Determine the value of (tangent of 88 degrees, 22 minutes, and 45 seconds). in this case, minutes are 1/60 of a degree and seconds are 1/3600 of a degree. a. 23.42583649 c. 35.34015106 b. 56.36842561 d. 47.69869523

  c.  35.34015106

Step-by-step explanation:

As with many problems of this nature, you only need to get close to be able to choose the correct answer. 22 minutes 45 seconds is just slightly less than 1/2 degree (30 minutes), so the tangent value will be just slightly less than tan(88.5°) ≈ 38. The appropriate choice is 35.34015106.

If you need confirmation, you can find tan(88°) ≈ 29, so you know the answer will be between 29 and 38.

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The above has to do with strategies for choosing answers on multiple-choice problems. Below, we will work the problem.

The angle is (in degrees) ...

  88 + 22/60 +45/3600 = 88 + (22·60 +45)/3600 = 88 +1365/3600

  ≈ 88.3791666... (repeating) . . . . degrees

A calculator tells you the tangent of that is ...

  tan(88.3791666...°) ≈ 35.3401510614

Many calculators will round that to 10 digits, as in the answer above. Others can give a value correct to 32 digits. Spreadsheet values will often be correct to 15 or 16 digits.

C.

Step-by-step explanation:

35.34015106

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752