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Dominik [7]
3 years ago
8

IN NEED OF A MATH WIZ!!!!!

Mathematics
2 answers:
densk [106]3 years ago
5 0
The unoccupied volume will be the volume of the can minus the volume of the three tennis balls.

V=HπR^2-3(4πr^3)/3

V=HπR^2-4πr^3  where H=height of can, R=radius of can, r=radius of ball

We are told H=7, R=1.5, and r=1.125  (2.25/2=d/2=r) so

V=7π1.5^2-4π1.125^3

V=15.75π-5.6953125π  in^3

V≈31.58 in^3
AnnZ [28]3 years ago
3 0

<u>Answer:</u> 31.58\ inches^3

<u>Step-by-step explanation:</u>

Given: The diameter of tennis ball = 2.25 inches

The radius of ball =\frac{2.25}{2}=1.125\ inches

The volume of ball (sphere) is given by :-

V=\frac{4}{3}\pi r^3\\\\\Rightarrow V=\frac{4}{3}(3.14)(1.125)^3\\\\\Rightarrow\ V=5.96109375\approx5.96\ inch^3

For cylindrical canister, Height = 7 inches

Radius = 1.5 inches

The volume of  cylindrical canister (cylinder) is given by :-

V=\pi r^2h\\\\\Rightarrow V=(3.14)(1.5)^2(7)\\\\\Rightarrow\ V=49.455\approx49.46\ inch^3

Now, the canister’s volume is unoccupied by tennis balls

= Volume of canister - volume of 3 balls

=49.46-3(5.96)=49.46-17.88=31.58\ inches^3

Hence, the canister’s volume is unoccupied by tennis balls=31.58\ inches^3

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40

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Answer:

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A minimum-phase continuous-time system has all its poles and zeros in the left-half s-plane. If a minimum-phase continuous-time
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Answer:

Yes, a minimum phase continuous time system is also minimum phase when converted into discrete time system using bilinear transformation.

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In digital signal processing, the bilinear transform is used to convert continuous time system into discrete time system representation.

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We know that a system is considered to be minimum phase if the zeros are situated in the left half of the s-plane in continuous time system. In the same way, a system is minimum phase when its zeros are inside the unit circle of z-plane in discrete time system.

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Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope
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Expression is

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To prove:

If r is any rational number, then 3r^2-2r+4 is rational.

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Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

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Let r be any rational number.

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3r^2-2r+4

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3r^2\text{ and }-2r are rational by Property 3.

3r^2+(-2r)+4 is rational by property 2.

So, 3r^2-2r+4 is rational.

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