An athlete runs two miles in 13.5 minutes. How many minutes is this per mile?

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

Answer:

6.75 minutes / mile.

Step-by-step explanation:

Time: 13.5 minutes

distance: 2 miles

rate: ?

You want the units to be minutes / mile. That's not the usual units for a rate. You have to be careful how you set this up.

13.5 minutes

2 miles

13.5 /2 = 6.75 minutes / mile = 6 minutes 45 seconds / mile

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Help me please, Find a, b, and c.

Mama L [17]

Answer:

a = $6*\sqrt{3}$

b = 12

c = $6\sqrt{2}$

Step-by-step explanation:

Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.

A 45-45-90 right triangle has side lengths $1-1-\sqrt{2}$ .

A 30-60-90 right triangle has side lengths $1 - \sqrt{3} -2$ .

Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.

Side a corresponds to side length $\sqrt{3}$ . Therefore, $a = 6*\sqrt{3}$ .

Side b corresponds to side length 2, b = 2*6 = 12.

The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to $\sqrt{2}$ . This means $\sqrt{2}$ was multiplied by $12 = \sqrt{2} * \sqrt{72}$ . This means that side c is $\sqrt{72}=6\sqrt{2}$ .