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Answer:
sum = ∑[n=1,5] 4^(n-4)
Step-by-step explanation:
First of all, you need to be able to describe the n-th term.
Here, we have ...
term #: 1, 2, 3, 4, 5
value: 4^-3, 4^-2, 4^-1, 4^0, 4^1
That is, the exponent of 4 is 4 less than the term number. So, the n-th term is 4^(n-4). The sum of the 5 terms shown is then ...
Answer:
The sum of the two vectors is the vector <-0.5 , 4+3.5 >
Step-by-step explanation:
The horizontal component (x) of a vector whose magnitude is b units and its direction is Ф° is b cos Ф
The vertical component (y) of a vector whose magnitude is b and its direction is Ф is b sin Ф
The vector is <b cos Ф , b sin Ф>
∵ The vector goes 7 units at an angle
- That means its magnitude is 7 and its direction is
∴ x = 7 cos( )
∴ y = 7 sin( )
∵ cos( ) =
∵ sin( ) =
- Substitute them in x and y
∴ x = (7)( )
∴ x = -3.5
∴ y = (7)( )
∴ y = 3.5
∴ The vector is <-3.5 , 3.5>
Now lets add the vectors by adding xs and ys components
∵ <3 , 4> + <-3.5 , 3.5 > = <3 + -3.5 , 4 + 3.5
>
∴ <3 , 4> + <-3.5 , 3.5> = <-0.5 , 4+3.5
>
∴ The sum of the two vectors is the vector <-0.5 , 4+3.5 >