The length of the sides of any right triangle are always less than the length of the hypotenuse. The sine and cosine functions find the ratio between a side and the hypotenuse, so it's always less than 1.

5 0

3 years ago

Find the simple interest rate needed in order for an investment of $2000 to grow to an account of $5000 in 3 years

Nutka1998 [239]

$\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\dotfill&\$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &3 \end{cases} \\\\\\ 5000=2000(1+r3)\implies \cfrac{5000}{2000}=1+3r\implies \cfrac{5}{2}=1+3r \\\\\\ 5=2+6r\implies 3=6r\implies \cfrac{3}{6}=r\implies 0.5=r\implies \stackrel{\textit{converting to percent}}{0.5\cdot 100\implies 50\%}$

5 0

3 years ago

Alex wrote the equation c=2n. Describe a situation that this equation could represent.

nevsk [136]

There were 2 times as many caps as nails
make an equation

there were c popsicles each child got 2 popsicles, make an equation for how many popsicles to order if there were n children

bob has c shirts
this is 2 times as many children he has. make an equation for how many shirts he has if he has n children

7 0

3 years ago