<span>We are given that ||e|| = 1, ||f|| = 1. </span>
<span>Since ||e + f|| = sqrt(3/2), we have </span>
<span>3/2 = (e + f) dot (e + f) </span>
<span>= (e dot e) + 2(e dot f) + (f dot f) </span>
<span>= ||e||^2 + 2(e dot f) + ||f||^2 </span>
<span>= 1^2 + 2(e dot f) + 1^2 </span>
<span>= 2 + 2(e dot f). </span>
<span>So e dot f = -1/4. </span>
<span>Therefore, </span>
<span>||2e - 3f||^2 = (2e - 3f) dot (2e - 3f) </span>
<span>= 4(e dot e) - 12(e dot f) + 9(f dot f) </span>
<span>= 4||e||^2 - 12(e dot f) + 9||f||^2 </span>
<span>= 4(1)^2 - 12(-1/4) + 9(1)^2 </span>
<span>= 4 + 3 + 9 </span>
<span>= 16. </span>
Answer:
8 (8x - 2)
(64) x X - 16
4 (16 x- 4)
Step-by-step explanation:
The answer to this expression is 2
The have been saving for 10 weeks.
Given:
Duane = $5 every other week. meaning every 2 weeks
Mick = $2 every week
Amount Saved = $45
First, divide Duane's $5 by 2 to get his weekly contribution.
$5/2 = $2.50
let x be the number of weeks.
Duane + Mick = $45
2.50x + 2x = 45
4.50x = 45
4.50x/4.50 = 45/4.50
x = 10 weeks
to check:
2.50x + 2x = 45
2.50(10) + 2(10) = 45
25 + 20 = 45
45 = 45
