| Topic | Problem | Solution |
|---|---|---|
| None | Find the average rate of change of the function $… | We are given the function \(f(x)=x^{2}+4 x\) and we need to find the average rate of change from \(… |
| None | The volume of a cube decreases at a rate of $0.8 … | We are given that the volume of a cube decreases at a rate of \(-0.8 \, \text{ft}^{3} / \text{min}\… |
| None | Use the rational zeros theorem to list all possib… | Given the function \(f(x)=7 x^{3}-3 x^{2}-x+2\). |
| None | Verify that the following equation is an identity… | The problem is asking to verify the given trigonometric identity. To do this, we need to use the tr… |
| None | Given that $\cos 2 \alpha=\frac{4}{5}$ and $\alph… | We are given that \(\cos 2 \alpha=\frac{4}{5}\) and \(\alpha\) is in quadrant I. |
| None | Given that $\cos \alpha=\frac{2}{3}$ and $0<\alph… | We are given that \(\cos \alpha=\frac{2}{3}\) and \(0<\alpha<\frac{\pi}{2}\). We need to find the v… |
| None | Use a double-angle identity to find the exact val… | The given expression is in the form of a double angle identity for cosine. The double angle identit… |
| None | Find the expression that is equivalent to $\frac{… | The given expression is \(\frac{\tan \frac{3 \pi}{4}+\tan \frac{\pi}{6}}{1-\tan \frac{3 \pi}{4} \ta… |
| None | Write the expression as a function of $x$, with n… | Given the expression \(\cos \left(\frac{\pi}{6}+x\right)\) |
| None | Write the expression as a function of $\theta$, w… | We know that \(\cos (a - b) = \cos a \cos b + \sin a \sin b\). |
| None | Find the exact value of the expression by using a… | Let's denote \(a = \sin 72^\circ\) and \(b = \cos 42^\circ\). Then we have \(\sin 72^\circ \cos 42^… |
| None | 24. Name the first five terms of the arithmetic s… | The first term of the arithmetic sequence is given as -16 and the common difference is -6. |
| None | Verify that the equation is an identity. \[ \frac… | Verify that the equation is an identity: \(\frac{1+\cot ^{2} \beta}{\csc \beta}=\csc \beta\) |
| None | The expression below simplifies to a constant, a … | Given the expression \(\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x\) |
| None | Perform the indicated operation and simplify the … | Given the expression is \(\tan x(\csc x-\cot x)\). |
| None | Write each expression in terms of sine and cosine… | Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in… |
| None | Find the remaining five trigonometic functions of… | We know that \(\cot \theta=\frac{4}{3}\), which is the reciprocal of \(\tan \theta\). So, \(\tan \t… |
| None | 5. Solve: 180 is what percent of 125 ? Round to t… | First, we need to set up the equation. Let's denote the unknown percentage as x. So, we have: \(180… |
| None | Find $\sin \theta$. \[ \sec \theta=\frac{13}{6}, … | We know that \(\sec \theta = \frac{1}{\cos \theta}\), so \(\cos \theta = \frac{1}{\sec \theta} = \f… |
| None | $=\frac{(\sqrt{x+1}-h)-\sqrt{x+1}}{h} \times \fra… | The question seems to be asking for the simplification of the given expression. To simplify this ex… |
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