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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:

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.

Answer:

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, let`s 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 $$r=1+sinθ$$. Convert this equation into Cartesian coordinates

Hassanin R.

Answer:

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

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