| Topic | Problem | Solution |
|---|---|---|
| None | 2 In the figure shown, all small squares are unit… | In the figure shown, all small squares are unit squares. If $B C$ is chosen to be the base of Trian… |
| None | Evaluate the integral \[ \int x^{3}\left(x^{4}-9\… | Let's start by making the substitution $u = x^4 - 9$. This means $du = 4x^3 dx$. However, our integ… |
| None | 4. Which fraction has a square root between 3 and… | Calculate the square roots of the given numbers: \(\sqrt{52}\), \(\sqrt{61}\), \(\sqrt{\frac{37}{4}… |
| None | Simplify and write the trigonometric expression i… | Rewrite the secant function in terms of cosine: \(\frac{1 + \cos y}{1 + \frac{1}{\cos y}}\) |
| None | a. \( \begin{aligned} 3 x-y & =6 \\ 3 x+y & =0\en… | 1. Add the two equations: \( (3x-y) + (3x+y) = 6 + 0 \) to eliminate variable y |
| None | 7. Solve for $x$ in the following equation. \[ 2 … | Simplify the equation by distributing the -4 to the terms inside the parentheses: \(2x = -4(\frac{1… |
| None | Of 10 possible books, you plan to take 7 with you… | This problem is about combinations. We are choosing 7 books out of 10, order does not matter, and w… |
| None | $y=\sqrt{x} e^{x}$, then $y^{(2)}=\frac{e^{x}}{\s… | Given the function \(y = \sqrt{x} e^{x}\), we need to find its second derivative \(y^{(2)}\) and ch… |
| None | The diagram below shows a square-based pyramid. P… | \(s^2 = 4^2 + 4^2 = 16 + 16 = 32\) |
| None | Use implicit differentiation to find $y^{\prime}$… | Given the equation \(x^{2} y-3 x^{2}-4=0\), we can differentiate both sides with respect to \(x\) u… |
| None | Um individuo cuja função de utilidade depende do … | \(U = 200X^{0.8}Y^{0.2}\) |
| None | Calcule a derivada a seguir: \[ \int x^{4} \ln x … | Choose \(u = \ln x\) and \(dv = x^4 dx\) |
| None | Find the inverse of the matrix \[ A=\left(\begin{… | Find the determinant of the matrix \(A\): \[\text{det}(A) = -1\] |
| None | Understanding Q15 Answer the following questions.… | Calculate the mean and median of the current set: \(data = [3, 4, 4, 6]\), \(mean = 4.25\), \(media… |
| None | Divide. \[ \frac{1}{2} \div \frac{3}{7}= \] | Find the reciprocal of the second fraction: \(\frac{3}{7} \rightarrow \frac{7}{3}\) |
| None | Evaluate the integral \[ \int(2 x+4)\left(x^{2}+4… | Let's start by making the substitution $u=x^{2}+4 x+8$. This simplifies the integral to $\int u^{4}… |
| None | Evaluate the expression. \[ \begin{array}{c} v=2 … | Substitute the values of v and w: \(5(6(2) - 10)\) |
| None | Use a change of variables or the table to evaluat… | Identify the integral is in the form of \(\int f'(x) e^{f(x)} dx\), where \(f(x) = x^{14}\) and \(f… |
| None | Solve for $t$ in terms of $q, r$, and $s$. \[ \be… | Divide both sides of the equation by \(sr\): \(t = \frac{q}{sr}\) |
| None | Question 8/9 8 Write the equation of a circle wit… | Plug in the values for h, k, and r into the standard form of a circle's equation: \((x - 6)^2 + (y … |
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