A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (6, 5). What is
1 answer:
Answer:
The vector joining the ship to the rock is t= 7 i + 5 j
The direction is 0.9505 radians east of north.
Step-by-step explanation:
The position vector of the ship:
r= 1 i + 0 j
The position vector of the ship:
s= 6 i + 5 j
The vector joining the ship to the rock is:
t = r + s
t = (1 i + 0 j) + (6 i + 5 j)
t = 7 i + 5 j
The bearing of the rock to the ship is:
Θ= = 0.9505 radians
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There are 21 ways Tim choose 2 books from the 7 recommended book
<em><u>Solution:</u></em>
Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program
To find: different ways can Tim choose 2 books from the 7 recommended books
This is a combination problem
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected
<em><u>The formula for combinations is:</u></em>
where n represents the number of items, and r represents the number of items being chosen at a time
Here we have to choose 2 books from 7 books
Therefore, n = 7 and r = 2
<em><u>Substituting values in above formula, we get</u></em>
For a number n, the factorial of n can be written as,
Therefore, we get
Thus there are 21 ways Tim choose 2 books from the 7 recommended book
= 9n + 63
generate the first few terms using the recursive equation
f(1) = 72
f(2) = 72 + 9 = 81
f(3) = 81 + 9 = 90
f(4) = 90 + 9 = 99
the sequence is 72, 81, 90, 99, .....
This is an arithmetic sequence whose n th term formula is
=
+ (n - 1 )d
where is the first term and d the common difference
d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and = 72
= 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula
Total number of possible outcomes of throwing two dice = 6×6 = 36
Number of outcomes of getting 9 i.e, (3+6),(4+5),(5+4),(6+3) = 4
Number of outcomes of getting 9 i.e, (3+6),(4+5),(5+4),(6+3) = 4