geometry help 2?

Question

What are the polar coordinates of the point K(-1, -√3)

A.(2,60*)
B.(2,240*)
C.(4, 120*)
D.(4,300*)


2.Find the value of f(0) of the function
f(x)=3x²+2x+5

A.F(0)=0
B. F(0)=5
C. F(0)=10
D. F(0)=36

Answer 1

1) B

Polar Coordinates are in the from (r, theta) where,

r = sqrt(x^2+y^2)
theta = arctan(y/x)

Since x = -1, y = -sqrt(3), plug in these values:

r = sqrt(1 + 3) = 2
theta = arctan(-1/-sqrt(3))

You can deduce the angle by figuring out which quadrant the point is in. Since both x and y are negative, the point lies in the 3rd quadrant. You know that the range of angles in this quadrant are 180->270 degrees. Therefore, out of your choices, only B fits this constraint.

2) B

Plug in x = 0 and solve for f(x):

f(x) = 3(0)^2 + 2(0) + 5 -----------> f(x) = 5

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Hope this helps

Answer 2

2.Find the value of f(0) of the function
f(x)=3x²+2x+5

just substitute the value of x in the function
f(x)=3x²+2x+5
f(0)=3(0)²+2(0)+5
f(0)=0 + 0 + 5
f(0)=5



A.F(0)=0
B. F(0)=5
C. F(0)=10
D. F(0)=36

Answer 3

1.The magnitude of (-1,-sqrt(3)) is 2 and it is obviously in the third quadrant, so the answer is B.

2. When evaluated at 0, the function will always return whatever the constant was: in this case 5--so the answer is B.

Answer 4

not sure what a polar coordinate is.. I never learned that but the answer to number 2 is B the answer is five..

~Rainbo

Answer 5

1) B
2) B