Hello,
s=48t-16t²
a)
s=0==>16t(3-t)=0==>t=0 or t=3
b)
s>32==>48t-16t²>32===>16(t²-3t+2)<0
Δ=9-8=1
==>16(t-1)(t-2)<0
==>1<t<2 (negative between the roots)
there are 14 green grapes in a bowl of fruits
A = LW + 0.5bh
0.5bh = A - LW
b = (A - LW) / 0.5h
Its B
Note to avoid ambiguity its better to put the A - LW in parentheses
Answer:
White: 2/5
Dark: 3/5
Step-by-step explanation:
There are 5 sections and there are 2 white spots and 3 dark spots.
So, 2 out of the 5 sections are white which is 2/5 and 3 out of the 5 sections is dark which is 3/5.
let's firstly convert the mixed fractions to improper fractions.
![\bf \stackrel{mixed}{24\frac{3}{4}}\implies \cfrac{24\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{99}{4}}~\hfill \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B24%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B24%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B99%7D%7B4%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B6%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B6%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B13%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf \stackrel{\textit{area of a rectangle}}{A=Lw}\implies \cfrac{A}{L}=w~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\frac{13}{2}\\\\ A=\frac{99}{4} \end{cases}\implies \cfrac{~~\frac{99}{4}~~}{\frac{13}{2}}=w \\\\\\ \cfrac{99}{4}\cdot \cfrac{2}{13}=w\implies \cfrac{99}{13}\cdot \cfrac{2}{4}=w\implies \cfrac{99}{13}\cdot \cfrac{1}{2}=w\implies \cfrac{99}{26}=w\implies 3\frac{21}{26}=w](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20a%20rectangle%7D%7D%7BA%3DLw%7D%5Cimplies%20%5Ccfrac%7BA%7D%7BL%7D%3Dw~~%20%5Cbegin%7Bcases%7D%20L%3Dlength%5C%5C%20w%3Dwidth%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20L%3D%5Cfrac%7B13%7D%7B2%7D%5C%5C%5C%5C%20A%3D%5Cfrac%7B99%7D%7B4%7D%20%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B~~%5Cfrac%7B99%7D%7B4%7D~~%7D%7B%5Cfrac%7B13%7D%7B2%7D%7D%3Dw%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B99%7D%7B4%7D%5Ccdot%20%5Ccfrac%7B2%7D%7B13%7D%3Dw%5Cimplies%20%5Ccfrac%7B99%7D%7B13%7D%5Ccdot%20%5Ccfrac%7B2%7D%7B4%7D%3Dw%5Cimplies%20%5Ccfrac%7B99%7D%7B13%7D%5Ccdot%20%5Ccfrac%7B1%7D%7B2%7D%3Dw%5Cimplies%20%5Ccfrac%7B99%7D%7B26%7D%3Dw%5Cimplies%203%5Cfrac%7B21%7D%7B26%7D%3Dw)