1.
v x w = 8 i - 24 j + 15 k + 10 j - 12 i - 24 k =
= - 4 i - 14 j - 9 k
Answer: D )
2.
v x w = -16 i - 16 j - 18 k + 12 j + 48 i - 8 k =
= 32 i - 4 j - 10 k
Answer: C )
3.
The cross product:
< - 6, 7, 2 > x < 8, 5, -3 > =
= - 21 i + 16 j - 30 k - 18 j - 10 i - 56 k =
= - 31 j - 2 j - 86 k = < - 31, - 2, - 86 >
Vectors are perpendicular if: cos ( u, v ) = 0
< - 6 , 7. 2 > * < -31, - 2, - 86 > = 186 - 14 - 172 = 0
< 8, 5 , - 3 > * < - 31, - 2, - 86 > = -248 - 10 + 258 = 0
Answer: A ) < - 31, - 2 , - 86 >, yes.
To get the mean distance that Jim jogged, you have to solve
for the total miles he was able to jogged divided by the number of days he
jogged.
6.5 miles + 5 miles + 3 miles + 2 miles + 3.5 miles + 4
miles = 24 miles / 6 days = 4
Therefore, the mean distance that Jim jogged is 4 miles.
Answer:
Step-by-step explanation:
The motion of the dolphin is quadratic
i.e y=-16t²+20t
To get the maximum height the dolphin will reach
We need to find the point of inflexion. i.e dy/dt=0
dy/dt=-32t+20
Then set dy/dt=0
0=-32t+20
Then, -32t=-20
t=0.625
Let find d²y/dt²
d²y/dt²=-32. Since this is negative then the point t=0.625 is the maximum point the dolphin can reach
Then substitute t=0.625 into y
y=-16t²+20t
y=-16(0.625)²+20(0.625)
y=6.25ft
Then the maximum height the dolphin can reach is 6.25ft
Using discriminant
Formular method
y=-16t²+20t
So the dog height y<7
y=-16t²+20t <7
-16t²+20t-7<0
a=-16, b= 20. c=-7
t=(-b±√b²-4ac)/2a
Using the a, b and c direct for the discriminant
D=b²-4ac
D=20²-4×-16×-7
D=-48
Which is a complex number
Then the dolphin can reach the height
Then we need to model the D to be greater than 0
Therefore,
D>0
b²-4ac>0
We cannot do anything to a and b it is already given
a=-16, b=20
(20)²-4(-16c)>0
400+64c>0
64c>-400
Then
c>-6.25
Divide both side by - and the inequality sign will change
Therefore -c<6.25
So the dog height y<6.25
y=-16t²+20t <6.25
Therefore the maximum height is 6.25.
If it is greater than that then, we are going to have a complex root movement which is not possible for the dolphin .
It’s graph 2 because it is. There is a pause for the taking the bath and then the emptiest mhm so it can’t be graph 3
Answer:
(-1, 6)
Step-by-step explanation:
A graphing calculator shows the vertex to be (x, y) = (-1, 6).
__
You can also find it by putting the equation into vertex form.
y = -2(x^2 +2x) +4
y = -2(x^2 +2x +1) +4 +2(1) . . . . . add 1 inside parens; the opposite outside
y = -2(x +1)^2 +6
Compare to ...
y = a(x -h)^2 +k
and you see a=-2, h=-1, k=6
The vertex is (h, k) = (-1, 6).
