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Home Question Bank Math Pre Calculus Archive 2025 January 13

Pre-calculus Questions from Jan 13,2025

Browse the Pre-calculus 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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For \( h(t)=\frac{t+1}{t-5} \) (a) Write the domain in set-builder notation. (b) Write the domain in interval notation. Express numbers as integers or simplified fractions. Part: \( \mathbf{0} / \mathbf{2} \) Part 1 of 2 (a) Write the domain in set-builder notation. The domain is the empty set. The domain in set-builder notation is \( \{t \mid t \) is a real number \( \} \) \( \{t \mid t \) is a real number and 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: Convert the line given by the parametric equations \( \left\{\begin{array}{l}x(t)=-2-2 t \\ y(t)=1-10 t \\ z(t)=5-3 t\end{array}\right. \) to symmetric equations. Enter the symmetric equations in alphabetic order. Now that you have the equation for your projectile, use it to calculate how far from the launcher the projectile landed. \( y=-4,13(x-1,5)^{2}+16.97 \) Sketch on the same set of axes the graphs of \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). \begin{tabular}{l} Pre-Cal 12 - Chapter 11 Assignment \\ \hline Name: \\ \( \begin{array}{ll}\text { 1. The number of different ways that } 9 \text { bikes can be locked in a bike rack is } \\ \text { B. } 2628800 & \text { C. } 40320 \\ \text { B. } 20160 & \text { D. } 362880\end{array} \) \\ \( \begin{array}{ll}\text { 3. After the tryouts for the volleyball team, the coach selects } 14 \text { people to join the team. Due to a problem with } \\ \text { transportation, only } 9 \text { people can travel. In how many ways can the coach pick the people to go? } \\ \text { A. } 726485760 & \text { C. } 630 \\ \text { B. } 2002 & \text { D. } 126\end{array} \)\end{tabular} Pre-Cal 12 - Chapter 11 Assignment Name: \( \qquad \) 1. The number of different ways that 9 bikes can be locked in a bike rack is A. 3628800 C. 40320 B. 20160 D. 362880 3. After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a problem with transportation, only 9 people can travel. In how many ways can the coach pick the people to go? A. 726485760 C. 630 B. 2002 D. 126 _ 5. For a mock United Nations, 6 boys and 7 girls are to be chosen. If there are 12 boys and 9 girls to choose from, how many groups are possible? A. 846720 C. 960 B. 33264 D. 120708403200 7. Determine the coefficient of the term containing \( x^{5} y^{7} \) in the binomial expansion of \( (x+y)^{12} \). A. 35 C. 792 B. 60 D. 3991680 9. Determine the 5 th term in the expansion of \( (x-2)^{12} \). A. \( -7920 x^{8} \) C. \( 202752 x^{12} \) B. \( -7920 x^{5} \) D. \( 7920 x^{8} \) 11. How many terms are there in the expansion of \( (2 x-4 y)^{12} \) ? A. 6 C. 12 B. 13 D. 11 13. The leadership committee at a high school has 4 grade 10 students, 2 grade 11 students, and 6 grade 12 students. This year, 12 grade 10,8 grade 11 , and 10 grade 12 students applied for the committee. How many ways are there to select the committee? A. 2910600 C. 733 B. 100590336000 D. 163136 15. While at the dollar store, Peter finds 19 items at \( \$ 1 \) each that he wants, but he only has \( \$ 3 \). The number of ways he could select which items to buy is A. \( { }_{19} C_{0}+{ }_{19} C_{1}+{ }_{19} C_{2}+{ }_{19} C_{3} \) C. \( \left({ }_{19} P_{0}\right)\left({ }_{19} P_{1}\right)\left({ }_{19} P_{2}\right)\left({ }_{19} P_{3}\right) \) B. \( \left({ }_{19} C_{0}\right)\left({ }_{19} C_{1}\right)\left({ }_{19} C_{2}\right)\left({ }_{19} C_{3}\right) \) D. \( { }_{19} P_{0}+{ }_{19} P_{1}+{ }_{19} P_{2}+{ }_{19} P_{3} \) 2. Solve for the variable. Algebraic work must be shown. \[ { }_{5} P_{r}=20 \] 14) Use logarithms to express the following equations in the form \( y=m x+c \) and state the gradients of each line (a) \( P=6 x^{5} \) (b) \( y=5 e^{3 x} \) MATH 1020 functions \& TI-83/84 intro Leaming Activity 1.1 S. (4 pts) Suppose that the valuc of a certain plece of property befween the years 1080 and 3007 is given by the model \( v(t)=2.7(1.083)^{t} \) thousands of dollars where \( t \) is the number of years since the end of 1980 a. In what year was the land worth \( \$ 18.000 \) ? 2004 Present your answer nounded to three decimal places and also present the year \( \qquad \) \( \qquad \) \( \log \left((1083)^{\circ}\right) \) \( \qquad \) \( \log (1083) \) \( 1980+t=1980+23793 \) \( \qquad \) \( t=\log 166667) \) \( \frac{18}{27}=6.6667 \) \[ \approx 23.793 \] \[ =2003+2004 \] b. Find \( v(7.2) \). Write a sentence interpreting the result. \[ v(7.2)=27 \times(1083)^{7.2} \approx 4.764 \] 4.764 After 7.2 years (from 1980-1987) 9. given output, SOLVE for input \[ \text { SOLVER } \begin{array}{ll} Y_{1} & 0=y_{1}-18 \\ & 18 \end{array} \] gritsin73@gmail b. given INPUT, EVALUATE OUTPUT \[ V(7.2) \quad 4 .(7.2) \]
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