Write the equation of a circle who's diameter has endpoints (6,-5) and (2,1)

(x+1)

2

+(y−1)

2

=13

Explanation:

The standard form of the equation of a circle is .

(x−a)

2

+(y−b)

2

=r

2

​

where (a,b) are the coordinates of the centre and r, the radius.

To establish the equation, we required to know it's centre and radius.

Since we are given the endpoints of the diameter. Then the centre will be at the midpoint and the radius will be the distance from the centre to either of the 2 endpoints.

The midpoint can be calculated using the midpoint formula.

2

1

​

(x

1

​

+x

2

​

),

2

1

​

(y

1

​

+y

2

​

)

​

where (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) are points

The 2 points here are (−2,3) and (4,−1)

⇒ centre =(

2

1

​

(−2+4),

2

1

​

(3−1))=(1,1)

To calculate the radius use the distance formula

r=

(x

2

​

−x

1

​

)

2

+(y

2

​

−y

1

​

)

2

​

​

where (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) are 2 points

The 2 points here are the centre (1,1) and the endpoint (−2,3)

r=

(−2−1)

2

+(3−1)

2

​

=

9+4

​

=

13

​

The equation of the circle can now be written.

(x−1)

2

+(y−1)

2

=(

13

​

)

2

⇒(x−1)

2

+(y−1)

2

=13 is the equation of the circle

Step-by-step explanation:

answer: the answer is c.

step-by-step explanation:

she’s dividing 1/3 of the flour into 2 jars.

hope this : )

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.