Total number of volunteer students for a committee = 7
Number of committee = 5
Number of ways of selecting the committee from the 7 volunteers = 7C5 = 7!/(5!*2!) = 21 ways.
There are 21 ways in which the 5-committee member can be selected from the 7 volunteers.
Answer:
x = -5/2 + i√19 and x = -5/2 - i√19
Step-by-step explanation:
Next time, please share the possible answer choices.
Here we can actually find the roots, using the quadratic formula or some other approach.
a = 1, b = 5 and c = 11. Then the discriminant is b^2-4ac, or 5^2-4(1)(11). Since the discriminant is negative, the roots are complex. The discriminant value is 25-44, or -19.
Thus, the roots of the given poly are:
-5 plus or minus i√19
x = -----------------------------------
2(1)
or x = -5/2 + i√19 and x = -5/2 - i√19
Using the law os cosines formula b^2 = a^2 + c^2 - 2*a*c*cos(B)
a = 17, b = 8, c = 16
8^2 = 17^2 + 16^2 - 2*17*16* cos(B)
64 = 289 + 256 - 544 * cos(B)
544*cos(B) = 289 + 256 - 64
544 * cos(B) = 481
cos (B) = 481/544
B = arccos(481/544)
B = 27.8 degrees
Take the vector u = <ux, uy> = <4, 3>.
Find the magnitude of u:
||u|| = sqrt[ (ux)^2 + (uy)^2]
||u|| = sqrt[ 4^2 + 3^2 ]
||u|| = sqrt[ 16 + 9 ]
||u|| = sqrt[ 25 ]
||u|| = 5
To find the unit vector in the direction of u, and also with the same sign, just divide each coordinate of u by ||u||. So the vector you are looking for is
u/||u||
u * (1/||u||)
= <4, 3> * (1/5)
= <4/5, 3/5>
and there it is.
Writing it in component form:
= (4/5) * i + (3/5) * j
I hope this helps. =)
