Answer:
∠ 1 = 123°
Step-by-step explanation:
One way
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 1 is an external angle of the triangle, thus
∠ 1 = 90° + 33° = 123°
Second way
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for third angle in Δ
third angle = 180° - (90 + 33)° = 180° - 123° = 57°
The third angle and ∠ 1 form a straight angle and are supplementary, thus
∠ 1 = 180° - 57° = 123°
The answer is x = -8. Hope this helps!
Total of 55 marbles.....if there are 11 red marbles, then there are (55 - 11) = 44 green marbles. So the ratio of red marbles to green marbles is :
11:44 which reduces to 1:4 or 1/4 or 1 to 4
They are traveling at right angles to each other so we can say one is traveling north to south and the other west to east. Then we can say that there positions, y and x are:
y=150-600t x=200-800t
By using the Pythagorean Theorem we can find the distance between these two planes as a function of time:
d^2=y^2+x^2, using y and x from above
d^2=(150-600t)^2+(200-800t)^2
d^2=22500-180000t+360000t^2+40000-320000t+640000t^2
d^2=1000000t^2-500000t+62500
d=√(1000000t^2-500000t+6250)
So the rate of change is the derivative of d
dd/dt=(1/2)(2000000t-500000)/√(1000000t^2-500000t+6250)
dd/dt=(1000000t-250000)/√(1000000t^2-500000t+6250)
So the rate depends upon t and is not a constant, so for the instantaneous rate you would plug in a specific value of t...
...
To find how much time the controller has to change the airplanes flight path, we only need to solve for when d=0, or even d^2=0...
1000000t^2-500000t+62500=0
6250(16t^2-8t+1)=0
6250(16^2-4t-4t+1)=0
6250(4t(4t-1)-1(4t-1))=0
6250(4t-1)(4t-1)=0
6250(4t-1)^2=0
4t-1=0
4t=1
t=1/4 hr
Well technically, the controller has t<1/4 because at t=1/4 impact will occur :)
