f (n + 1) = f(n) – 5 is the recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1
<h3><u>Solution:</u></h3>
Given that,
f(1) = 6 and n ≥ 1
Given sequence is 6, 1, -4, -9, -14
<em><u>Let us first analyse the logic used in this sequence</u></em>
6 - 5 = 1
1 - 5 = -4
-4 - 5 = -9
-9 - 5 = -14
Thus the next terms in sequence are obtained by subtracting 5 from previous term
Thus a recursive formula can be formed as:
f (n + 1) = f(n) – 5
Where "n" is the nth term
Let us check our recursive formula:
f(1+ 1) = f(1) - 5
f(2) = f(1) - 5
f(2) = 6 - 5 = 1
Thus we have got f(2) = 1 which is correct as per given sequence
Answer:
The longest day of the year is day 172
Step-by-step explanation:
Since the length of day is L(t)=727+22sin[2π(t−80.75)/365], the maximum length of day is obtained when sin[2π(t−80.75)/365] is at its maximum value which is 1. So. sin[2π(t−80.75)/365] = 1
We now solve this to find the day at which this maximum value occurs.
sin[2π(t−80.75)/365] = 1
[2π(t−80.75)/365] = sin⁻¹(1)
[2π(t−80.75)/365] = π/2
dividing both sides by 2π/365, we have
[2π(t−80.75)/365] ÷ 2π/365 = π/2 ÷ 2π/365
t−80.75 = 365/4
t−80.75 = 91.25
t = 91.25 + 80.75
t = 172
The longest day of the year is day 172
Answer:
The Rome data center is best described by the mean. The New York data center is best described by the median
Step-by-step explanation:
Before moving forward, first we should understand that what is mean and median. Mean is the average of all the values in the data set. Median is the middle value of the data set in ascending order. As we noticed that there is an outlier in the data for NEW YORK (An outlier is an extreme value in the data set which is much higher or lower as compared to other numbers. It affects the mean value). Since outlier is found in the data of New York therefore mean is not a good representation on the central tendency of the data and gets distorted by the outlier. Therefore it is better to use median. While Rome does not have any outlier, so we can use mean for this.
Therefore we can say that the Rome data center is best described by the mean. The New York data center is best described by the median.
Thus option C is correct....
Answer:
perimeter = (18 +9π) cm
area = (81 -20.25π) cm^2
Step-by-step explanation:
The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...
p = 2(9 cm) + π(9 cm) = (18 +9π) cm
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The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.
A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2
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Comment on circle area
The formula you often see is ...
A = πr^2 . . . . r is the radius
since r = d/2, where d is the diameter, this can also be written as ...
A = π(d/2)^2 = (π/4)d^2
Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.
