$d^3 a^3 + e^3 a^3 + f^3 a^3 + 3 d e^2 a^3 + 3 d f^2 a^3 + 3 e f^2 a^3 + 3 d^2 e a^3 + 3 d^2 f a^3 + 3 e^2 f a^3 + 6 d e f a^3 \\+ 3 b d^3 a^2 + 3 c d^3 a^2 \\+ 3 b e^3 a^2 + 3 c e^3 a^2 + 3 b f^3 a^2 \\+ 3 c f^3 a^2 + 9 b d e^2 a^2 + 9 c d e^2 a^2 + 9 b d f^2 a^2 + 9 c d f^2 a^2\\ + 9 b e f^2 a^2 + 9 c e f^2 a^2 + 9 b d^2 e a^2 + 9 c d^2 e a^2 + 9 b d^2 f a^2 + 9 c d^2 f a^2 \\+ 9 b e^2 f a^2 + 9 c e^2 f a^2 + 18 b d e f a^2$

$+ 18 c d e f a^2 + 3 b^2 d^3 a + 3 c^2 d^3 a \\+ 6 b c d^3 a + 3 b^2 e^3 a + 3 c^2 e^3 a + 6 b c e^3 a + 3 b^2 f^3 a \\+ 3 c^2 f^3 a + 6 b c f^3 a + 9 b^2 d e^2 a \\+ 9 c^2 d e^2 a + 18 b c d e^2 a + 9 b^2 d f^2 a\\ + 9 c^2 d f^2 a + 18 b c d f^2 a + 9 b^2 e f^2 a + 9 c^2 e f^2 a + 18 b c e f^2 a + 9 b^2 d^2 e a \\+ 9 c^2 d^2 e a + 18 b c d^2 e a + 9 b^2 d^2 f a + 9 c^2 d^2 f a + 18 b c d^2 f a \\+ 9 b^2 e^2 f a + 9 c^2 e^2 f a + 18 b c e^2 f a$

$+ 18 b^2 d e f a + 18 c^2 d e f a + 36 b c d e f a \\+ b^3 d^3 + c^3 d^3 + 3 b c^2 d^3 + 3 b^2 c d^3 + b^3 e^3 + c^3 e^3 \\+ 3 b c^2 e^3 + 3 b^2 c e^3 + b^3 f^3 + c^3 f^3 + 3 b c^2 f^3 + 3 b^2 c f^3 + 3 b^3 d e^2 \\+ 3 c^3 d e^2 + 9 b c^2 d e^2 + 9 b^2 c d e^2 + 3 b^3 d f^2 + 3 c^3 d f^2 + 9 b c^2 d f^2 \\+ 9 b^2 c d f^2 + 3 b^3 e f^2 + 3 c^3 e f^2$

$+ 9 b c^2 e f^2 + 9 b^2 c e f^2 + 3 b^3 d^2 e \\+ 3 c^3 d^2 e + 9 b c^2 d^2 e + 9 b^2 c d^2 e + 3 b^3 d^2 f + 3 c^3 d^2 f \\+ 9 b c^2 d^2 f + 9 b^2 c d^2 f + 3 b^3 e^2 f + 3 c^3 e^2 f + 9 b c^2 e^2 f \\+ 9 b^2 c e^2 f + 6 b^3 d e f + 6 c^3 d e f + 18 b c^2 d e f + 18 b^2 c d e f$

8 0

3 years ago

If you were filling the cylinder up with water using a cone that has the same height and diameter, how many cones will it take t

aleksandrvk [35]

Answer:

It required 3 cones to fill up the cylinder with the same height and diameter.

Step-by-step explanation:

Let the radius of the cone and cylinder be r.

Let the height of the cone and cylinder be h.

As we know that $\text{Volume of cylinder}=\pi r^2h$ ....(1)

$\text{Volume of cone}=\frac{1}{3}\pi r^2h$

It can be observed that the volume of a cone is $\frac{1}{3}$ rd the volume of the cylinder. so, multiply the volume of the cone by 3.

$3 \times \text{Volume of cone}=3 \times \frac{1}{3}\pi r^2h$

$3 \times \text{Volume of cone}= \pi r^2h$

$3 \times \text{Volume of cone}= \text{Volume of cylinder}$ (From equation 1 )

Hence, It required 3 cones to fill up the cylinder with the same height and diameter.

3 0

3 years ago

Which number produces a rational number when added by 1/5

Blababa [14]

Answer:

-2/3

Step-by-step explanation:

= 1/5 + (-2/3) = -7/15

(A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Rational number can be both positive and negative.)

7 0

2 years ago