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$\frac{20b}{{\left(4b^3\right)}^3}$

Solving a differential equation with trigonometric functions
How could I approach
${\displaystyle y-A\cdot \sin \left(\frac{d^{2}y}{{dx}^2}\right)=0}$

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What is the volume of this cone?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

 

 cubic centimeters

A function f is define f(x)=-x^2+x+2

(a) express f in standard form

(b) sketch the graph of f

(c) find the maximum value of f

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Let A and B represent two linear inequalities:
$A:a_1{x}_1+...+a_n{x}_n\ge <!--\; \ge \; -->k_1$
$B:b_1{x}_1+...+b_n{x}_n\ge <!--\; \ge \; -->k_2$
If A and B is unsatisfiable (does not have solution), does the following hold in general (the conjunction of two inequalities implies the summation of them )? If so, I am looking for a formal proof?
$A\wedge <!--\; \wedge \; -->B⟹<!--\; ⟹\; -->A+B$
${𝑎}_1{𝑥}_1+...+{𝑎}_n{𝑥}_n\ge <!--\; \ge \; -->𝑘1\wedge <!--\; \wedge \; -->{𝑏}_1{𝑥}_1+...{𝑏}_n{𝑥}_n\ge <!--\; \ge \; -->{𝑘}_2⟹<!--\; ⟹\; -->{𝑎}_1{𝑥}_1+...+{𝑎}_n{𝑥}_n+{𝑏}_1{𝑥}_1+...{𝑏}_n{𝑥}_n\ge <!--\; \ge \; -->{𝑘}_1+{𝑘}_2$
and then I would like to generalize the above theorem to summation of several inequalities.

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Determine which of the following must change when a sound gets louder. a. amplitude b. frequency c. wavelength d. intensity e. speed of the sound waves

Discrete Math: Induction and Recurrence
Show that the terms of the sequence that satisfy $a_n=3a_{n-<!--\; -\; -->1}-<!--\; -\; -->2$ and $a_1=4$ are given by the formula $a_n=3^n+1$ for all $n\ge <!--\; \ge \; -->1$.
I know this problem has to do with induction. In this case I think $n=n+1$ so I would have $3^n+1$ but i'm not sure what to do with the rest of the problem. Can someone help please?

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The first term in a certain geometric sequence is x and the fourth term in the sequence is 27x, where x is a nonzero number. Which of the following represents the tenth term?

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