Answer:
The answer to your question is 12.55 cm
Step-by-step explanation:
Data
Adam Cara
height = 159 cm height = 140 cm
shadow = 105 cm shadow = x
Process
1.- To solve this problem use the Thales' theorem
Cara's shadow / Cara's height = Adam's shadow / Adam's height
- Substitution
x / 140 = 105 / 159
-Solve for x
x = 105 (140) / 159
-Simplification
x = 14700 / 159
x = 92.45 cm
Cara's shadow is 92.45 cm long.
2.- If both shadows are in line, then Cara must walk forward
105 - 92.45 cm
12.55 cm
Answer:
-12
Step-by-step explanation:
You can find the value of k(-3) by substituting t = -3 into the absolute value function k(t) = -|4t|.
k(-3) = -|4*-3| = -|-12| = -12
Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).
B(y)=b-c
B(y)=100y-18y²
Now that we have a net benefits function we need find it's derivate with respect to y.

Now we must find at which point this function is equal to zero.
0=100-36y
36y=100
y=2.8
Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.
B(2.8)=100(2.8)-18(2.8)²=138.88≈139.
One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.
Answer:
10
Step-by-step explanation:
| | means absolute value. Absolute value is always positive, so your equation would be evaluated to 9 + 1 = 10