5 2/5×5 3/5 plz answer
2 answers:
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Answer:
Part 11) ,
Part 2) 4+3i
Step-by-step explanation:
Part 11) write a recursive rule for the sequence
Let
we know that
---->
---->
---->
This is an arithmetic sequence
In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference (d).
In this problem the common difference is equal to
therefore
A recursive rule for the sequence is
substitute the value of d
where
Part 12) What is the complex conjugate of 4-3i?
we know that
The <u><em>complex conjugate</em></u> of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign
so
we have that
the real part of the given number is 4 and the the imaginary part is -3i
so
the imaginary part equal in magnitude but opposite in sign is +3i
therefore
the complex conjugate of the given number is equal to
Answer:
- restaurant: 89
- car: 43
- home: 59
Step-by-step explanation:
Let r, c, h represent the numbers of purchased meals eaten in a restaurant, car, or home, respectively. The given data tells us ...
r + c + h = 191
-r + c + h = 13
r + 0c - h = 30
___
Subtracting the second equation from the first, we have ...
2r = 178
r = 89
Substituting into the third equation gives ...
89 -h = 30
h = 59
Then substituting into the second equation, we have ...
-89 +c +59 = 13
c = 43
The number of purchased meals eaten in a restaurant is 89; in a car, 43; and at home, 59.
_____
<em>Comment on the solution</em>
We have used an <em>ad hoc</em> method of solution of these equations. This is a result of the observation that the only difference in the first two equations is the sign of "r". Knowing r, the last equation lets us find h. Then we can use either of the first two equations to find c.
There are algorithmic methods of solving a system of 3 equations in 3 unknowns. One of these is Cramer's Rule. Row reduction or elimination techniques are not so different from what we have done. The difference is in the presentation. For some of the elimination techniques, a matrix form, or augmented matrix form, of the equations is used.
a^2 + b^2 = c^2
a = sqrt(c^2 - b^2) = sqrt (20^2 - 16^2)
= 12
sin = a/c = 12/20
= 3/5
cos = b/c = 16/20
= 4/5
tan = a/b = 12/16
= 3/4
csc = c/a = 20/12
= 5/3
= 1 2/3
sec = c/b = 20/16
= 5/4
= 1 1/4