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QUESTION 7 (Start on a new page.) 7.1 Reflection of light (and other forms of electromagnetic radiation) occurs when the waves meet a surface or other boundary that does not absorb the energy of the radiation and reflects the waves off the surface. Draw a fully labelled ray diagram to illustrate reflection.

if \( f\left(x+\frac{1}{x}\right)=x^{3}+\frac{1}{x^{3}} \), what is the \( f(3)= \)

Determine whether the following statment is true or false. The graph of \( y=\frac{1}{7} g(x) \) is the graph of \( y=g(x) \) stretched by a factor of 7 . Choose the correct answer below. A. True, because the graph of the new function is obtained by adding 7 to each \( x \)-coordinate. Balse, because the graph of the new function is obtained by multiplying each \( y \)-coordinate of \( y=g(x) \) by \( \frac{1}{7}<1 \). C. True, because the graph of the new function is obtained by multiplying each \( y \)-coordinate of \( y=g(x) \) by 7 and \( 7>1 \). D. False, because the graph of the new function is obtained by adding 7 to each \( x \)-coordinate.

Complete the sentence below. Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \). Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \).

Evaluate the integral \( \int \sin(5t) \cos(5t) \, dt \) by making an appropriate substitution.

b. \( \left(-7 p^{3} q^{2}\right)^{2} \times 2 p q^{4} \)

What is \( 8-7 x+2 y-3 x+2 y+3 \) written in simplest form?

\( \int _ { 0 } ^ { \frac { 1 } { 2 } } e ^ { x ^ { 2 } } = \)

What is \( 4 a+7 c-2-5 a+2 c \) written in simplest form?

\( ( 7 \times 5 ) \quad \bmod 6 \)