Solve the problem.The unit vectors u and v are combined to produce two new vectors 
and 
Show that a and b are orthogonal. Assume 
What will be an ideal response?
u = ux i + uyj and v = vx i + vyj , so
a = u + v = (ux + vx) i + (uy + vy)j and b = u - v = (ux - vx) i + (uy - vy)j
Take the dot product a ? b:
a ? b = (u + v) ? (u - v) = (ux + vx)(ux - vx) + (uy + vy)(uy - vy)
= 
- 
+ 
- 
= (
+ 
) - (
+ 
)
= 
- 
= 1 - 1 = 0
Since the dot product of the two non-zero vectors is zero they are orthogonol.
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Solve the equation for x, where x is restricted to the given interval.y = cos (x + 12), for x in [-12, ? - 12]
A. x = arccos y + 12 B. x = arccos (y + 12) C. x = arccos y - 12 D. x = arccos (y - 12)
Indicate whether the statement is true or false.1.15 is an integer.
A. true B. false
Find the expected value.Mr. Cameron is sponsoring an summer concert. He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain. The weather bureau predicts the chance of rain is 0.34 for the day of the concert. What are Mr. Cameron's expected concert earning?
A. $300,000 B. $360,000 C. $60,000 D. $218,400
Write the fraction as a decimal. If necessary, use repeating decimal notation.- 
A. -0.
B. -0.1
C. -0.
D. -0.15