Simplify: (-7x + 5) - (2x2 – 8x + 6). Choose the standard form of the answer.
1 answer:
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Answer:
angle CAB = 113.8 degree
angle ABC = 35.6 degree
angle BCA = 30.6 degree
Step-by-step explanation:
Given data:
A(1, 0, −1),
B(5, −3, 0),
C(1, 5, 2)
calculate the length of side by using the distance formula
so
AB = (5,-3,0) - (1,0,-1) = (4,-3,1)
AC= (1,5,2) - (1,0,-1) = (0,5,3)
|AB|
|AC| =
From following formula, calculate the angle between the two side i.e Ab and AC
AB.AC = |AB|*|AC| cos ∠CAB
(4,-3,1).(0,5,3)
4*0 -3*5 +1*3
-12 =
cos ∠CAB = - 0.404
angle CAB = 113.8 degree
BA =B- A = (1,0,-1) - (5,-3,0) = (-4,3,-1)
BC = (1,5,2)-(5,-3,0) = (-4,8,2)
|BA| = \sqrt{(26)}
|BC|
BA.BC = |BA|*|BC|* cosABC
(-4,3,-1).(-4,8,2) =
16+24-2
cos ∠ABC = 0.813
angle ABC = 35.6 degree
we know sum of three angle in a traingle is 180 degree hence
sum of all three angle = 180
angle BCA + 35.6 + 113.8 = 180
angle BCA = 30.6 degree
Step-by-step explanation:
Given that,
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,
We know that,
Speed = distance/time
The rate while moving downstream
The rate while moving upstream
The rate of the boat in still water is the average of these:
The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph
Hence, this is the required solution.