Answer:
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.
hope this helps good luck
Answer:
b. an = 2 • (-3)^(n - 1)
Step-by-step explanation:
Before we test a solution or two, we can easily discard most of them.
We see the values alternate of signs (-5 for the 2nd term and +162 for the 5th term)... so the progression factor has to be negative (in order to alternate sign). <u>That already excludes answers A and C.</u>
Normally, a geometric progression has the (n-1) exponent, not (n+1), so our chances seem to be better with B.
We can test both D and B with n = 2, to obtain -6
Let's test answer D before:
The result is -54, not -6... so it's not the right result.
Let's test answer B then:
Right! Let's verify with n=5 to get 162:
Confirmed, answer is B. an = 2 • (-3)^(n - 1)
Given:
Miguel's height:
Actual = 5 feet 10 inches
Shadow = 4 feet 2 inches
Tower's height
Actual = x
Shadow = 8 feet 9 inches
First, we need to convert the height into inches to avoid confusion.
1 foot = 12 inches.
Miguel:
5 ft x 12in/ft = 60 inches + 10 inches = 70 inches ACTUAL
4 ft x 12in/ft = 48 inches + 2 inches = 50 inches SHADOW
Tower:
8 ft x 12in/ft = 96 inches + 9 inches = 105 inches SHADOW
Ratio of Actual to shadow:
Miguel: 70 : 50
Tower: x : 105
70 : 50 = x : 105
70*105 = 50x
7350 = 50x
7350 / 50 = x
147 = x
Actual height of the tower is 147 inches or 12 feet 3 inches long.
To check:
Miguel : 70 / 50 = 1.40
Tower : 147 / 105 = 1.40
The area of the parallelogram spanned by the given vectors is equal to the magnitude of their cross product.
(i + j + k) × (-2i + 3j + k)
= -2 (i × i) - 2 (j × i) - 2 (k × i)
… + 3 (i × j) + 3 (j × j) + 3 (k × j)
… + (i × k) + (j × k) + (k × k)
= - 2 (j × i) - 2 (k × i) + 3 (i × j) + 3 (k × j) + (i × k) + (j × k)
= 2 (i × j) - 2 (k × i) + 3 (i × j) - 3 (j × k) - (k × i) + (j × k)
= 5 (i × j) - 3 (k × i) - 2 (j × k)
= 5 k - 3 j - 2 i
Then the area of the parallelogram is
||-2 i - 3 j + 5 k|| = √((-2)² + (-3)² + 5²) = √38
Answer: have you found the answer yet????
