The day length in Manila, Philippines, varies over time in a periodic way that can be modeled by a trigonometric function.

Mathematics

1 answer:

iris [78.8K]3 years ago

8 0

Answer:

L(t) = 727.775 -51.875cos(2π(t +11)/365)
705.93 minutes

Step-by-step explanation:

a) The midline of the function is the average of the peak values:

(675.85 +779.60)/2 = 727.725 . . . minutes

The amplitude of the function is half the difference of the peak values:

(779.60 -675.85)/2 = 51.875 . . . minutes

Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.

Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.

Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.

Our formula is ...

L(t) = 727.775 -51.875cos(2π(t +11)/365)

b) L(55) ≈ 705.93 minutes

You might be interested in

My sister needs help !!!!!!!

yuradex [85]

A coin has one of two outcomes: heads or tails.
Each has an equal probability of occurring, meaning that they each have a 50% chance to occur. (They need to add up to 100% because they include all the outcomes, divide that into two equal parts and...)

This is what we call theoretical probability. It's a guess as to how probability should work. Like in the experiment, it's not always going to be 50-50.

What actually happens is called experimental probability. This may vary slightly from theoretical probability because you can't predict probability with complete certainty, you can only say what is most likely to happen.

We want to find the probability of getting heads in our experiment so we can compare it to the theoretical outcome. To do this, we need to compare the number of heads to the total number of outcomes.

We have 63 heads, and a total of 150 coin flips.
That makes the probability of getting a heads 63/150.
The hard part is getting this ratio into a percent.

You can try simply dividing, but you should be able to notice something here.
SInce the top and the bottom of our fraction are both divisible by 3, we can simiplify.
63 ÷ 3 = 21
150 ÷ 3 = 50
So we could say that 63/150 = 21/50.

A percent is basically a fraction out of 100.
Just like you can divide the parts of a ratio by the same number and it will stay the same, you can also multiply. To get the fraction out of 100, let's multiply by 2.
(since 50 × 2 = 100)

21 × 2 = 42
50 × 2 = 100
21/50 = 42/100 = 42%

Comparing our experimental probability to the theoretical one...it is 8% lower.

7 0

3 years ago

Read 2 more answers

Which polynomial functions are written in

PolarNik [594]

Answer:

c and d

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

You scored 31 out of 40 points on a test. What percent did you get?

elena-14-01-66 [18.8K]

Answer:

Step-by-step explanation:

Divide 31 by 40. Since you get .775, you make it a percent and it's 77.5% correct.

5 0

3 years ago

Divide. (3 3/4)÷(−2 1/2) Enter your answer as a mixed number, in simplified form, in the box.

neonofarm [45]

$3 \frac{3}{4} = \frac{15}{4}$

Because (4*3) + 3 = 15. Similary find the improper fraction for -2 1/2.

(15/4) / (-5/2) = -3/2

Convert -3/2 into a mixed fraction.

Therefore, -3/2 = -1 1/2.

6 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!! an onion soup recipe calls for 3 2/3 cups of chopped onions. katrina has already chopped 1 1/3 cups of onions

ivanzaharov [21]

Answer:

$x+1\frac{1}{3}=3\frac{2}{3}$