geno3141

1) Life is too short to say and write all those extra s's. (After all, we have 'color', not 'colour'.)

2) All of math is interconnected in some zen-like, gordian knot way.

L = 10+W

P = 2L + 2W   and   P = 86  --->  2L + 2W = 86 

Substituting:  2(10+W) + 2W = 86

                      20 + 2W + 2W = 86

                             20 + 4W = 86

                                     4W = 66

                                       W = 16.5              L = 16.5 + 10  =  26.5

Where do the right parentheses belong?

If you have a division problem like these,  then subtract exponents; the answer is  x^4.

 x^10 / x^6  =  x^4

x^8 / x^8  =  x^0  =  1

x^4 / x^7  =  x^-3      which is the same as 1 / x^3

[a^5·b^3] / [a^2·b^7]  =  a^3·b^-4  =  a^3 / b^4

If you have some specific problems, please ask...

√(-v + 27)  =  v + 3

To get rid of a square root, square both sides:

  -v + 27  =  (v + 3)²                         (v + 3)²   =  (v + 3)(v + 3)  =  v²  + 3v + 3v + 9  =  v²  + 6v + 9

  -v + 27  =  v²  + 6v + 9

Since it is a quadratic, get all terms to one side; add v to both sides and subtract 27 from both sides.

  0  =  v²  + 7v - 18

  0  =  (v + 9)(v - 2)

So, either v = -9 or v = 2.

Checking answers, 2 works but -9 doesn't.

I believe that the way to find this is to divide the peak voltage value by √2.

The graph of 140sin(100πt) has a maximum value of 140 (since the maximum value for sin is 1).

140/√2  ≈  98.99 ≈ 100

If p = 2/3 and q = 1/3,

then p² + 2pq  =  (2/3)² + 2(2/3)(1/3)

                       =  4/9 + 4/9  =  8/9

When you multiply fractions, multiply the numerator times the numerator and the denominator times the denominator.

If you draw a right triangle ABC, with C the right angle. Let point A be the location of the plane and location B be the locaion of the station.  AC will be the height of the plane (5.9 km). The angle at B is 78.6°. Side BC represents the distance from the plane to the station (both in the air and across the ground).

For angle B, the side AC is the opposite side and BC is the adjacent side. If we want to find the length of BC, let's use tangent, because tangent = opposite / adjacent.

tan(78.6)  =  5.9 / BC

Cross-multiply:  BC · tan(78.6)  =  5.9

Divide:              BC  =  5.9 / tan(78.6)     --->     BC  =  1.19 km

Speed of the plane  =  distance / time  =  1.19 km / 10 sec  =  0.119 km/s

0.119 km/s x 60s/1min x 60min/1hr  =  428 km/hr

To what decimal location are we to round the answer?