Answer:
- d, series and sequence diverge
- d, geometric/divergent
- c, e (geometric, |r|<1)
Step-by-step explanation:
<h3>1.</h3>
The sequence terms have a common difference of -5/8. That make it a non-trivial arithmetic sequence, so it diverges.
The series is the sum of terms of the sequence. Any non-trivial arithmetic series diverges.
(A "trivial" arithmetic series has a first term of 0 and a common difference of 0. It is the only kind of <em>arithmetic</em> series that doesn't diverge.)
__
<h3>2.</h3>
The terms of the series have a common ratio of -2. That makes it a geometric series. The ratio magnitude is greater than 1, so the series diverges.
__
<h3>3.</h3>
A sequence will converge only if the terms have a common difference of 0 or a common ratio with a magnitude less than 1. Of the offered choices, only C and E will converge:
c. geometric, r = 3/5
e. geometric, r = -1/6
_____
<em>Additional comment</em>
The convergence criteria stated for problem 3 applies only to arithmetic and geometric sequences. There are many other kinds of sequences that converge, but these are the kinds being considered in this problem set.
<h2>
For a = 1 and b = 10 x+1 and x+2 factors of x³-ax²-bx-8 = 0</h2><h2>
Other factor is (x-4)</h2>
Step-by-step explanation:
We have
x³-ax²-bx-8 = 0
Its factors are x+1 and x+2
That is x = -1 and x = -2 are its roots
Substituting x = -1
(-1)³-a(-1)²-b(-1)-8 = 0
-1 - a + b - 8 = 0
b - a = 9 ---------------------eqn 1
Substituting x = -2
(-2)³-a(-2)²-b(-2)-8 = 0
-8 - 4a + 2b - 8 = 0
2b - 4a = 16 ---------------------eqn 2
eqn 1 x -2
-2b + 2a = -18 ---------------------eqn 3
eqn 2 + eqn 3
-2a = -2
a = 1
Substituting in eqn 1
b - 1 = 9
b = 10
For a = 1 and b = 10, x+1 and x+2 factors of x³-ax²-bx-8 = 0
The equation is x³-x²-10x-8 = 0
Dividing with x + 1 we will get
x³-x²-10x-8 = (x+1)(x²-2x-8)
Dividing (x²-2x-8) with x + 2 we will get
x²-2x-8 = (x+2)(x-4)
So we have
x³-x²-10x-8 = (x+1)(x+2)(x-4)
Other factor is (x-4)
Answer:
#1
<u>Sum of interior angles is 180:</u>
- y = 180 - (42 + 31) = 107
<u>The law of sines:</u>
- x / sin 107 = 11 / sin 42
- x = 11 sin 107deg / sin 42deg
- x = 15.72
#2
<u>The law of cosines:</u>
- cos 76 = (6² + 17² - x² )/2(6)(17)
- 204*0.24 = 325 - x²
- x² = 325 - 48.96
- x² = 276.04
- x = √276.04
- x = 16.61
#3
<u>Same as above:</u>
- 2*9.4*10*cos 20 = (10² + 9.4² - x²)
- 176.66 = 188.36 - x²
- x² = 188.36 - 176.66
- x² = 11.7
- x = √11.7
- x = 3.42
#4
<u>Sum of interior angles is 180:</u>
<u>The law of sines:</u>
- x / sin 34 = 15 / sin 94
- x = 15 sin 34 / sin 94
- x = 8.41
Answer:
5, x = 0, y = -2
6, x = 4, Y = 9
7, X = -2, Y = -2
Step-by-step explanation:
The unit price for best cookies is $0.5
The unit price for Okay cookies is $0.4
Step-by-step explanation:
The unit cost is obtained by dividing the total cost by the quantity
Given
<u>Best Cookies:</u>
Cost = $6.00
Quantity = 12
So the unit price will be:
<u>Okay Cookies:</u>
Cost = $8.00
Quantity = 20
The unit price is:
The unit price for best cookies is $0.5
The unit price for Okay cookies is $0.4
Keywords: Unit price, division
Learn more about unit price at:
#LearnwithBrainly
