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Hassanin R.
Math Tutor for 4 years
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Geometry
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Question:

Question: For positive real numbers x, y, and z, which of the following expressions is equivalent to $$x^{1/2} y^{2/3} z^{5/6}$$ ? a) $$5\sqrt{x^ 2 y^3z^5}$$ b) $$2\sqrt{x^ 5 y^4z^3}$$ c) $$6\sqrt{x^ 3 y^4z^5}$$ d) $$3\sqrt{x^ 4 y^2z^5}$$

Hassanin R.

Answer is C: $$6\sqrt{x^ 3 y^4z^5}$$ If we reformat our function into $$x^{3/6} y^{4/6} z^{5/6}$$ , our function will be equal to $$(x^{3} y^{4} z^{5})^{1/6}$$ which means $$6\sqrt{x^ 3 y^4z^5}$$

Basic Math
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Question:

Solve the following problem: $$2.75 + .003 + .158$$

Hassanin R.

Ans: $$2.911$$ ⇒ First rearrange the format of each number in order to make the addition more easier $$2.750 + 0.003 + 0.158$$ ⇒ Now, lets count the number from right to left. Like $$0.000 + 0.003 + 0.008=0.011$$ ⇒ At the end we get our final answer= $$2.911$$

Calculus
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Question:

Q: A curve is given by the polar equation $$r=1+sin⁡θ$$. Convert this equation into Cartesian coordinates

Hassanin R.

Ans: polar equation has $$(r,⁡θ)$$ and Cartesian coordinates has $$(x,⁡y)$$ Now lets solve the question: $$∵r=1+sin⁡θ$$ $$⇒ r^2=r+r sin⁡θ$$ ⇒ $$y^2 +x^2= \sqrt{y^2 +x^2 }+y$$ where $$r^2=y^2 +x^2$$ and $$y=r sin⁡θ$$

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