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svetoff [14.1K]
3 years ago
14

(2.5 • 10^4) - (1.5 • 10^3) Evaluate please, can you show the steps

Mathematics
1 answer:
Usimov [2.4K]3 years ago
8 0


According to PEMDAS, you would look in the parenthesis first. In the first set of parenthesis we have an exponent. 10x10x10x10 is 10,000. Then we multiply this by 2.5. We now have 25,000. We put this to the side..


Next, we do the same thing on the other side -- 10x10x10 is 1,000 and then you multiply that answer by 1.5 and we have 1,500. Now we can subtract. 25,000 - 1500 = 23,500 :)

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cricket20 [7]

As soon as I read this, the words "law of cosines" popped
into my head.  I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.

The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.

To find angle-B, the law of cosines says

       b² = a² + c² - 2 a c cosine(B)

B  =  angle-B
b  =  the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9

                  (1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)

                 1.96  =  (1) + (3.61)  -  (3.8) cos(B)

Add  3.8 cos(B)  from each side:

                 1.96 + 3.8 cos(B) = 4.61

Subtract  1.96  from each side:

                             3.8 cos(B) =  2.65

Divide each side by  3.8 :

                                  cos(B)  =  0.69737  (rounded)

Whipping out the
trusty calculator:
                                 B  = the angle whose cosine is 0.69737

                                      =  45.784° .

Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...

By gosh !  Choice 'B' is  45.8° !                    yay !
I'll bet that's it !

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