MATH 200 Web Work Assignment 1 PDF

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Chaeyeon Ryu Assignment Assignment1 due 09/13/2019 at 11:59pm PDT

1. (1 point) What is the distance from the point (9, 4, -1) to the xz-plane? Distance =

2019W1 MATH 200 ALL

= 0. Answer(s) submitted: • (x+4)ˆ2+(y-9)ˆ2+(z+8)ˆ2-4 • (x+4)ˆ2+(y-9)ˆ2-3

Answer(s) submitted:

(correct)

• 4

6. (1 point)

(correct) 2. (1 point) Find the center and radius of the sphere x2 − 0x + y 2 − 4y + z2 − 14z = 11 Center: ( , , ) Radius:

Write down an (in)equality which describes the solid ball of radius 8 centered at (4, 6, -8). It should have a form like x2 + y 2 + (z − 2)2 − 4 >= 0, where you use one of the following symbols

Answer(s) submitted:

The first blank is for the algebraic expression; the second for the (in)equality. 0.

• • • •

0 2 7 8

Answer(s) submitted: • (x-4)ˆ2+(y-6)ˆ2+(z+8)ˆ2-64 • 0 or y < 0? The smaller of the two angles formed by ~u and ~v is between 0◦ and 180◦ , and so ~w must make an acute angle with ~u and ~v. This will be the case when ~u · ~w > 0, so we want to pick y so that this is the case. If y > 0 then ~u ·~w = ((12)(−21) + 5)y = −247y < 0. Therefore we want to take y < 0. ~i − ~j. Thus ~w can be any positive multiple of the vector 21

Answer(s) submitted: • • • •

T F T F

(correct) 24. (1 point) Let ~a, ~b, ~c and ~y be the three dimensional vectors ~a = ˜j + 2 ˜k, ~b = − ˜i + ˜j + ˜k, ~c = 5 ˜i + 2 ˜j, ~y = −7 ˜i − 3 ˜j

Answer(s) submitted:

•

Perform the following operations on these vectors: (a) ~c ·~a +~a ·~y =

(correct)

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