| Topic | Problem | Solution |
|---|---|---|
| None | 1. (a) (10 pts) Find the spherical coordinates of… | Given the Cartesian coordinates $(\sqrt{3},-3,2)$, we need to convert these to spherical coordinate… |
| None | x^{3}-3 x^{2}-4 x+12=0 Use synthetic division to … | Given the equation \(x^{3}-3 x^{2}-4 x+12=0\) |
| None | Solve the equation 45 x^{3}+69 x^{2}-13 x-5=0 giv… | Given that -5/3 is a root of the equation, we can use synthetic division to find the other roots. S… |
| None | For f(x)=x/x+1 and g(x)=11/x, find a. (f of g)(x)… | Given the functions \(f(x) = \frac{x}{x + 1}\) and \(g(x) = \frac{11}{x}\), we are asked to find (f… |
| None | Find the zeros for the polynomial function and gi… | Set the function equal to zero: \(x^{3}+4 x^{2}-9 x-36 = 0\) |
| None | For f(x)=1-x and g(x)=2 x^{2}+x+5, find the follo… | We are given two functions, \(f(x) = 1 - x\) and \(g(x) = 2x^2 + x + 5\). We are asked to find the … |
| None | Find the exact value of $\cos \left(\cos ^{-1}(-2… | The cosine function only takes values between -1 and 1. |
| None | g(x)=x^{4}+3x Determine if function is even, odd,… | We are given the function \(g(x) = x^4 + 3x\). |
| None | Use transformations of the absolute value functio… | The function g(x)=-4|x+6|-5 is a transformation of the absolute value function f(x)=|x|. |
| None | Solve the absolune value equation or indicate tha… | The absolute value equation is \(|6x - 3| + 4 = 4\). |
| None | $7(x-8) ?$ | Distribute the 7 to both terms inside the parentheses: \(7(x-8) = 7x - 7(8)\) |
| None | Find polar coordinates of the point that has rect… | The rectangular coordinates of the point are given as $(-3 \sqrt{3}, 3)$. |
| None | Solve the absolute value equation or indicate tha… | The absolute value equation is \(|6x - 3| + 4 = 4\). |
| None | 14. GIfTS A git box is a rectangular prism 14 inc… | Given a gift box which is a rectangular prism with dimensions 14 inches long, 5 inches wide, and 4 … |
| None | $\lim _{x \rightarrow-1} \frac{x^{4}+2 x^{3}+x^{2… | Factor the numerator: $x^{4}+2x^{3}+x^{2} = x^{2}(x+1)^{2}$ |
| None | olve the following inequality. \[ 2 x^{\frac{2}{3… | The inequality is \(2x^{2/3} \leq -4\). |
| None | $f(x)=\sqrt{10 x+5}$ \[ \begin{array}{l} f(x)=\sq… | Given the function \(f(x)=\sqrt{10 x+5}\), we need to find the value of \(f(3)\). |
| None | Find the volume of each rectangu and height. 1. $… | Given the dimensions of the rectangular prism are: length (l) = 5 cm, width (w) = 3 cm, and height … |
| None | Find the exact value of $\sin ^{-1}\left(\sin \le… | The inverse sine function, or arcsine, is defined as the inverse of the sine function. It returns t… |
| None | Find polar coordinates of the point that has rect… | Given a point with rectangular coordinates (-5,-5), we can find the polar coordinates using the fol… |
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