After demonstrating the procedure by algebraic means, the expression ![(2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )](https://tex.z-dn.net/?f=%282%5Csqrt%5B3%5D%7B12%7D%20%29%5Ccdot%20%283%5Csqrt%5B3%5D%7B2%7D%20%29)
<em>is equivalent to</em> ![6\cdot \sqrt[3]{24}](https://tex.z-dn.net/?f=6%5Ccdot%20%5Csqrt%5B3%5D%7B24%7D)
.
In this question we proceed to <em>simplify</em> by <em>algebraic</em> means into a <em>single</em> <em>radical</em> expression when possible, whose procedure is shown below and explained by appropriate definitions and theorems:
- Given.
-
![(2\cdot 3) \cdot (\sqrt[3]{12} \cdot \sqrt[3]{2} )](https://tex.z-dn.net/?f=%282%5Ccdot%203%29%20%5Ccdot%20%28%5Csqrt%5B3%5D%7B12%7D%20%5Ccdot%20%5Csqrt%5B3%5D%7B2%7D%20%20%29)
Commutative property/ Associative property. - Definition of cubic root/
![\sqrt[n]{a} = \sqrt[n]{b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20%3D%20%5Csqrt%5Bn%5D%7Bb%7D)
/Result
After demonstrating the procedure by algebraic means, the expression <em>is equivalent to</em> .
To learn more on radical expressions, we kindly invite to check this verified question: brainly.com/question/1810591
You need to be more specific. What did the two teachers receive, and what did Ms. Lopez receive? If you want us to help you, you have to give <em>numbers</em>.
Diagram of two triangles
The two triangles are similar because they are both right triangles, meaning that one angle is 90° and the other two are acute (less than 90°).
The diagram on the left is missing its hypotenuse - the variable <em>c</em><em>.</em><em> </em>The hypotenuse is opposite of the right angle. The diagram on the right side is missing one of its legs.
Note: The hypotenuse is the <em>longest</em><em> </em>side of a right triangle.
Word Problen
The legs are 21 blocks and 20 blocks because they are by the right angle. Use the Pythagorean theorem to find the diagonal path's length, which is the hypotenuse.
Standard form of Pythagorean theorem.
Equation with the legs substituted and the missing hypotenuse value - <em> </em><em>c</em><em>.</em>
Square the legs and add.
Take the square root and simplify. The square root of 841 is 29 and -29, but distance is positive.
Thus the diagonal distance is 29 blocks.
Check by substituting.
Fractal Generating Function, is
f(z)=z²-3+2i
⇒f(0)=0²-3+2i
f(0)= -3+2i
⇒f(-3+2i)
=(-3+2i)²-3+2i
=9-4-12 i-3+2i
=2-10 i
⇒f(2-10i)
=(2-10i)²-3+2i
=4-100-40i-3+2i
= -38 i-99
So, First three output values of the fractal generating function are
1.⇒ -3+2i
2. ⇒ 2-10 i
3.⇒-38 i -99
