Answer:
Step-by-step explanation:
Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola
This parabola has vertex at (0,100) and symmetrical about y axis.
Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.
Hence coordinates of any rectangle are
Length of rectangle = 2a and width = 
Area of rectangle = lw = 
To find max area, use derivative test.
Hence maxima when first derivative =0
i.e. when a =2
Thus we find dimensions of the rectangle are l =4 and w = 96
Maximum area = 
part A)
![\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Ccccccc%7Cll%7D%20%5Ccline%7B1-7%7D%20x%268%2627%2664%26125%26%26x%5C%5C%20%5Ccline%7B1-7%7D%20y%26%5Cstackrel%7B%5Csqrt%5B3%5D%7B8%7D%7D%7B2%7D%26%5Cstackrel%7B%5Csqrt%5B3%5D%7B27%7D%7D%7B3%7D%26%5Cstackrel%7B%5Csqrt%5B3%5D%7B64%7D%7D%7B4%7D%26%5Cstackrel%7B%5Csqrt%5B3%5D%7B125%7D%7D%7B5%7D%26%26%5Csqrt%5B3%5D%7Bx%7D%20%5C%5C%20%5Ccline%7B1-7%7D%20%5Cend%7Barray%7D~%5Chspace%7B10em%7Dy%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
part B)
f(x) = 10 + 20x
so if you rent the bike for a few hours that is
1 hr.............................10 + 20(1)
2 hrs..........................10 + 20(2)
3 hrs..........................10 + 20(3)
so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.
f(100) = 10 + 20(100) => f(100) = 2010.
f(100), the cost of renting the bike for 100 hours.
Answer:
umm... there is no problem
Answer: 27cm²
Step-by-step explanation:
lets take the width as x and length as 3x( since length is 3 times the width)…
Perimeter of the rectangle is 24 cm( 2*(l+b))= 2×(3x+x):24
2×4x=24
8x=24
X( width): 24/8=3cm
Length= 3x: 3*3=9cm
Area of the rectangle: ( l*w)= 9×3: 27cm²
Answer:
He would walk 10 miles in 5 hours, and it would take him 2 hours to walk 4 miles.
Step-by-step explanation:
