In the xy-plane, c and d are circles centered at the origin with radii p 17 and p 5, respectively. quantity a: the number of points (a; b) on circle c where both a and b are integers quantity b: the number of points (a; b) on circle d where both a and b are integers a. quantity a is greater. b. quantity b is greater. c. the two quantities are equal. d. the relationship cannot be determined from the information given.

Quantity A is greater

Step-by-step explanation:

Well, to solve this we'll do it by parts.

Quantity A) 809 coordinate points

Since it's centered at the origin we can write the circle equation as

For now, we set apart the following points (0,17) (0,-17), (17,0) and (-17,0) because those points already belong to the circumference and circle.

Now we're going to enlist the cartesian points. The parameter is the Radius. No point can be outside the circle, i.e. with a distance longer than 289 units.

Doing it with the Quadrant I. We'll enlist them. And test by squaring

(x,y) x²+y²≤289

(0,0) Origin

(1,1); ...(1,16) (1,16)∈ for 1²+16² ≤289

(1,1); ...(1,16) = 16 points

(2,1)....(2,16) =16 points (7,1)...(7,15) =15 points (12,1)...(12,12)=12 points

(3,1)....(3,16) =16 points (8,1)....(8,15) =15 points (13,1)...(13,10)= 10 points

(4,1)....(4,16) =16 points (9,1)...(9,14) =14 points (14,1)...(14,9)= 9 points

(5,1)....(5,15) =15 points (10,1)...(10,13) =13 points (15,1)...(15,8) =8 points

(6,1)...(6,15) =15 points (11,1)...(11,12)= 12 points (16,1)...(16,5) =5 points

So

16+16+16+15+15+15+15+14+13+12+12+10+9+8+5=

48+60+27+24+27= 186 coordinate points for the Quadrant I

186*4=744 coordinate points for all four Quadrants

y axis points: (0,1)..(0,16) =16 points (0,-1)...(0,-16)=16 points

x-axis points (1,0)...(16,0)=16 points (-1,0)...(-16,0)=16 points

Origin (0,0)= 1 coordinate point

Notice that I'm only counting the points on the circle not on the circumference, as the question asks.

Adding it all up:

744 +16+16+16+16+1=809 coordinate points

2) Quantity B: 77 coordinate points

Similarly:

x²+y²=5²

x²+y²=25

Points on the y-axis: 8 coordinate points. Points on x-axis: 8 coordinate points

(1,1)...(1,4) =4 points (2,1)...(2,4) =4 points (3,1)..(3,4)=4 points (4,1)...(4,3) =3 points

In Quadrant I = 15

In 4 quadrants = 60 coordinates points

60 coordinates points +4+4+4+4+1=77 coordinate points

Final comments:

We could solve it this only estimating. Just based on the radii of those circles. Since the question does not ask any quantity, but just the relationship. This could be a time saver way.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

the forst and 3rd

step-by-step explanation: