Find the approximate values of the trigonometric functions of θ given the following information. Enter the values correct to 2 d
ecimal places. θ is in standard position the terminal side of θ is in quadrant III the terminal side is parallel to the line 2y - 5x + 16 = 0
sin θ =
cos θ =
tan θ =
cot θ =
sec θ =
csc θ =
sin θ =
cos θ =
tan θ =
cot θ =
sec θ =
csc θ =
1 answer:
Answer:
Step-by-step explanation:
slope of any line is same as the tan θ . so we first try to find the slope of the given line and then using that we can find remaining trigonometric functions .
To find the slope of a line we need to change the equation of line to slope intercept form .
2y - 5x +16 =0
move all terms to right
2y = 5x - 16
divide all by 2
y = 5/2 x - 8
compare this with y =mx+b
slope = m = 5/2
It means
tan θ = 5/2 = 2.5
tan θ = 2.50
now use the trigonometric ratios (see the image attached )
sin θ =
cos θ =
tan θ = 2.50
cot θ =
sec θ =
csc θ =
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Answer with explanation:
The given function is:
y=x³+3 x²-x-3
=x²(x+3) -1(x+3)
= (x²-1)(x+3)
= (x-1)(x+1)(x+3)
Put, y=0 , gives
⇒ (x-1)(x+1)(x+3)=0
≡→x-1=0 ∧ → x+1=0 ∧→x+3=0
≡x=1, -1, -3
So, there are three breaking points in the curve.
1.⇒Putting, x=1 , in the function
y(1)=1³+3×1²-1 -3
=1 +3-4
=0
2. ⇒Putting, x=-1 , in the function
y(-1)=(-1)³+3×(-1)²-(-1) -3
= -1 +3+1-3
=0
3.⇒Putting, x=-3 , in the function
y(-3)=(-3)³+3×(-3)²-(-3) -3
=-27+27+3-3
=0
So, These are points where curve crosses the X axis, which are , (1,0),(-1,0) and (-3,0).
But turning points are those points where curve takes the turn , that is, if it is increasing function then it starts decreasing or becomes constant function after that point, and if it is a decreasing function then it becomes increasing or constant function.
So,turning points of the given function by looking at the graph of the function by approximation
Option B:→(-2,3) and (0, -3)
Answer:
The probability that at lest one job will be missed in 57 second is =0.819134
Step-by-step explanation:
Poisson distribution:
A discrete random variable X having the enumerable set {0,1,2,....} as the spectrum, is said to be Poisson distribution.
for x=0,1,2...
λ is the average per unit time
Given that, a job arrives at a web server with the probability 0.03.
Here λ=0.03, t=57 second.
The probability that at lest one job will be missed in 57 second is
=P(X≥1)
=1- P(X<1)
=1- P(X=0)
=0.819134