Answer:  The magnitude of the vector u is √12 units.
Step-by-step explanation: Â Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
Thus, the magnitude of the vector u is √12 units.
Answer:
The value of i3 is equal to D. -i
Step-by-step explanation:
We can find the answer by taking the definition of i :
i = sqrt(-1) Â Â Â Â (1)
i ^2 = (sqrt(-1)) ^2 = -1 Â Â Â Â Â Â (2) because square root and squaring are inverse operations
so from (2)
i ^3= i ^2* i = -1*i = -i
So -i is the final answer or  – (sqrt(-1))     which is the same
Answer with Step-by-step explanation:
We are given that:
f(x)=ax²+bx+c
also at x=0 f(x)=15
Putting x=0 in f(x)
a×0+b×0+c=15
⇒ c=15
now, f(2)=15.5
⇒ a×2²+b×2+c=15.5
⇒ 4a+2b+15=15.5
⇒ 4a+2b=0.5  -------(1)
f(4)=17
⇒ a×4²+b×4+c=17
⇒ 16a+4b+15=17
⇒ 16a+4b=2   --------(2)
equation (2)- 2×equation(1)
⇒ 16a+4b-8a-4b=2-2×0.5
⇒ 8a=2-1
⇒ 8a=1
⇒ a=1/8
⇒ a=0.125
Putting value of a and c in equation (1)
⇒ 4×0.125+2b=0.5
⇒ 0.5+2b=0.5
⇒ 2b=0
⇒ b=0
Hence
a=0.125
b=0
c=15
and f(x)=0.125x²+15