Answer:
perimeter is 12x-6
Step-by-step explanation:
perimeter is the sum of all sides
3(x+2) + 2x+11 + 7x-23
distribute the 3 in the first term, then combine 'like terms'
3x+6 + 2x+11 + 7x-23
3x+2x+7x + 6+11+(-23)
12x-6
Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
Answer:

Step-by-step explanation:
We are given that
is in <em>fourth</em> quadrant.
is always positive in 4th quadrant and
is always negative in 4th quadrant.
Also, we know the following identity about
and
:

Using \theta_1 in place of \theta:

We are given that 

is in <em>4th quadrant </em>so
is negative.
So, value of 
Hello!
As you can see, 22 is the opposite angle. We are looking for the adjacent angle. Let's just call it x. Using SOH CAH TOA, we see that the tangent is the opposite divided by the adjacent side. Let's use that.
tan54≈1.38
This gives us the equation below.
1.38=22/x
Let's solve this equation for x.
1.38x=22
x=22/1.38
x=15.94
Therefore, the length of the shadow is about 15.94 meters.
I hope this helps!
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