33) through: (2,-2) and (2-1)<br />
Please help

y = 3 4 x − 25 4

Explanation:

We could use calculus but first as with all Mathematical problems one should step back and think about what the question is asking you, and in this case we can easily answer the question using knowledge of the equation, in this case:

x 2 + y 2 = 25

represents a circle of centre ( a , b ) = ( 0 , 0 ) and radius r = 5

First verify that ( 3 , − 4 ) actually lies on the circle;

Subs x = 3 oito the circle equation:

⇒ 3 2 + y 2 = 25 = y 2 = 16 ⇒ y = ± 4 So ( 3 , − 4 )

So does indeed lie on the circle. A straight line passing between that point and the centre of the circle ( 0 , 0 ) will be perpendicular to the tangent. So the gradient of the normal is given by:

m N = Δ y Δ x = − 4 − 0 3 − 0 = − 4 3 Then as the normal is perpendicular to the tangent the product of their gradients is − 1 , so then: m T = 3/4

So using the point/slope form y − y 1 = m ( x − x 1 ) the equation we seek is;

y − ( − 4 ) = 3/4 ( x − 3 )

∴ y + 4 = 3/4 x − 9/4

∴ y = 3/4 x − 25/4

We can confirm this solution is correct graphically:

If x 2 + y 2 = 25 then differentiating wrt x implicitly gives us:

2 x + 2 y d y d x = 0

∴ d y d x = − x/y

When x = 3 and y = − 4 ⇒ d y d x = − 3 − 4 = 3 4 , which is what we obtained.

Hoped I helped

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d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi