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zimovet [89]
3 years ago
6

Compare the functions shown below: g(x) f(x) = −6x − 3 cosine function with y intercept at 0, negative 3 h(x) = 2 cos(x + π) − 1

Using complete sentences, explain which function has the greatest y-intercept.
Mathematics
1 answer:
anastassius [24]3 years ago
8 0

Answer:

because of the product

Step-by-step explanation:

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A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a
mezya [45]

Answer:

  • See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

     y=sin(x)

That function has:

  • Midline, also known as rest or equilibrium position: y = 0
  • Minimum: - 1
  • Maximum: 1
  • Amplitude: the distance between a minimum or a maximum and the midline = 1
  • period: the interval of repetition of the function = 2π

The more general sine function is:

             y=Asin(Bx+C)+D

That function has:

  • Midline: y = D (it is a vertical shift from the parent function)
  • Minimum: - A + D
  • Maximum: A + D
  • Amplitude: A
  • period: 2π/B
  • phase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

  • Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
  • Amplitude, A = 3
  • midline y = - 1 ⇒ D = - 1
  • y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

       

            y=3sin(2x/\pi+C)-1

Substitute (0, -1)

             

              -1=3sin(0+C)-1\\ \\ 3sin(C)=0\\ \\ sin(C)=0\\ \\ C=0

Hence, the function to graph is:

              y=3sin(\pi x/2)-1

To draw that function use this:

  • Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
  • Minima: 3(-1) - 1 = - 3 - 1 = -4
  • y-intercept: (0, - 1)
  • x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
  • first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.

4 0
3 years ago
Use these digits once,1,2,4,and 8 to get an answer of 0
Ilya [14]

Answer:

(8-(4*2)) / 1 =0

Step-by-step explanation:

(8-(4*2)) / 1 =0

6 0
3 years ago
Read 2 more answers
SQUARE ROOT OF 8<br><br>THANKS -,-​
sergey [27]

Answer:

it's 2

Step-by-step explanation:

square root of 8 is 2

5 0
3 years ago
Read 2 more answers
An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles.
Mazyrski [523]

Answer:

(The image is not provided, so i draw an idea of how i supposed that the problem is, the image is at the bottom)

Ok, we have a rectangle of length x by r.

At the extremes of length r, we add two semicircles.

So the perimeter will be equal to:

Two times x, plus the perimeter of the two semicircles (that can be thought as only one circle).

The radius of the semicircles is r, and the perimeter of a circle is:

C = 2*pi*r

where pi = 3.14

Then the perimeter of the track is:

P = 2*x + 2*pi*r.

b) now we want to solve this for x, this means isolating x in one side of the equation.

P - 2*pi*r = 2*x

P/2 - pi*r = x.

c) now we have:

P = 660ft

r = 50ft

then we can replace the values and find x.

x = 660ft/2 - 3.14*50ft = 173ft

5 0
3 years ago
The number of bacteria in a culture doubles every 5 minutes. At first there are 10, after 5 minutes there are 20, after 10 minut
garik1379 [7]
The answer is 160 because as you stated in the question the number of bacteria doubles every five minutes, and after 10 minutes there are 40. Therefore, after 15 minutes there are 80 (40 doubled is 80), and after 20 (another 5 minutes), the number of bacteria is the double of 80, which is 160.
- Hope I helped :)
- PeaceLoveHappiness
6 0
3 years ago
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