rectangle = 6 x ³ - 13 x ² + 28

step by step explanation

Given That :-

To Find :-

Area of rectangle = Length × Width

Using Formula

Area of rectangle = Length × Width

substitute the values.

Area of rectangle = ( 2 x - 7 ) × ( 3 x ² + 4 )

= 2 x ( 3 x ² + 4 ) - 7 ( 3 x ² + 4 )

= 6 x ³ + 8 x - 21 x ² + 28

= 6 x ³ - 13 x ² + 28

Answer:

Sulio needs 28 feet of fencing.

Step-by-step explanation:

P = 2l + 2w

P = 2(8) + 2(6)

P = 16 + 12

P = 28

Answer:

The answer is

First, write the formula for the perimeter of a parallelogram, P = 2l + 2w.

Next, use parentheses when you substitute 8 for l and 6 for w.

After multiplying, add 16 and 12.

Sulio needs 28 feet of fencing.

Step-by-step explanation:

this is your answer

Answer:

116

Step-by-step explanation:

116 is parallel to y so that are the same its called corresponding angles

When a transversal cuts two parallel lines, the corresponding angles are equal.

In the given figure, the corresponding angles are 116° and y

So, they are equal

⇒   y = 116°

Answer:

[tex]\sqrt{x+6}[/tex]

Step-by-step explanation:

So, there are a few things we need to go over to graph a function,

When a number is outside of a root, it changes the y value. For example:

y=[tex]\sqrt{x}+6[/tex]

With the +6, y will always be 6 higher than normal.

If it was -6, then y will always be 6 lower than normal.

What if the number is inside the root? Well, it works a little differently.

Instead of changing the y value, it changes the x value. For example:

y=[tex]\sqrt{x+6}[/tex]

So if you put a number in for x, lets say -6, wht would you get?

You would get -6+6=0

The square root of 0 is 0, so when x=-6, y=0

Normally, x would have to equal 0 for the y value to be 0.

So basically, when we see the number isnide of the root, we can think the our x coordinate being subtracted by that number.

This makes since, because if we subtract the +6 from x:

x-(+6)= x-6, and -6 is our x coordinate.

If it was -6 at the start, this would also work:

x-(-6)= x+6. So our x coordinate would start at 6.

Now, lets look at our graph.

As we can see, the x values start at -6, and the y values starts at 0.

This eliminates A and D, since the +6 would change the y value, not the x.

Remember that x-6 would make x a postive 6.

x+6 however, would make x a negative 6.

So we need x+6 in a square root.

This eliminates B, since it has a x-6, making the x coordinate postive 6, not negative 6.

So c is our answer.

Hope this helps!

Answer:

OA . -6

Step-by-step explanation:

correct me if I'm wrong

Answer:

k = 11

Step-by-step explanation:

Given the points are collinear then the slopes between consecutive points are equal.

Using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)

m = [tex]\frac{-1-1}{1-5}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with another 2 points and equate to [tex]\frac{1}{2}[/tex]

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)

m = [tex]\frac{4+1}{k-1}[/tex] , then

[tex]\frac{5}{k-1}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

k - 1 = 10 ( add 1 to both sides )

k = 11

[tex]R_2[/tex]  is 3 ohms

In a circuit containing two resistors [tex]R_1[/tex] and [tex]R_2[/tex] connected together in parallel, the total resistance [tex]R_T[/tex] is given by;

[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]              ---------(i)

Make [tex]R_2[/tex] subject of the formula;

=> [tex]\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}[/tex]  

=> [tex]\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}[/tex]

=>   [tex]{R_2} = \frac{R_TR_1}{R_1 - R_T}[/tex]       ---------------(ii)

From the question,

[tex]R_1[/tex] = 6Ω

[tex]R_T[/tex] = 2Ω

Substitute these values into equation (ii) as follows;

=> [tex]{R_2} = \frac{2*6}{6 - 2}[/tex]

[tex]{R_2} = \frac{12}{4}[/tex]

[tex]R_2[/tex] = 3Ω

Therefore, the value of [tex]R_2[/tex] = 3 ohms or [tex]R_2[/tex] = 3Ω

Answer: is 3 ohms.

Explanation: edmentum/plato :)

[tex]y = \frac{1}{4} {x}^{4} + \frac{5}{2} {x}^{2} - 18x + k[/tex]

Step-by-step explanation:

[tex]dy = ( {x}^{3} + 5x - 18)dx[/tex]

Integrating the above expression, we get

[tex]y = \int( {x}^{3} + 5x - 18)dx[/tex]

[tex] = \frac{1}{4} {x}^{4} + \frac{5}{2} {x}^{2} - 18x + k[/tex]

where k is the constant of integration

Answer:

8

Step-by-step explanation:

Since AB is tangent to the circle, ABC is a 90 degree angle. Using either knowledge about special triangles (3-4-5) or the Pythagorean theorem, BC will equal 8.

Hope this helped.

Answer:

9

Step-by-step explanation:

Since we want the fewest number of groups possible, we need to maximize the number of people in each group. Since there can be a maximum of four people in each group, we can have a maximum of [tex]\left\lfloor \frac{35}{4}\right \rfloor=8[/tex] groups of four. The final three students can form the last group, hence the smallest number of groups possible is [tex]8+1=\boxed{9}[/tex]

Step-by-step explanation:

the answer is in the above image

Answer:

[tex]-12^{2}[/tex] + 9a - 5

Step-by-step explanation:

combine like terms :

-7[tex]a^{2}[/tex] - 5[tex]a^{2}[/tex] = -12[tex]a^{2}[/tex]  

+3a - (-6a) = 9a    

-9 - (-4) = -5          

Answer:

(0,4)

Step-by-step explanation:

Here, we want to find the y-intercept of the quadratic function

g(x) = 5x^2 + 9x + 4

Mathematically, we know that the y-intercept is the position on the graph where we have x = 0

so, to find the y-intercept value, we have to find g(0)

simply put, we have to substitute the value of 0 for x

Mathematically, we have this as;

g(0) = 5(0)^2 + 9(0) + 4

g(0) = 0 + 0 + 4

g(0) = 4

thus, we have the y-intercept point as (0,4)

Answer:

64

Step-by-step explanation:13+51=64

Answer: go to symbolab i swear it will help if not apologies

Step-by-step explanation:

Answer:

2a³

Step-by-step explanation:

2a³ can divide all these without living a remainder

Answer:

C/3rd one. (y=2x+4)

Step-by-step explanation:

In the equation y=mx+b, m=slope of the line and b=y-intercept. From the graph, we know the y-intercept is 4 so we can write y=mx+4. To find the slope: (0-4)/(-2-0) = (-4)/(-2) = 2. We can replace the m with 2 to get the final equation of y=2x+4 which is also the third answer.

Answer:

CE = 20

Step-by-step explanation:

Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

[tex]\frac{6}{8}[/tex] = [tex]\frac{15}{CE}[/tex] ( cross- multiply )

6 CE = 120 ( divide both sides by 6 )

CE = 20

Answer:

2x²+9x-5

Step-by-step explanation:

Area of a rectangle = Length * Width

If the adjacent sides are 2x – 1) and (x + 5), the area is calculated as;

A = (2x – 1) * (x + 5).

A = 2x²+10x-x-5

A = 2x²+9x-5

Hence the area of the rectangle with the adjacent sides is  2x²+9x-5

Step-by-step explanation:

the value of x is 18 degree and the value of Y is 15 degree

Answer:

31 degrees

Step-by-step explanation:

Subtract 94 from 125 to get the measure of angle DBC.

Answer:

the answer for your question is b

Answer:

64

Step-by-step explanation:

a rectangle with length and width equal is a square.

32/4 sides

equals 8 for each side.

l x w = A

8 x 8 = 64

Answer: 64 m ^2

Step-by-step explanation:

Ok well if it's length is the same as the width then we can divide the perimeter by 4 to see the length of each side

[tex]\frac{32}{4} =8[/tex]

Each side is 8m long so it's an 8x8 rectangle. Now we can find the area.

8x8=64

The area is 64 meters squared

Answer:

11b^3+14b^2+b+9

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

         b2

Step-by-step explanation: