Answer:
h = 6 cm
Step-by-step explanation:
Atriangle = b×h/2
18cm² = 6cm×h/2
36cm² = 6cm×h
h = 36cm²/6cm
h = 6 cm
Substitute
![u=\ln x](https://tex.z-dn.net/?f=u%3D%5Cln%20x)
, so that
![\mathrm du=\dfrac{\mathrm dx}x](https://tex.z-dn.net/?f=%5Cmathrm%20du%3D%5Cdfrac%7B%5Cmathrm%20dx%7Dx)
. The integral is then equivalent to
![\displaystyle\int\frac{\mathrm dx}{x\ln^px}=\int\frac{\mathrm du}{u^p}=\begin{cases}\dfrac{u^{p+1}}{p+1}+C&\text{for }p\neq1\\\\\ln|u|+C&\text{for }p=1\end{cases}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5Cln%5Epx%7D%3D%5Cint%5Cfrac%7B%5Cmathrm%20du%7D%7Bu%5Ep%7D%3D%5Cbegin%7Bcases%7D%5Cdfrac%7Bu%5E%7Bp%2B1%7D%7D%7Bp%2B1%7D%2BC%26%5Ctext%7Bfor%20%7Dp%5Cneq1%5C%5C%5C%5C%5Cln%7Cu%7C%2BC%26%5Ctext%7Bfor%20%7Dp%3D1%5Cend%7Bcases%7D)
Then transforming back to
![x](https://tex.z-dn.net/?f=x)
gives
<h3>Answer: Draw a straight line through (0,-7) and (1,-5)</h3>
Explanation:
You could use any two points you want. For me, the easiest is when x = 0. Plug this into the equation to get
y = 2x-7
y = 2(0)-7
y = -7
So we have x = 0 and y = -7 pair up to get (0,-7) as our first point. This is the y intercept.
Repeat for x = 1
y = 2x-7
y = 2(1)-7
y = -5
So (1,-5) is another point on this line. You only need two points at minimum to graph a straight line.
Answer:
(1,1) and (-2,-11) are the correct solutions