There is a trig identity called the sum of 2 angles for sin its<span>
sin(a+b)=sin(a)cos(b)+cos(a)(sin(b)
</span>
You will need to use it. So in your question split the 4x in 2 equal parts 2x and 2x
<span>
</span><span>sin(4x)=sin(2x+2x)
</span>Now using the expansion above you will get
<span>sin(2x+2x)=sin(2x)×cos(2x)+cos(2x)×sin(2x)
</span>And it will simplify to
<span><span>2sin(2x)cos(2x)
I hope this helps you! Good luck :)</span></span>
C=480
solve
480=24n+35
minus 35 both sides
445=24n
divide both sides by 24
18.541666666666666666666666666667=n
<span>so about 18 cakes</span>
Answer:
$36.8
Step-by-step explanation:
i just calculated it!
32*15% = 4.8
32+4.8= 36.8
Answer
Find out how much money did she start with.
To proof
let us assume that the money she had be x.
As given
woman spent two thirds of her money

Money she had after spent two thirds of her money = Total money - money spent


As given she lost two thirds the remainder


we get

Money she had after lost two thirds the remainder = Money she had after spent two thirds of her money - she lost two thirds the remainder


As given
she had $4 left
thus

x = $36
she start with $36.
Hence proved
let's firstly convert the mixed fractions to improper fractions and then divide.
![\bf \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}}~\hfill \stackrel{mixed}{1\frac{5}{8}\implies \cfrac{1\cdot 8+5}{8}}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%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~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B5%7D%7B8%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%208%2B5%7D%7B8%7D%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B13%7D%7B8%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \stackrel{\textit{total salad}}{\cfrac{13}{2}}\div \stackrel{\stackrel{\textit{conainer's}}{\textit{capacity}}}{\cfrac{13}{8}}\implies \cfrac{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\underset{1}{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\cdot \cfrac{\stackrel{4}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies 4](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Btotal%20salad%7D%7D%7B%5Ccfrac%7B13%7D%7B2%7D%7D%5Cdiv%20%5Cstackrel%7B%5Cstackrel%7B%5Ctextit%7Bconainer%27s%7D%7D%7B%5Ctextit%7Bcapacity%7D%7D%7D%7B%5Ccfrac%7B13%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B%5Cbegin%7Bmatrix%7D%2013%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D%7D%7B%5Cunderset%7B1%7D%7B%5Cbegin%7Bmatrix%7D%202%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D%7D%7D%5Ccdot%20%5Ccfrac%7B%5Cstackrel%7B4%7D%7B%5Cbegin%7Bmatrix%7D%208%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D%7D%7D%7B%5Cbegin%7Bmatrix%7D%2013%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D%7D%5Cimplies%204)