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Kate C.
Tutor for six years
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Calculus
TutorMe
Question:

Solve: $$\frac{\delta}{\delta y}\left(\frac{x+y^{2x}}{x}+\frac{x+y^{2x}}{y}\right)$$

Kate C.
Answer:

$$\frac{\delta\left(\frac{x+y^{2x}}{x}+\frac{x+y^{2x}}{y}\right)}{\delta y}$$ $$=\frac{x+2xy^{2x-1}}{x}+2xy^{2x-2}-\frac{x+y^{2x}}{y^2}$$ $$=2y^{2x-1}+2xy^{2x-2}-\frac{x+y^{2x}}{y^2}$$ $$=\frac{y^{2x}\left(2y-1\right)+x\left({2y}^{2x}-1\right)}{y^2}$$ $$=\frac{y^{2x}\left(2x+2y-1\right)-x}{y^2}$$

Statistics
TutorMe
Question:

What would the two-tailed inverse of the Student’s t-distribution be if the degree of freedom is 31, while there probabilities are: $$\left[\matrix{0.75&0.11&0.9\cr0.2&0.882&0.5\cr0.31&0.812&0.1\cr}\right]$$ The answer is to be rounded to four decimal places.

Kate C.
Answer:

$$\left[\matrix{0.4589&0.9131&0.3751\cr0.8428&0.3846&0.6206\cr0.7586&0.4230&0.9210\cr}\right]$$

Algebra
TutorMe
Question:

You have the following expression $$0=\frac{a+ab}{b}+1$$ Find a.

Kate C.
Answer:

$$0=\frac{a+ab}{b}+1$$ $$\frac{a+ab}{b}=-1$$ $$a+ab=-b$$ $$a\left(1+b\right)=-b$$ $$a=-\frac{b}{1+b}$$

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