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Questions in mathematics

📝 Answered - Given that the non-exact DE $\left(5 x y^2-2 y\right) d x+\left(3 x^2 y-x\right) d y=0$ has an $I F$ in the form $\mu(x, y)=x^a y^b$ for some positive integers $a$ and $b$, find the general solution of the equation.

📝 Answered - Find the measure of an interior angle of a regular hendecagon (11-sided polygon). [tex]x=[?]^{\circ}[/tex] Hint: Sum [tex]=(n-2) 180[/tex] Round to the nearest tenth.

📝 Answered - Determining If Two Events Are Independent or Dependent. The following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are independent or independent. [tex]P(blue)=\frac{3}{10}, P(green)=\frac{1}{5}, \text{ and } P(blue and green)=\frac{3}{100}[/tex] A. Independent, because the product of [tex]P(blue)[/tex] and [tex]P(green)[/tex] does not equal [tex]P(blue and green)[/tex] B. Independent, because the product of [tex]P(blue)[/tex] and [tex]P(green)[/tex] equals [tex]P(blue and green)[/tex] C. Dependent, because the product of [tex]P(blue)[/tex] and [tex]P(green)[/tex] does not equal [tex]P(blue and green)[/tex] D. Dependent, because the product of [tex]P(blue)[/tex] and [tex]P(green)[/tex] equals [tex]P(blue and green)[/tex]

📝 Answered - Find \(\frac{dy}{dx}\) if \(y=6x^2 \sin x \cos x\)

📝 Answered - Which is equivalent to [tex]$80^{4^x}$[/tex]? A. [tex]$\left(\frac{80}{4}\right)^x$[/tex] B. [tex]$\sqrt[4]{80}^x$[/tex] C. [tex]$\sqrt[x]{80^4}$[/tex] D. [tex]$\left(\frac{80}{x}\right)^4$[/tex]

📝 Answered - Simplify the complex fraction. Use either method. $\frac{\frac{t}{t+4}}{\frac{5}{t^2-16}}$

📝 Answered - For all functions of the form $f(x)=a x^2+b x+c$, which is true when $b=0$? A. The graph will always have zero $x$-intercepts. B. The function will always have a minimum. C. The $y$-intercept will always be the vertex. D. The axis of symmetry will always be positive.

📝 Answered - The vertex of this parabola is at $(-1,-3)$. Which of the following could be the equation?

📝 Answered - It is given that [tex]$\sin 50^{\circ}=0.766$[/tex] and [tex]$\cos 124^{\circ}=-0.559$[/tex] when corrected to three decimal places. Without using a calculator, find the value of [tex]$\sin 130^{\circ}+\cos 56^{\circ}$[/tex].

📝 Answered - Find the partial derivative of $z=3 x^2 y^3$.