Simplify using the vertical method. (3k + 5)(2k^2 – 5k – 3)

Mathematics

2 answers:

inna [77]3 years ago

6 0

Answer:

6k^3 - 5k^2 - 34k - 15

Step-by-step explanation:

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Nikolay [14]3 years ago

4 0

(3k + 5)(2k^2 – 5k – 3)
= 6k^3 - 15k^2 - 9k + 10k^2 - 25k - 15
= 6k^3 - 5k^2 - 34k - 15

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A rescue helicopter flew from its home base for 35 kilometers on a course of 330 degrees to pick up an accident victim. It then

artcher [175]

I've drawn a triangle to represent the journey (see attached.

The angle from Home to Victim to Hospital is:

a = $90 - (360 - 330) = 90- 30 = 60^o$

Using the cos rule, we can solve for the length x:

$a^2 = b^2 +c^2 - 2bccosA
\\x^2 = 35^2+25^2-2(35)(25)cos60
\\x^2 = 1850 - 875
\\x^2 = 975
\\x = \sqrt{975}
\\x = 31.2249...$

Using the cos rule, we can solve for angle b:

$a^2 = b^2 +c^2 - 2bccosA
\\35^2 = 31.22...^2+25^2-2(31.22...)(25)cosb
\\1225 = 975 + 625 - 1561.249...cosb
\\-375 = -1561.249...cosb
\\b = cos^{-1}( \frac{-375}{-1561.249...}) 
\\b = 76.1...$

So the bearing the helicopter has to travel is:

270 - 76.1 = 193.9 degrees (1 dp)

And the distance it travels is 31.2 km (1 dp)