<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:
Step-by-step explanation:
At the end of practice, Joseph will need to run another 1.75 miles or 1 3/4 miles.
To determine this we need to subtract the amounts he already has run during practice from the goal of 3 miles.
3 miles - 1/2 miles - 1/4 miles - 1/4 miles - 1/4 miles = 1.75 miles
Answer:
The cost of hardbook is $9 and cost of paperback is $5.
Step-by-step explanation:
Let x be the price for hardback book and y be the price for paperback book.
Mr. Yamamoto purchased 42 new hardcover books and 64 new paperback books, which cost a total of $698.
We can write the equation as:
He also purchased 42 new hardcover books and 58 new paperback books, which cost a total of $668.
We can write the equation as:
We have to use the elimination method to solve the two equations.
We eliminate x by subtracting the two equations.
Thus, the cost of hardbook is $9 and cost of paperback is $5.
Answer:
3:1 in simplest form
Step-by-step explanation:
