Compute the coordinates of the point (1, 1) in the basis formed by the columns of AB. Express your computation abstractly in terms of A and B before you use the specific A and B given above.

Use the Cauchy-Schwarz inequality

|v · w| ≤ ||v|| · ||w||

to prove the Triangle Inequality

||v + w|| ≤ ||v|| + ||w||.

(Hint: Begin by computing ||v + w||2 with dot products, and then plug in the

Cauchy-Schwarz inequality when the opportunity arises.)

Solution.

||v + w||2 = (v + w) · (v + w)

= v · v + v · w + w · v + w · w

= ||v||2 + 2(v · w) + ||w||2

≤ ||v||2 + 2||vw|| + ||w||2 by the C.S. Inequality

= (||v|| + ||w||)

2

Taking the square root of both sides, we conclude that

||v + w|| ≤ ||v|| + ||w||Step-by-step explanation:

the answer is 31.27mph

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²