$\tan \theta = \frac{3}{4} \\ \\ \sec \theta = \sqrt{1 + { \tan }^{2} \theta} \\ \hspace{22 pt} = \sqrt{1 + {( \frac{3}{4} )}^{2} } \\ \hspace{22 pt} = \sqrt{1 + {\frac{9}{16} }} \\ \hspace{22 pt} = \sqrt{ {\frac{16 + 9}{16} }} \\ \hspace{22 pt} = \sqrt{ {\frac{25}{16} }} \\ \red{ \boxed{\bold{ \therefore \sec \theta = { {\frac{5}{4} }} }}} \\ \\ \cos \theta = \frac{1}{\sec \theta } = \frac{4}{5} = \frac{a}{b} \\ \\ \implies \: a = 4 \: and \: b = 5$

6 0

4 years ago

Justin recently drove to visit his parents who live 96 miles away. On his way there his average speed was 20 miles per hour fast

never [62]

Answer:

Justin's average speed to his parents' house: x= 40mph

Justin's average speed from his parents' house: x+20=60 mph

Step-by-step explanation:

Let the average speed be x +20

Then average speed from his parents' x

And the distance is S=96

Then we know :

$\displaystyle \frac{S}{x+20} +\frac{S}{x} =4 \\\\\\ \frac{96}{x+20} +\frac{96}{x}=4 \ |\div 4 \\\\\\ 24\bigg(\frac{1}{x+20} +\frac{1}{x} \bigg) =1 \\\\\\ 24\cdot \frac{x+x+20}{(x+20)x} =1 \ |\cdot (x+20)x \ \ \\\\\\48x+480=x^2+20x \\\\ x^2-28x-480=0 \\\\ \rm D=28^2+4\cdot 480=2704 =52^2 \\\\ \boxed{x_1=\frac{28+52}{2} =40} \\\\x_2=\frac{28-52}{2} =-12 \ \ \varnothing$

Justin's average speed to his parents' house: x= 40mph

Justin's average speed from his parents' house: x+20=60 mph

4 0

3 years ago