Acertain circle in the xy-plane has its center at the origin. if p is a point on the circle, what is the sum of the squares of the coordinates of p ? (1) the radius of the circle is 4.(2) the sum of the coordinates of p is 0.

Statement (1) is sufficient.

Statement (2) is not sufficient.

Step-by-step explanation:

Consider we need to find check whether the given statements are sufficient or not.

The standard form of a circle is

where, (h,k) is center and r is the radius.

The center of the circle is (0,0). So, the equation of circle is

Statement (1) : The radius of the circle is 4.

The sum of the squares of the coordinates of P is 16. So statement (1) is sufficient.

Statement (2) : The sum of the coordinates of P is 0.

We can not solve these two equation because radius is not given.

Therefore, the statement (2) is not sufficient.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours