Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
Answer:
Tn = 2Tn-1 - Tn-2
Step-by-step explanation:
Before we can generate the recursive sequence, we need to find the nth term of the given sequence.
nth term of an AP is given as:
Tn = a+(n-1)d
If a17 = -40
T17 = a+(17-1)d = -40
a+16d = -40 ...(1)
If a28 = -73
T28 = a+(28-1)d = -73
a+27d = -73 ...(2)
Solving both equations simultaneously using elimination method.
Subtracting 1 from 2 we have:
27d - 16d = -73-(-40)
11d = -73+40
11d = -33
d = -3
Substituting d = -3 into 1
a+16(-3) = -40
a - 48 = -40
a = -40+48
a = 8
Given a = 8, d = -3, the nth term of the sequence will be
Tn = 8+(n-1) (-3)
Tn = 8+(-3n+3)
Tn = 8-3n+3
Tn = 11-3n
Given Tn = 11-3n and d = -3
Tn-1 = Tn - d... (3)
Tn-1 = 11-3n +3
Tn-1 = 14-3n
Tn-2 = Tn-2d...(4)
Tn-2 = 11-3n-2(-3)
Tn-2 = 11-3n+6
Tn-2 = 17-3n
From 3, d = Tn - Tn-1
From 4, d = (Tn - Tn-2)/2
Equating both common difference
(Tn - Tn-2)/2 = Tn - Tn-1
Tn - Tn-2 = 2(Tn - Tn-1)
Tn - Tn-2 = 2Tn-2Tn-1
2Tn-Tn = 2Tn-1 - Tn-2
Tn = 2Tn-1 - Tn-2
The recursive formula will be
Tn = 2Tn-1 - Tn-2
To solve this problem, we need to first find the dimensions of the side of the blue and purple squares.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
[recall
or 20(x+5) if you wish.
Answer:
c. x21 + x22 + x23 less or equal than 2800 y2
Step-by-step explanation:
The plant has a maximum capacity of 2800 then the sum of all these operations must be equal to or less than 2800. The site of the plant has capacity constraint which needs to be determine through equation. The total capacity for the plant 2 is only 2800 the operation has to be distributed with keeping in mind the capacity limit.
The mean of the data is 11
now we find the difference between the mean and each number
1, 2, 3, 0.5, 0.25, 1.25, 1.
now we square the numbers
1, 4, 9, 0.25, 0.0625, 1.
now we find the mean of the new numbers
which is 2.1875
2.1875 is your standard deviation.
