Can someone please help me thank you

Mathematics

2 answers:

kondor19780726 [428]3 years ago

8 0

Its' b' your welcome

zubka84 [21]3 years ago

3 0

The answer is choice A.
When you rotate the trapezoid 90 deg clockwise about the origin, the long parallel side of the trapezoid ends up on the negative x-axis. Then you translate it 3 units up, and you end up with the long side 3 units above the x-axis. That is what the first choice shows you.

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Determine the effective rate for $1 for 1 year at 5.9% compounded quarterly.

kenny6666 [7]

Keeping in mind that the effective rate, is in effect the APY or Annual Percentage Yield,

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 5.9\%\to \frac{5.9}{100}\to &0.059\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four times}
\end{array}\to &4
\end{cases}
\\\\\\
\left(1+\frac{0.059}{4}\right)^{4}-1\implies (1.01475)^4-1 \approx 0.0603
\\\\\\
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3 years ago

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Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

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$x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\$