Answer:
b)0, yes
Step-by-step explanation:
Given:
Vectors (4,8) . (6,-3)
Finding inner product of vectors:
= 4x6 + 8x-3
=24-24
=0
Now to check the angle between them using formula a.b=|a|.|b|cosθ
|a|=
=8.9
|b|=
=6.7
Putting values of a.b=0 and |a|=8.9, |b|=6.7 in a.b=|a|.|b|cosθ we get,
0= 8.9(6.7)cosθ
cosθ =0
θ=90 degrees
Hence the two vectors are perpendicular !
Interest rate of the account is 5.5%, if Nadia deposited $3000 into an account that earns annual simple interest after 6 years, she had earned $990 in interest.
Step-by-step explanation:
The given is,
Nadia deposited $3000
After 6 years, she had earned $990 in interest
Simple interest
Step:1
Formula to calculate the future amount with simple interest is,
...........................(1)
Where, F - Future amount
P - Initial investment
r - Rate of interest ( simple interest )
t - No. of years
Step:2
From the given,
I = $990
P = $3000
F = Initial investment + Interest amount
F = P + I = 3000 + 990 = $3990
t = 6 years
Equation (1) becomes,
3990 = 3000 ( 1 + (r)(6) )
1.33 = 1 + (r)(6)
1.33 - 1 = (r)(6)
0.33 = (r)(6)
r = 0.055 × 100
r = 5.5%
Result:
Interest rate of the account is 5.5%, if Nadia deposited $3000 into an account that earns annual simple interest after 6 years, she had earned $990 in interest.