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kondor19780726 [428]
3 years ago
12

Find the equation of the circle in standard form given the center, point or radius. Show your solution.

Mathematics
1 answer:
djyliett [7]3 years ago
7 0

Answer:

(x + 3)^2 + (y - 5)^2 = 17

Step-by-step explanation:

To find the radius: distance from point (-2,1) to the center from point (-3,5).

d = sqrt [(-2 - -3)^2 + (1 -5)^2]

d = sqrt [(-2 + 3)^2 + (1 -5)^2]

d = sqrt (1)^2 + (-4)^2 = sqrt 17

Radius = sqrt 17

Equation of the circle:

(x - h)^2 + (y - k)^2 = r^2

h = 3, k = 5, r = sqrt 17

(x - -3)^2 + (y - 5)^2 = (sqrt 17)^2

(x + 3)^2 + (y - 5)^2 = 17

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A pencil consists of a cone stacked on top of a cylinder. The diameter of the cylindrical base of the pencil is 10 mm and the he
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Answer:

790π

Step-by-step explanation:

We are given;

Diameter of cylinder;d = 10 mm

So, radius;r = 10/2 = 5 mm

Height of cylinder;h = 70mm

Surface area of cylinder is given by the formula; S.A = 2πr² + 2πrh

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S.A = 50π + 700π

S.A = 750π

Now, because one base of the cylinder is hidden as the cone is stacked on that face, we will deduct the area of that base face;

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For the cone,

Height;h = 12mm

Since this is stacked directly on the cylinder, it will have the same radius. Thus; radius;r = 5mm

Now,formula for surface area of cone is;

S.A = πr² + πrL

Where L is slant height.

We can use pythagoras theorem to get L.

So, L² = r² + h²

L = √r² + h²

L = √(5² + 12²)

L = √(25 + 144)

L = √169

L = 13

So, S.A of cone = π(5)² + (π×5×13)

S.A = 25π + 65π = 90π

Similar to what was done to the Cylinder, since the circular base of the cone is stacked on the cylinder, we will deduct the surface area of that base as it is hidden.

So, S.A is now = 90π - π(5)²

= 90π - 25π = 65π

Thus,total surface area of the pencil = 725π + 65π = 790π

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