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CaHeK987 [17]
3 years ago
8

Alexis wants to make a paperweight at pottery class. He designs a pyramid-like mode l with a base area of 100 square centimeters

and a height of 6 centimeters. He wants the paperweight to weigh at least 300 grams. What is the lowest possible density of the material Alexis uses to make the paperweight.
Mathematics
1 answer:
olga55 [171]3 years ago
4 0

Answer:

\frac{3}{2} g/cm²

Step-by-step explanation:

First, we need to find the volume of the prism. The volume of a square pyramid is V = Bh/3

B = 100 cm²

h = 6 cm

V = 100 cm² * 6 cm /3

V = 600 cm³ /3

V = 200 cm³

Next, we need to solve for the density based on the desired volume and mass.

m = mass = 300 g

V = volume

density = m/V

density = 300 g / 200 cm³

density = 3/2 g/cm³

The lowest possible density of the material to make the paperweight would be \frac{3}{2} g/cm²

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Find the value of x such that 365 based seven + 43 based x = 217 based 10.
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We need to find the base x in the following equation:

365_7+43_x=217_{10}

First, lets convert 365 from base 7 to base 10. This is given by

365_7=3\times7^2+6\times7^1+5\times7^0

where the upperindex denotes the position of eah number. This gives

\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}

that is, 365 based 7 is equal to 194 bases 10.

Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

43_x=4\times x^1+3\times x^0

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

43_x=(4x+3)_{10}

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

194_{10}+(4x+3)_{10}=217_{10}

For simplicity, we can omit the 10 and get

194+4x+3=217

so, we can solve this equation for x. By combining similar terms. we have

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and by moving 197 to the right hand side, we obtain

\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}

Finally, we get

\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}

Therefore, the solution is x=5

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