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Norma-Jean [14]
2 years ago
5

Point A is the point of concurrency of the angle bisectors of ΔDEF. Point A is the point of concurrency of triangle D E F. Lines

are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Y, and A Z. The length of F A is 6 centimeters, the length of A D is 5 centimeters, the length of A X is 3 centimeters, and the length of Y D is 4 centimeters. What is the length of ZA?
Mathematics
1 answer:
fiasKO [112]2 years ago
8 0

Answer:

  ZA = 3 cm

Step-by-step explanation:

Point A is the incenter of the triangle, so segments AX, AY, and AZ are radii of the circle. They are all the same length, given as 3 cm and confirmed by 3-4-5 right triangle AYD.

  ZA = 3 cm

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4 0
3 years ago
A gumball has a diameter that is 66 mm. The diameter of the gumball's spherical hollow core is 58 mm. What is the volume of the
grigory [225]

Answer:

Volume of gumball without including its hollow core is 48347.6 cubic mm.

Step-by-step explanation:

Given:

Diameter of Gumball = 66 mm

Since radius is half of diameter.

Radius of gumball = \frac{diameter}{2}=\frac{66}{2} =33 \ mm

Now We will first find the Volume of Gumball.

To find the Volume of Gumball we will use volume of sphere which is given as;

Volume of Sphere = \frac{4}{3}\pi r^3

Now Volume of Gumball = \frac{4}{3}\times3.14 \times (33)^3 = 150456.24 \ mm^3

Also Given

Diameter of gumball's spherical hollow core = 58 mm

Since radius is half of diameter.

Radius of gumball's spherical hollow core = \frac{diameter}{2}=\frac{58}{2} =29 \ mm

Now We will find the Volume of gumball's spherical hollow core.

Volume of Sphere = \frac{4}{3}\pi r^3

So Volume of gumball's spherical hollow core = \frac{4}{3}\times3.14 \times (29)^3 = 102108.61 \ mm^3

Now We need to find volume of the gumball without including its hollow core.

So, To find volume of the gumball without including its hollow core we would Subtract Volume of gumball spherical hollow core from Volume of Gumball.

volume of the gumball without including its hollow core = Volume of Gumball - Volume of gumball's spherical hollow core = 150456.24\ mm^3 - 102108.61\ mm^3 = 48347.63\ mm^3

Rounding to nearest tenth we get;

volume of the gumball without including its hollow core = 48347.6\ mm^3

Hence Volume of gumball without including its hollow core is 48347.6 cubic mm.

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3 years ago
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Answer:

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Step-by-step explanation:

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