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insens350 [35]
4 years ago
14

A package is dropped from a helicopter that is moving upward at 20.0 m/s. If it takes 18.0s before the package strikes the groun

d, how high above the ground was the package when it was released? (UNITS)
Mathematics
1 answer:
tekilochka [14]4 years ago
6 0

Answer:

We have for velocity of package v= 20 - 9.8t and for distance from the ground y = h + 20t - 4.9t2.

We have y = 0 and t = 18.0 s we have h = 4.9·182 - 20·18 = 1227.6 m.

Velocity at landing v = 20 - 9.8·18 = - 156.4 m/s

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Graph the following sequence of transformations for
Sedbober [7]
\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}
\end{array}\\\\
--------------------

\bf \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{  B}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the y-axis}

\bf \bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{  D}}\\
\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\
\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{  B}}}

with that template in mind.

\bf f(x)=\sqrt[3]{x}\qquad \boxed{-f(x+2)+4}\implies f(x)=\stackrel{A}{-1}\sqrt[3]{\stackrel{B}{1}x\stackrel{C}{+2}}\stackrel{D}{+4}\qquad 
\\\\\\
f(x)=-\sqrt[3]{x+2}+4

A  = -1, reflected over the x-axis

B = 1, C = 2,  horizontal shift of C/B or 2, to the left.

D = 4, shifted upwards by 4 units.

check the picture below.

7 0
3 years ago
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BaLLatris [955]
Converting 9 3/8 to an improper fraction is 75/8. Converting 8 7/8 to an improper fraction is 71/8. Subtracting these, we get 75/8 - 71/8 = 4/8 = 1/2.
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Hope this helps!
7 0
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4 0
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Answer:

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Step 1:

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