Topic
Q:
11. Evaluate \( \ln e^{-5} \)
Q:
1) En utilisant le raisonnement par contraposée montrer que :
\[ \forall(x, y) \in \mathbb{R}^{*} ;\left(x \neq y \text { et } x y \neq 1 \Rightarrow \frac{x}{x^{2}+1} \neq \frac{y}{y^{2}+1}\right) \]
Q:
Starting with the graph of \( f(x)=2^{x} \), write the equattion of the graph that results when:
(a) \( f(x) \) is shifted 3 units upward. \( y=\square \)
(b) \( f(x) \) is shifted 8 units to the right. \( y=\square \)
(c) \( f(x) \) is reflected about the \( x \)-axis and the \( y \)-axis. \( y=\square \)
Q:
Find a formula for the exponential function passing through the points \( \left(-2, \frac{3}{16}\right) \) and \( (2,48) \).
\( y= \)
Q:
22. On considère la suite \( \left(u_{n}\right) \) définie pour tout
\( n \in \mathbb{N} \) par \( u_{0}=10 \) et \( u_{n+1}=\frac{1}{4} u_{n}+6 \).
1. Conjecturer à la calculatrice le sens de variation de
la suite \( \left(u_{n}\right) \).
2. Prouver par récurrence que \( u_{n} \geqslant 8 \) pour tout \( n \in \mathbb{N} \).
3. En déduire sur le sens de variation de la suite \( \left(u_{n}\right) \).
4. La suite \( \left(u_{n}\right) \) est-elle convergente?
Q:
Determine the vertical asymptote(s) of the function. If none exists, state that fact.
\( f(x)=\frac{8 x-3}{x-7} \)
Q:
Pregunta:
Si \( x=\pi-\sqrt{2} \) y \( y=\pi+\sqrt{2} \), ¿Qué tipo de número se obtendría al resolver \( x-y \) ?
Opciones de respuesta:
A) Es un número entero.
B) Es un número racional.
C) Es un número irracional.
Q:
Finding a final amount in a word problem on exponentinl growth or decay
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 135 grams of a
radioactive isotope, how much will be left after 3 half-lives?
Use the calculator provided and round your answer to the nearest gram.
Q:
The radioactive substance uranium- 240 has a half-life of 14 hours. The amount \( A(t) \) of a sample of uranium- 240 remaining (in grams) after \( t \) hours is given by
the following exponential function.
\[ A(t)=5600\left(\frac{1}{2}\right)^{\frac{t}{14}} \]
Find the amount of the sample remaining after 11 hours and after 40 hours.
Round your answers to the nearest gram as necessary.
Q:
Question 14 (1 point)
Given the function \( f(x)=\sqrt{x-h}+k \) with a domain of \( \{x \mid x \geq-5, x \in R\} \) and a range of \( \{y \mid y \geq 8, y \in R\} \),
which of the following best describes the vertical and horizontal translations with respect to the graph of
\( f(x)=\sqrt{x} \) ?
5 units to left and 8 units up
8 units to left and 5 units down to left and 5 units up
5 units to left and 8 units down
Question 15 (1 point)
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