Rod made a scale drawing of a petting zoo. He used the

Mathematics

1 answer:

SCORPION-xisa [38]2 years ago

6 0

Answer: 15m

Step-by-step explanation:

Since 1cm is to 5m, just multiply 3 by 5 and you will get 15.

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Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

Mademuasel [1]

An hemispherical dome is half a sphere. If the diameter is 60 m, then the radius is 30 m.

We can use differentials to solve this problem because we are adding a thin layer to the original dome, so the volume of the dome in increased by a differential of itself.

This differential volume that the dome is increased is equal to the volume of the coat of paint.

The volume of the dome can be written as:

$\begin{gathered} V=\frac{4\pi}{3}r^3 \\ \frac{dV}{dr}=\frac{4\pi}{3}\cdot3r^2\Rightarrow dV=\frac{4\pi}{3}\cdot3r^2\cdot dr=4\pi r^2\cdot dr \end{gathered}$

Now, we can calculate dV as:

$\begin{gathered} dV=4\pi r^2\cdot dr \\ dV\approx4\cdot3.14\cdot(30m)^2\cdot0.07\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}} \\ dV\approx12.57\cdot900m^2\cdot0.0007m \\ dV\approx7.92m^3 \end{gathered}$

Answer: the paint needed for this coat is approximately 7.92 m^3

5 0

1 year ago

Evaluate -1 - [-z] where z = -2

slega [8]

$\huge\textbf{Hey there!}$

$\huge\textsf{-1 - [-z]}\\\\\huge\textsf{= -1 - [- -2]}\\\\\huge\textsf{= -1 - - 2}\\\\\huge\textsf{= -1 + (-2)}\\\\\huge\textsf{= -1 - 2}\\\\\huge\textsf{= -3}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-3}}}\huge\checkmark$