If your heart beats 80 times per minute and you live to be 90 years old, estimate the number of times your heart beats during your lifetime. state your answer in scientific notation

The heart beat is given in units of beats per minute, therefore before we can do any calculations let us make sure that all units are similar by converting the age in terms of minutes.

We know that there are 365 days per year, therefore:

90 years (365 days / year) = 32,850 days

We know that in a day, there are 24 hours, therefore:

32,850 days (24 hours / day) = 788,400 hours

And in an hour, there are 60 minutes, therefore:

788,400 hours (60 minutes / hour) = 47,304,000 minutes

Now calculating for the total heart beats in a lifetime:

total heartbeats = (80 beats / minute) * 47,304,000 minutes

total heartbeats = 3,784,320,000

Writing this into scientific notation:

3.78 x 10^9 beats

or

3.8 x 10^9 beats

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

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