The number of hours of daylight in a city in the northern hemisphere shows periodic behavior over time. - the average number of daylight hours is 12 - the maximum number of daylight hours is 14.4 - the period is 365 days - the day with the least sunlight is december 20 which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year
a) h(t)= -14.4 sin(0.017t)
b) h(t)= 14.4 sin(0.017t)
c) h(t)= -2.4 sin(0.017t) + 12
d) h(t)= 2.4 sin(0.017t) + 12

Option D

Step-by-step explanation:

Given that the number of hours of daylight in a city in the  northern hemisphere shows periodic behavior over time

Let t be the independent variable and no of hours H(t) be the dependent variable on t.

Maximum H(t) = 14.4 and average =12

Period = 365 days

If we fix a sine curve for this since period is 365, we must have coefficient of t as

So the function H(t) will have sine term as sin 0.017t ... i

Since average = 12, we have

H(t) = 12+a sin 0.017t

for some suitable a.

To find a, use maximum

Maximum is when angle is 90 degrees i.e. when sine value =1

max H(5) = 14.4 = 12+a (1)

a =2.4

Hence correct equation would be'H(t) = 2.4sin(0.017t)+12

OPtion D is right answer.

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have