To decrease an amount by 7%, what single multiplier should you use?

Mathematics

1 answer:

notka56 [123]3 years ago

4 0

To decrease an amount by 7% what single multiplier would you use. You want 7% less than 100%, so the answer is (100%-7%)=93% =0.93. Hope I helped!

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How do I do this? please detail steps.

vladimir2022 [97]

Define
${x} = \left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right]$

Then
x₁ = cos(t) x₁(0) + sin(t) x₂(0)
x₂ = -sin(t) x₁(0) + cos(t) x₂(0)

Differentiate to obtain
x₁' = -sin(t) x₁(0) + cos(t) x₂(0)
x₂' = -cos(t) x₁(0) - sin(t) x₂(0)

That is,
$\dot{x} = \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right] x(0)$

Note that
$\left[\begin{array}{ccc}0&1\\-1&09\end{array}\right] \left[\begin{array}{ccc}cos(t)&sin(t)\\-sin(t)&cos(t)\end{array}\right] = \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right]$

Therefore
$x(t) = \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] x(t)$

7 0

3 years ago

if your bill at a restaurant is $56.43 and you want to leave 20% tipe,how much tipe should you leave

morpeh [17]

$\hspace{34em}|\\ \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 56.43}}{\left( \cfrac{20}{100} \right)56.43}\implies 11.286~\hfill \stackrel{about}{\approx 11.29}$