Please help this is due in tomorrow!!

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

iris [78.8K]

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)

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b) L(55) ≈ 705.93 minutes

8 0

3 years ago

Nancy is running on a trail that's 5.3 miles long. After 20 minutes, she has run 1.45 miles. Write an addition to fine how much

mars1129 [50]

Answer:

5.3-1.45=3.85

Step-by-step explanation:

she has 3.85 miles left to go because she already ran 1.45 and if you subtract that from the 5.3 you get 3.85 left to run.

5 0

4 years ago

Suppose y = 48 + 3(2n - 1) is an explicit representation of an arithmetic sequence for integer values n ≥ 1. Find the xth partia

omeli [17]

$a_n=48+3(2n-1)$

The formula of the sum of the arithmetic sequence:
$S_n=\dfrac{a_1+a__n}{2}\cdot n$
calculate:
$a_1=48+3(2\cdot1-1)=48+3=51$
substitute
$S_n=\dfrac{51+48+3(2n-1)}{2}\cdot n=\dfrac{99+6n-3}{2}\cdot n=\dfrac{96+6n}{2}\cdot n=3n^2+48n$
Your answer is:
$\boxed{f(x)=3x^2+48x}$

5 0

3 years ago

Read 2 more answers

Please help ASAP!!<br>What is the sum of the square root of 676 and square of 24

Amiraneli [1.4K]

Step-by-step explanation:

square root of 676 is equal to 26

square of 24 is equal to 576

576+26 = 602

8 0

3 years ago

Read 2 more answers

You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provid

ohaa [14]

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 250, \sigma = 75$