Answer:
See Below.
Step-by-step explanation:
We want to show that the function:
Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:
Simplify:
Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Answer:Use a calculator
Explanation:it’s easier
Answer:
-5x^2-2x
Step-by-step explanation:
When distributing, you multiply the term outside the brackets to all the terms in brackets.
If the term outside the bracket is negative, then when distributing/opening the brackets, the signs of the terms changes.
So in this prob. -x would multiply to both +5x and +2
-x*5x+-x*2
∴-5x^2-2x
y = - 3
Since y varies directly as x then
y = kx ← ( k is the constant of variation )
to find k use y = - 1 when x = 3
k = 
= 
= - 
hence y = - x
when x = 9, then
y = - × 9 = - 3
Answer:
Given the 2 values, height and the base, of these 2 triangles, we can assume that they are similar (meaning they share the same angles) as we have no other information to determine the height of the tree.
Therefore, if these triangles are similar, their corresponding sides are proportional. In other words, PZ/RT = QZ/ST or RT/PZ=ST/QZ
Hence, if we find the ratio of this, we can use it to find the side <em>h</em>
<em>QZ/ST=PZ/RT</em>
<em>48/12=PZ/4</em>
<em>PZ/4=48/12</em>
<em>(PZ/4)3=48/12</em>
<em>PZ(3)/12=48/12</em>
<em>48/3=16</em>
16=PZ.
3Step-by-step explanation:
