1. The answer is C. cos180=-1, sin180=0. 2*(cos180+i*sin180)=2*(-1+0)=-2. Check every other answer, none of which gets -2.
2. The answer is C. cos270=0, sin270=-1. (You can draw out these angles to see). 2*(cos270+i*sin270)=2*(0-i)=-2i, as desired. Other choices don't work.
3. Answer A. Modulus of z is \sqrt(6^2+(-6)^2)=6*\sqrt(2). <span>The </span>angle<span> of the </span>point<span> on the complex </span>plane<span> is the </span>inverse tangent<span> of the complex portion over the real portion. Theta=arctan(-6/6), and arctan(-1)=-pi/4, so theta=-pi/4=-pi/4+2pi=7pi/4. So A is the correct answer.
4. The answer is A. As above, cos270=0, sin270=-1. 3(cos270+sin270*i)=3*(0-i)=-3i. This problem is similar to question 2.
5. </span>z1 = 7(cos 40° + i sin 40°), and z2 = 6(cos 145° + i sin 145°). z1*z2=7*6*(cos 40° + i sin 40°)*(cos 145° + i sin 145°)=42*(cos40*cos145-sin40*sin145+i*sin40*cos145+i*sin145*cos40). Use formula for sum/difference formula of cosines, cos40*cos145-sin40*sin145=cos(40+145)=cos185. Again, sin40*cos145+sin145*cos40=sin(40+145)=sin185. The answer is <span>42(cos 185° + i sin 185°).</span>
Answer:
B- 3
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The measure of the brick wall in inches is given by 14.5 x 12 by 5.5 x 12 by 0.5 x 12 = 174 by 66 by 6
Total volume of the brick wall is given by 174 x 66 x 6 = 68,904 cubic inches.
Volume of each brick = 6 x 4 x 2 = 48 cubic inches.
Therefore, number of bricks needed is given by 68,904 / 48 = 1,435.5 bricks.
Answer:
0/-2; undefined
Step-by-step explanation:
Answer:
-390 mph
Step-by-step explanation:
Let a and b represent, respectively, the distances of A and B from the airport. The distance d between the planes is then given by the Pythagorean theorem as ...
d² = a² + b²
Differentiating with respect to time, we have ...
2d·d' = 2a·a' +2b·b'
Solving for d', we get ...
d' = (a/d)a' +(b/d)b'
The value of d at the time of interest is ...
d = √(a² +b²) = √(30² +40²) = √2500 = 50
Then the rate of change of separation is ...
d' = (30/50)(-250 mph) +(40/50)(-300 mph) = (-150 -240) mph
d' = -390 mph
The distance between planes is decreasing at 390 miles per hour.
