[answered] 1) A Pentagon is 921 feet long on each of the five exterior

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[answered] 1) A Pentagon is 921 feet long on each of the five exterior

I need help with three homework problems. ?Please see attached.

1) A Pentagon is 921 feet long on each of the five exterior sides. C

A 54 54 82

ft. B What is the distance from a vertex to the center of the Pentagon? That is, what is the

distance between A and C? Show work. Round the distance to the nearest foot.

I came up with 698 feet. Just trying to confirm. Show work if able.

2) An airplane proceeds at a bearing of S30E, flying at 540 miles per hour. (no

explanations required)

(a) State the angle in standard position which corresponds to the bearing S30E.

(b) Find the easterly and southerly components of the airplane's velocity. That is, find the

component form of the vector which has a magnitude of 540 and makes the angle with

the positive x-axis. (Use the value of you stated in part (a).) State the exact values and

also give approximations to the nearest mile per hour.

3) Let v (a) Find and

4,2 w . 1,3 and state the result in component form.

7v 3w (b) State the exact magnitude (length) of and the exact magnitude of v .

w (c) State the dot product . v w (d) Find projw ( v ) projw ( v ) in component form. Give exact values. Show work. (e) Determine the angle between and . Show work. Write the exact angle as the v w arccosine of an appropriate number. Also, use a calculator to approximate the value of

the angle, rounding the result to the nearest degree.

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