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Cerrena [4.2K]
3 years ago
13

The height of the tide over time is shown on the graph. Which of the following equations can be used to reasonably model the dat

a represented in the graph? Select two of the following that apply. There needs to be two selections!

Mathematics
2 answers:
Ne4ueva [31]3 years ago
7 0

Answer:

The correct options are the first and the fourth

f(x) = -3sin(\frac{\pi}{6}x) + 3

and

f(x) = 3cos(\frac{\pi}{6}x+\frac{\pi}{2}) + 3

Step-by-step explanation:

We can observe in the graph that when x = 0 then y = 3. Therefore f(0) must be equal to 3.

We also observe in the graph that f(x) = 0 when x = 3+12k, {3, 15, 27...}

where k is a Whole number k : {0, 1, 3, 4, 5....n}

The function that meets these two conditions is

f(x) = -3sin(\frac{\pi}{6}x) + 3

and

f(x) = 3cos(\frac{\pi}{6}x+\frac{\pi}{2}) + 3

We can check it by substituting x = 3+12k and verifying that f(x) = 0

f(3+12k) = -3sin(\frac{\pi}{6}(3+12k)) + 3

f(3k) = -3sin(\frac{\pi}{2} + 2\pi(k)) + 3

We know that sin(\frac{\pi}{2})) = 1 and sin(2k\pi) = 0

Then

f(3+12k) = -3+ 3 = 0

Also

f(3+12k) = 3cos(\frac{\pi}{6}(3k) + \frac{\pi}{2})+ 3

We know that cos(\frac{\pi}{2}k) = -1  and cos(2k\pi) = 1

f(3+ 12k) = -3 +3 = 0

Therefore The correct options are the first and the fourth

polet [3.4K]3 years ago
7 0

Answer:

Option 1 and 4 are the two functions.

Step-by-step explanation:

The given graph may be of sine function or cosine function.

So we start with sine function first.

f(x) = asin(bx+c) +d

Here the features of given graph are

1). Amplitude a = (6-0)/2 =3

2). Period = 12 therefore b = 2π/period = 2π/12 = π/6

3). Midline is y = 3

4). Horizontal shift c = 0

5). vertical shift d = 3 in upward direction

5). Since graph starts below the midline means the function will start with negative notation

So we design the function as y = -3sin(π/6+0)+3

Now for cosine function f(x) = a cos(bx+c)+d

1). Amplitude a = 3

2). Midline is y = 3

3). period = 2π therefore b = 2π/period = 2π/12 = π/6

4). Horizontal shift which is in right side, c = +(π/2)

5). Vertical shift d = 3

Therefore the cosine function will be f(x) = 3cos(π/6+π/2)+3

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Answer:

135 grams

Step-by-step explanation:

you want to find the mass of only the grapes, not including the bowl. so in this case, you would subtract the mass of the bowl from the total mass. you do this because you dont need the mass of the bowl. 256g - 121g = 135g :)

4 0
3 years ago
How many seconds it takes for the ball to hit the ground
Dovator [93]
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3 0
3 years ago
Please solve this question!!​
GaryK [48]

Answer:  (i) 1/221     (ii) 11/221      (iii) 95/663        (iv) 1/663

<u>Step-by-step explanation:</u>

(i) A deck of cards contains 4 Kings out of 52 total cards

1st draw: 4 Kings out of 52 total cards → 4/52 = 1/13

2nd draw: 3 remaining Kings out of 51 total remaining cards  →  3/51 = 1/17

  <u>1st Draw </u>                   <u>2nd Draw </u>                  <u>Outcome</u>         <u>Probability</u>

 King: P(K) = 1/13        King: P(K₂/K₁) = 1/17     King, King       (1/13) x (1/17) = 1/221

*************************************************************************************************

(ii) A deck of cards contains 4 Jacks, 4 Queens, & 4 Kings out of 52 total cards

1st draw: 12 Face cards out of 52 total cards → 12/52 = 3/13

2nd draw: 11 remaining Face cards out of 51 total remaining cards  →  11/51

<u>1st Draw </u>                 <u>2nd Draw </u>                  <u>Outcome</u>       <u>Probability</u>

 Face: P(F) = 3/13    Face: P(F₂/F₁) = 11/51   Face,Face     (3/13) x (11/51) = 11/221

*************************************************************************************************

(iiI) A deck of cards contains 26 black cards out of 52 total cards but there are 2 black Jacks, 2 black Queens, and 2 black Kings.

1st draw: 20 Black (not Face) cards out of 52 total cards → 20/52 = 5/13

2nd draw: 19 remaining Black (not Face) cards out of 51 total remaining cards  →  19/51

  <u>1st Draw </u>                 <u>2nd Draw </u>                       <u>Outcome</u>   <u>Probability</u>

Black: P(B~) = 5/13   Black: P(B~₂/B~₁) = 19/51    B~,B~    (5/13) x (19/51) = 95/663

*************************************************************************************************

(ii) A deck of cards contains 4 Aces out of 52 total cards

1st draw: 4 Aces out of 52 total cards → 4/52 = 1/13

2nd draw: 1 Queen of Hearts out of 51 total remaining cards  →  1/51

  <u>1st Draw </u>                 <u>2nd Draw </u>                   <u>Outcome</u>         <u>Probability</u>

 Ace: P(A) = 1/13      Qh: P(Qh₂/A₁) = 1/51   Ace,Queen(h)   (1/13) x (1/51) = 1/663

7 0
3 years ago
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mojhsa [17]

Step-by-step explanation:

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8 0
2 years ago
A brand of grape juice that's is 25% grape juice is mixed with another brand that is 75% grape juice. The result is 7 gallons of
garri49 [273]

Answer:

5.6 gallons.

Step-by-step explanation:

If we take x gallons of 25% grape juice then it will contain \frac{x}{4} gallons of pure grape juice.

Again, if we take y gallons of 75% grape juice then it will contain \frac{3y}{4} gallons of pure grape juice.

If we mix them then the total volume will become x + y = 7 gallons  ...... (1)

Again the mixture will become 35% juice.

So, \frac{\frac{x}{4} +\frac{3y}{4} }{x+y} =\frac{35}{100}

⇒ 0.25x + 0.75y = 0.35x + 0.35y

⇒0.1x = 0.4y

⇒x = 4y........ (2)

Now, solving equations (1) and (2) we get, 5y = 7, ⇒ y = 1.4 gallons

Hence, x = 4y = 5.6 gallons

Therefore, the 25% grape juice was mixed by 5.6 gallons. (Answer)

4 0
3 years ago
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