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aniked [119]
2 years ago
14

Write the equation of the trigonometric graph.

Mathematics
1 answer:
prisoha [69]2 years ago
6 0

Answer:

f(x)= \sin(6x)+3

Step-by-step explanation:

The parent function of this graph is:  y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

f(x) = \sf A \sin (B(x + C)) + D

  • A = amplitude (height from the mid-line to the peak)
  • 2π/B = period (horizontal distance between consecutive peaks)
  • C = phase shift (horizontal shift - positive is to the left)
  • D = vertical shift

The parent function y = sin(x) has the following:

  • Amplitude (A) = 1
  • Period = 2π
  • Phase shift (C) = 0
  • Vertical shift (D) = 0
  • Mid-line:  y = 0

From inspection of the given graph:

  • Amplitude (A) = 1
  • \sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}
  • Phase shift (C) = 0
  • Vertical shift (D) = +3  (as mid-line is y = 3)

\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6

Substituting the values into the standard form:

\implies f(x) =1 \sin (6(x + 0)) + 3

\implies f(x) = \sin (6x) + 3

Therefore, the equation of the given trigonometric graph is:

f(x)= \sin(6x)+3

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Which is answer is correct
horsena [70]

Answer:

i think it is b and c im trying

Step-by-step explanation:


6 0
3 years ago
Among all monthly bills from a certain credit card company, the mean amount billed was $465 and the standard deviation was $300.
Fynjy0 [20]

Answer:

0.02% probability that the average amount billed on the sample bills is greater than $500.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

Normal probability distribution

Problems of normally distributed samples can be 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 = 465, \sigma = 300, n = 900, s = \frac{300}{\sqrt{900}} = 10.

What is the probability that the average amount billed on the sample bills is greater than $500?

This probability is 1 subtracted by the pvalue of Z when X = 500. So

Z = \frac{X - \mu}{s}

Z = \frac{500 - 465}{10}

Z = 3.5

Z = 3.5 has a pvalue of 0.9998.

So there is a 1-0.9998 = 0.0002 = 0.02% probability that the average amount billed on the sample bills is greater than $500.

8 0
3 years ago
Eight two-person teams are participating in a three-legged race. Find the number of orders in which all 8 teams can finish the r
Wewaii [24]
Each team needs two people for a 3-legged race.
Therefore, the number of orders (combinations) of 2 people at a time from 8 is
₈C₂ = 8!/(2!6!)
      = (8*7*6!)/(2*6!)
      = (8*7)/2
      = 56/2
      = 28

Answer: 28
8 0
3 years ago
You have an ant farm with 27 ants. The population of ants in your farm will double every 3 months. The table shows the populatio
disa [49]

Answer:

It represents a linear function and there will be 216 ants after 1 year

8 0
2 years ago
A plane can fly 7 miles per minute. The plane will fly 8 trips, and each trip is 810 miles. How many hours will the plane fly? S
ELEN [110]

7*60 = 420

 810/420 = 1.9285

93- 100 = 53-60

subtract 40 from 93. 

1.53*8 = 12.24

Answer: 12 hours and 24 Minutes

If this helps give a brainliest :)

4 0
3 years ago
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