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Home Question Bank Math Archive 2025 January 13

Math Questions from Jan 13,2025

Browse the Math Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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ation and Percents ACB radio is rated at 7.5 watts, and actual measurements show that it delivers 6.3 watts to its antenna. What is its efficiency? The efficiency is \( \square \% \) Points: 0 of 1 (Type a whole number or decimal rounded to two decimal places as needed.) Let \( \vec{a}(t)=\langle 4,1,-4\rangle t+\langle-7,2,6\rangle \) and \( \vec{b}(u)=\langle-4,-1,4\rangle u+\langle 8,6,9\rangle \) Find the acute angle (in degrees) between the lines: \( 1 \leftarrow \quad \begin{array}{l}\text { Divide the fractions. } \\ \frac{2}{15} \div \frac{14}{21} \\ \frac{2}{15} \div \frac{14}{21}=\square \text { (Type an integer or a simplified fraction.) }\end{array} \) Determine the function values, if possible. Express all numbers as integers or simplified fractions. Select "Undefined" if applicable. \[ f(x)=\frac{4}{x+2} \] Let \( \vec{a}(t)=-4,4,-3\rangle t+\langle 1,2,-1\rangle \) and \( \vec{b}(u)=\langle 2,-3,-1\rangle u+\langle-3,8,-4\rangle \). Find the acute angle (in degrees) between the lines: Find the point at which the line \( \vec{r}(t)=\langle 1,2,4\rangle+t\langle-3,7,-1\rangle \) intersects the \( x y \) plane. Multiply. \( \frac{7}{20} \cdot \frac{8}{49} \) \( \frac{7}{20} \cdot \frac{8}{49}=\square \) (Type an integer or a simplified fraction.) Convert the line determined by the symmetric equations \( \frac{x-5}{10}=\frac{y}{7}=\frac{z+2}{-3} \) to parametric form. \( x(t)=\square \) \( y(t)=\square \) \( z(t)=\square \) ¿Por qué se puede hacer esto? \[ \)\begin{tabular}{l|}\( \mathcal{L}^{-1}\left\{\frac{4}{s^{2}+s}\right\}=4-4 e^{-t}=4\left(1-e^{-t}\right) \) \\ \( \mathcal{L}^{-1}\left\{\frac{4}{s^{2}+s}\right\}=4\left(1-e^{-t}\right) \)\end{tabular}\( | \text { Resultado final } \] Rounding to the Nearest Ten, Hundred \& Thousand When you are rounding, look at the digit one place to the right of where you want to round. If youround to the nearest ten, look at the digit in the ones place. If you round to the nearest hundred, look at the digit in the tens place. If you round to the nearest thousand, look at the digit in the hundreds place. If the digit is 5 or higher, round up. If it is less than 5 , round down. 1 Underline the number in the ones place. Then circle \( u p \) or down to show whether you are rounding up or down. Then round the number to the nearest ten. example 64 rounds up down to 60 \( \begin{array}{ll}\text { b } 182 \text { rounds up/down to } 26 \text { rounds up/down to }\end{array} \) C C 1,208 rounds up/down to
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