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MAXImum [283]
3 years ago
13

Write one sine and one cosine equation for each graph below.

Mathematics
1 answer:
pychu [463]3 years ago
6 0

Answer:

Q13. y = sin(2x – π/2); y = - 2cos2x  

Q14. y = 2sin2x -1; y = -2cos(2x – π/2) -1

Step-by-step explanation:

Question 13

(A) Sine function

y = a sin[b(x - h)] + k

y = a sin(bx - bh) + k; bh = phase shift

(1) Amp = 1; a = 1

(2) The graph is symmetrical about the x-axis. k = 0.

(3) Per = π. b = 2

(4) Phase shift = π/2.  

2h =π/2

h = π/4

The equation is

y = sin[2(x – π/4)} or

y = sin(2x – π/2)

B. Cosine function

y = a cos[b(x - h)] + k

y = a cos(bx - bh) + k; bh = phase shift

(1) Amp = 1; a = 1

(2) The graph is symmetrical about the x-axis. k = 0.

(3) Per = π. b = 2

(4) Reflected across x-axis, y ⟶ -y

The equation is y = - 2cos2x  

Question 14

(A) Sine function

(1) Amp = 2; a = 2

(2) Shifted down 1; k = -1

(3) Per = π; b = 2

(4) Phase shift = 0; h = 0

The equation is y = 2sin2x -1

(B) Cosine function

a = 2, b = -1; b = 2

Phase shift = π/2; h = π/4

The equation is

y = -2cos[2(x – π/4)] – 1 or

y = -2cos(2x – π/2) - 1

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Step-by-step explanation:

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5 0
3 years ago
What is the solution to the system that is created by the equation y= 2x + 10 and the graph shown below? (–8, –6) (–4, –2) (0, 2
Natasha_Volkova [10]

Answer:

The solution to the system that is created by the equation y = 2x + 10 is

( -8 , -6 )

Step-by-step explanation:

Given:

y = 2x + 10

Justification:

For a Point to be a solution of the system of the equation of a line then it must satisfy the equation by substituting the X coordinate and Y coordinate.

Left hand side  = Right-hand side

For point (–8, –6)

Put x = -8 and y = -6 in the given equation then

Left hand side = y

                        = -6

Right-hand side = 2× -8 + 10

                           = -16 + 10

                           = -4

∴ Left hand side = Right-hand side

∴ Point (–8, –6) is the Solution for y = 2x + 10

For points (–4, –2), (0, 2), and (2, 4)

Left hand side ≠ Right-hand side

∴ Points (–4, –2), (0, 2), and (2, 4) are not a Solution.

3 0
4 years ago
Read 2 more answers
Math Solve the equation:-
Katena32 [7]

Answer:

y = -27

Step-by-step explanation:

  • Multiply the entire equation by 6

         \sf 6*\dfrac{y+1}{3}-6*\dfrac{3y-1}{6}=6*5\\\\\\

             2*(y + 1) - (3y - 1 )    = 30

  •  Multiply (y +1) by 2 and (3y - 1) by (-1)

          2y + 2 - 3y + 1 = 30

  • Isolate y term by taking the constant term to RHS

                  2y - 3y = 30 - 2 - 1

  •  Combine like terms

                        -y      = 27

                             y = -27

3 0
2 years ago
Meredith bought 2/5 kg of shrimps.
Ghella [55]

Answer:

Step-by-step explanation:

if Meredith bought 20 kg and Courtney bough 10 kg less you'd do 20-10 to find how much Courtney bought, hopefully that makes sense.  We are going to do the same thing here.

That means 2/5 - 1/10.  To subtract fractions you need common denominators, like 5/6 - 1/6 = 4/6.  The bottom numbers need to be the same.  So how do we do that?  Well, that 4/6 can be rewritten as 2/3, they are the same number.  So we want to do the same with either 2/5 or 1/10... or maybe both.  Well 4/6 becomes 2/3 because 4/2 = 2 and 6/2 = 3, so we need to use that thinking.

in 2/5 - 1/10, do you see something we can multiply by to make the bottom numbers the same?  What if you multiplied 2/5 by 3 on the top and bottom?  that would get us 6/15.  Well that's too high, maybe we try 2 then.  4/10.  And hey, that got us a 10, so we idn't have to change 1/10.  Now we can do the problem.

2/5 - 1/10 = 4/10 - 1/10 = 3/10.

So Courtney bought 3/10 kg

To find the total weight we add.  So now we have a similar problem.

2/5 + 3/10  Well we know what to change 2/5 to to get a 10 at the bottom.  

2/5 + 3/10 = 4/10 + 3/10 = 7/10.

So in total they bought 7/10 (seven tenths) of a kilogram.  

Let em know if something didn't make sense.

3 0
3 years ago
If there are 2 red marbles , 1 white marble and 1 green marble put in a bag, what are the chances that you will reach in and wit
Misha Larkins [42]

Answer:

50% chance

Step-by-step explanation:

2/4 marbles = 0.50 = 50%

3 0
3 years ago
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