11. Determine how much water can be in cuboid with
dimensions of 2 m x 1 m x 0.5 m? If the water density is equal to 1 g/cm3
determine how much kilograms of water can be inside the cuboid?
$$\begin{align}
& a=2\text{ m} \\
& b=1\text{ m} \\
& \underline{\begin{align}
& c=0.5\text{ m} \\
& \rho \text{=1g/c}{{\text{m}}^{3}} \\
\end{align}} \\
& V=? \\
& m=? \\
& \rho =1\left[ \frac{\text{g}}{\text{c}{{\text{m}}^{3}}} \right]\frac{1\text{ }\left[ \text{kg} \right]}{1000\text{ }\left[ \text{g} \right]}\frac{1000000\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]}{1}=1000\text{ kg/}{{\text{m}}^{3}} \\
& V=abc=2\cdot 1\cdot 0.5=1\text{ }{{\text{m}}^{3}} \\
& m=\rho V=1000\cdot 1=1000kg \\
\end{align}$$
12. How much seconds has one day?
$$\begin{align}
& \underline{n=1\text{ day}=24\text{ h}} \\
& n=?s \\
& 1\text{ h}=60\text{ min} \\
& n=24\left[ \text{h} \right]\cdot \frac{60\text{ }\left[ \min \right]}{1\text{ }\left[ \text{h} \right]}=1440\text{ }\min \\
& 1\text{ min}=60\text{ s} \\
& n=1440\text{ }\left[ \min \right]\cdot \frac{60\text{ }\left[ \text{s} \right]}{1\text{ }\left[ \min \right]}=86400\text{ s} \\
\end{align}$$
13. What is the height of an equilateral triangle with
side length of 10 cm?
$$\begin{align}
& \underline{a=10\text{ cm}=0.1\text{ m}} \\
& \text{h=?} \\
& h=\frac{\sqrt{3}}{2}a=\frac{\sqrt{3}}{2}\cdot 0.1=0.0866025\text{ m} \\
\end{align}$$
14.The height of an equilateral triangle is 5 cm.
Determine the side length?
$$\begin{align}
& \underline{h=5\text{ cm}=0.05\text{ m}} \\
& a=? \\
& h=\frac{\sqrt{3}}{2}a \\
& a=\frac{2h}{\sqrt{3}}=\frac{2\cdot 0.05}{\sqrt{3}}=0.0577\text{ m} \\
\end{align}$$
15. Rectangular triangle with cathetus of length 3 cm and
4 cm. What is the length of the hypotenuse?
$$\begin{align}
& a=3\text{ cm}=0.03\text{ m} \\
& \underline{b=4\text{ cm}=0.04\text{ m}} \\
& c=? \\
& c=\sqrt{{{a}^{2}}+{{b}^{2}}}=\sqrt{{{0.03}^{2}}+{{0.04}^{2}}}=0.05\text{ m} \\
\end{align}$$
16.Dependence of position of the body which is moving
along x axis on time t is shown in the next figure.
Determine:
a. Where
was the body at the moment: t1 = 1 s, t2 = 3 s, t3
= 5 s, t5 = 8 s
b. In
which time interval is the body at rest?
c. In
what intervals the body has positive shift and in what has a negative shift?
$$\begin{align}
& {{t}_{1}}=1\text{ s} \\
& {{t}_{2}}=3\text{ s} \\
& {{t}_{3}}=5\text{ s} \\
& \underline{{{t}_{4}}=8\text{ s}} \\
& a){{s}_{1}}=40\text{ m}\text{, }{{s}_{2}}=80\text{ m}\text{, }{{s}_{3}}=80\text{ m}\text{, }{{s}_{4}}=20\text{ m} \\
& \text{b)t}\in \left[ 2,6 \right] \\
& c)\text{ Positive shift in time interval t}\in \left[ 0,2 \right] \\
& \text{Negative shift in time interval t}\in \left[ 6,10 \right] \\
\end{align}$$
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