(4) Human skin has a thickness of about \( 5 \times 10^{-3} \) meter. A grain of sand has a thickness of about \( 1 \times 10^{-3} \) meter. (4) About how many grains of sand would it take to match the thickness of human skin?

Q 1. Find \( \sin \theta \) and \( \tan \theta \), if \( \cos \theta=-\frac{12}{13} \) and \( \theta \) lies in the third quadrant.

Q 2. Find the values of \( \cos \theta \) and \( \tan \theta \), if \( \sin \theta=-\frac{3}{5} \) and \( \pi<\theta<\frac{3 \pi}{2} \)

evidencia. \( \frac{\frac{3}{4}+\frac{y}{2}}{\frac{5}{4}}=\frac{3}{7} \)

In 2018 , the citizens of a country spent a total of \( \$ 73.6 \) billion on their pets. In 2015 , the citizens of the same country spent \( \$ 66.79 \) billion on their pets. Let \( y \) be the amount spent by those citizens on their pets in year \( x \), where \( x=0 \) represents the year 2015 . a. Write a linear equation that models the amount the citizens of the country spent on their pets in the year \( x \). [Hint: The line must pass through the points \( (0,66.79) \) and \( (3,73.6) \).] b. Use this equation to predict the amount citizens spend on their pets in 2027 .

19. \( 1+2+3+4+5+\ldots+n=\frac{n(n+1)}{2} \) (a) i) Show that this formula is true for the sum of the first 8 natural numbers. ii) Find the sum of the first 400 natural numbers. (b) i) Show that \( 2+4+6+8+\cdots+2 n=n(n+1) \). ii) Find the sum of the first 200 even numbers. iii) Find the sum of the first 200 odd numbers. (c) i) Use the formula at the beginning of the question to find the sum of the first \( 2 n \) natural numbers. ii) Find a formula, in its simplest form, for \( 1+3+5+7+9+\cdots+(2 n-1) \).