A visitor is staying in a cottage that is 7 miles west of the closest point on a shoreline to an island. The island is 4 miles due north of the shoreline. The visitor plans to travel from the cottage to the island by running and swimming. If the visitor runs at a rate of 6 mph and swims at a rate of 2 mph, how far should the visitor run to minimize the time it takes to reach the island?

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step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the diver is 33 feet below the surface.

step-by-step explanation:

hope this

yes

step-by-step explanation:

so of course you want to start by plugging the 5 in which goes to 7(5)+3(5)=50 because 7*5=35 and 3*5=15 and then add them together, then plug in the 5 to the other equation as well 9(5)+5=50 because 9*5= 45 and then add 5 and so yes they are equivalent.