Answer:
diameter = 4√17;
radius = 2√17; and
center: (4,6)
Step-by-step explanation:
The end points J (12,4) and K(-4,8) define the diameter of a circle, as well as the radius and center.
Using the distance formula to find the diameter, d, we get:
d = √ ( (12+4)^2 + (4-8)^2 ) = √ ( 256 + 16 ), or √272 = √(8)(34)
= √(17)(2^4)) = 4√17
and the radius is half that, or 2√17. The coordinates of the center can be found using the midpoint rule: ( [12-4]/2, [4+8]/2 ), or (4, 6).
Answer:
173.82cm²
Step-by-step explanation:
A=2(1+2)a2=2·(1+2)·62≈173.82338cm²
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:
77
Step-by-step explanation:
10*2+9+3*4^2
10*2+9+3*16
20+9+48
20+57
77
Answer:
The 1st graph will be perfectly matching the conditions.
Step-by-step explanation:
A wholesaler requires a minimum of 4 items in each order from its retail customers.
The manager of one retail store is considering ordering a certain number of sofas, x and a certain number of pillows that come in pairs, y.
Therefore, for y = 0, x ≥ 4 and for x = 0, y ≥ 2 to make the order of 4 items or more.
Therefore, the equation for the order to be of 4 items will be
x + 2y = 4.
So, the 1st graph will be perfectly matching the conditions. (Answer)