Eva is making a pattern using these shapes can you arrange Evas shapes to make a symmetrical pattern

Mathematics

1 answer:

ratelena [41]4 years ago

6 0

Answer:

pyramid, cone, sphere, cube

Step-by-step explanation:

A symmetrical pattern is one that is arranged in such a way that there is a progressive repetition of a pattern. Each pattern formed is the same with respect to each other.

Eva could form series symmetrical patterns with the shapes he has, which depends on the arrangement of the shapes to form desired pattern.

One simple pattern to be formed is;

pyramid, cone, sphere, cube

pyramid, cone, sphere, cube.

Thus, this would generate four symmetrical continuous patterns.

pyramid, cone, sphere, cube : pyramid, cone, sphere, cube : pyramid, cone, sphere, cube : pyramid, cone, sphere, cube.

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What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"

salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is $27 + 64x^{3}$

Now, the equation is $27 + 64x^{3} = 0$

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be $- \frac{3}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.

Again, we have to solve the difference of two cubes which is $64m^{3} - 1$

Now, the equation is $64m^{3} - 1 = 0$

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be $\frac{1}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation. (Answer)