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1 year ago

Caffeine concentration is 1.99 mg/oz how many cans would be leathal if 10g was leathal and there where 12oz in a can

1 answer:

5 0

The number of cans that would be considered lethal if 10g was lethal and there where 12oz in a can is 419 cans.

<h3>How to convert mass?</h3>

According to this question, caffeine concentration is 1.99 mg/oz.

1.99 milligrams can be converted to grams as follows:

1.99milligrams ÷ 1000 = 0.00199grams

This means that 0.00199grams per oz is the caffeine concentration.

If there were 12 oz in a can, then, 0.00199grams × 12 = 0.02388 grams in 1 can.

This means that if 10grams is considered lethal, 10grams ÷ 0.02388 grams = 419 cans would be lethal for consumption.

Therefore, the number of cans that would be considered lethal if 10g was lethal and there where 12oz in a can is 419 cans.

Learn more about conversion factor at: brainly.com/question/14479308

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Calculate the distance between origin O $\left( {0\;{\rm{cm,}}\;0\;{\rm{cm}}} \right)$ and the point $\left( { - 5.0\;{\rm{cm,}}\;5.0\;{\rm{cm}}} \right)$ as follows:

Substitute 0 cm for ${x_1} ,0cm$ for ${y_1} , - 5.0\;{\rm{cm}}$ for ${x_2}$ , and $5.0\;{\rm{cm}}$ for ${y_2}$ in $r = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}$

$\begin{array}{c}\\r = \sqrt {{{\left( { - 5.0\;{\rm{cm}}\; - 0\;{\rm{cm}}} \right)}^2} + {{\left( {5.0\;{\rm{cm}}\; - 0\;{\rm{cm}}} \right)}^2}} \\\\ = 5\sqrt 2 \;{\rm{cm}}\\\end{array}$

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$E = k\frac{q}{{{r^2}}}$

Substitute $9 \times {10^9}\;{\rm{N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}$ for k, 10 nC for q, and $5\sqrt 2 \;{\rm{cm}}$ for r in $E = k\frac{q}{{{r^2}}}$

$\begin{array}{c}\\E = \frac{{\left( {9 \times {{10}^9}} \right)\left( {10\;{\rm{nC}}} \right)}}{{{{\left( {5\sqrt 2 \;{\rm{cm}}} \right)}^2}}}\\\\ = \frac{{\left( {9 \times {{10}^9}\;{\rm{N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}} \right)\left( {10\;{\rm{nC}}} \right)\left( {\frac{{{{10}^{ - 9}}{\rm{C}}}}{{1\;{\rm{nC}}}}} \right)}}{{{{\left( {\left( {5\sqrt 2 \;{\rm{cm}}} \right)\left( {\frac{{{{10}^{ - 2}}\;{\rm{m}}}}{{1\;{\rm{cm}}}}} \right)} \right)}^2}}}\\\\ = 1.8 \times {10^4}\;{\rm{N/C}}\\\end{array}$

Therefore, the electric field at the position $\left( { - 5.0\;{\rm{cm,}}\;5.0\;{\rm{cm}}} \right)$ is $1.8 \times {10^4}\;{\rm{N/C}}$

The electric field is inversely proportional to the square of the distance r.

The electric field in vector form is,

$\vec E = {\vec E_{2x}}i + {\vec E_{2y}}j$

Here, ${\vec E_{2x}}$ is the x component of electric field vector, and ${\vec E_{2y}}$ is the y component of electric field vector.

The x component of electric field vector is $- E\cos \theta$ , and the y component of electric field vector is $E\sin \theta$ .

Substitute $- E\cos \theta$ for ${\vec E_{2x}}$ , and $E\sin \theta$ for ${\vec E_{2y}}$ in $\vec E = {\vec E_{2x}}i + {\vec E_{2y}}j$

$\begin{array}{c}\\\vec E = \left( { - E\cos \theta } \right)i + \left( {E\sin \theta } \right)j\\\\ = \left( E \right)\left( {\left( { - \cos \theta } \right)i + \left( {\sin \theta } \right)j} \right)\\\end{array}$

Substitute $1.8 \times {10^4}\;{\rm{N/C}}$ for E, and 450 for $\thetaθ$ in $\vec E = \left( E \right)\left( {\left( { - \cos \theta } \right)i + \left( {\sin \theta } \right)j} \right)$

$\begin{array}{c}\\\vec E = \left( {1.8 \times {{10}^4}\;{\rm{N/C}}} \right)\left( { - \cos 45i + \sin 45j} \right)\\\\ = - \left( {1.27\;{\rm{N/C}}} \right)i + \left( {1.27\;{\rm{N/C}}} \right)j\\\end{array}$

Therefore, the electric field vector in component form is,

$\left( {{{\vec E}_{2x}},{{\vec E}_{2y}}} \right) = \left( { - 1.27\;{\rm{N/C}},\,1.27\;{\rm{N/C}}} \right){\rm{N/C}}$

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