QuestionCalculate $\left[\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}-\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}\right] \div 2$ .

Studdy Solution

STEP 1

Assumptions1. We are given two fractions and we need to subtract them. . After subtraction, we need to divide the result by.

STEP 2

First, we need to calculate the value of each fraction. The general formula for a fraction is $\frac{a}{b}$ where 'a' is the numerator and 'b' is the denominator.

STEP 3

Calculate the value of the first fraction.
$\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}$

STEP 4

Calculate the cube of the denominator in the first fraction.
$(3.0 \mathrm{~cm})^{3} =27 \mathrm{~cm}^{3}$

STEP 5

Now, divide the numerator by the calculated cube of the denominator in the first fraction.
$\frac{45.82 \mathrm{~g}}{27 \mathrm{~cm}^{3}} \approx1.697 \mathrm{~g/cm}^{3}$

STEP 6

Calculate the value of the second fraction.
$\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}$

STEP 7

Calculate the cube of the denominator in the second fraction.
$(0.859 \mathrm{~cm})^{3} \approx0.633 \mathrm{~cm}^{3}$

STEP 8

Now, divide the numerator by the calculated cube of the denominator in the second fraction.
$\frac{0.64 \mathrm{~g}}{0.633 \mathrm{~cm}^{3}} \approx1.011 \mathrm{~g/cm}^{3}$

STEP 9

Now that we have the values of both fractions, subtract the second fraction from the first.
$.697 \mathrm{~g/cm}^{3} -.011 \mathrm{~g/cm}^{3} \approx.686 \mathrm{~g/cm}^{3}$

STEP 10

Now that we have the result of the subtraction, divide this by2.
$\frac{0.686 \mathrm{~g/cm}^{3}}{2}$

STEP 11

Calculate the final result.
$\frac{0.686 \mathrm{~g/cm}^{3}}{} \approx0.343 \mathrm{~g/cm}^{3}$ So, the solution to the problem is approximately $0.343 \mathrm{~g/cm}^{3}$ .

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QuestionCalculate $\left[\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}-\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}\right] \div 2$ .

Studdy Solution

STEP 1

Assumptions1. We are given two fractions and we need to subtract them. . After subtraction, we need to divide the result by.

STEP 2

First, we need to calculate the value of each fraction. The general formula for a fraction is $\frac{a}{b}$ where 'a' is the numerator and 'b' is the denominator.

STEP 3

Calculate the value of the first fraction.
$\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}$

STEP 4

Calculate the cube of the denominator in the first fraction.
$(3.0 \mathrm{~cm})^{3} =27 \mathrm{~cm}^{3}$

STEP 5

Now, divide the numerator by the calculated cube of the denominator in the first fraction.
$\frac{45.82 \mathrm{~g}}{27 \mathrm{~cm}^{3}} \approx1.697 \mathrm{~g/cm}^{3}$

STEP 6

Calculate the value of the second fraction.
$\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}$

STEP 7

Calculate the cube of the denominator in the second fraction.
$(0.859 \mathrm{~cm})^{3} \approx0.633 \mathrm{~cm}^{3}$

STEP 8

Now, divide the numerator by the calculated cube of the denominator in the second fraction.
$\frac{0.64 \mathrm{~g}}{0.633 \mathrm{~cm}^{3}} \approx1.011 \mathrm{~g/cm}^{3}$

STEP 9

Now that we have the values of both fractions, subtract the second fraction from the first.
$.697 \mathrm{~g/cm}^{3} -.011 \mathrm{~g/cm}^{3} \approx.686 \mathrm{~g/cm}^{3}$

STEP 10

Now that we have the result of the subtraction, divide this by2.
$\frac{0.686 \mathrm{~g/cm}^{3}}{2}$

STEP 11

Calculate the final result.
$\frac{0.686 \mathrm{~g/cm}^{3}}{} \approx0.343 \mathrm{~g/cm}^{3}$ So, the solution to the problem is approximately $0.343 \mathrm{~g/cm}^{3}$ .

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QuestionCalculate [45.82 g(3.0 cm)3−0.64 g(0.859 cm)3]÷2\left[\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}-\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}\right] \div 2[(3.0 cm)345.82 g​−(0.859 cm)30.64 g​]÷2.

Studdy Solution

STEP 1

Assumptions1. We are given two fractions and we need to subtract them. . After subtraction, we need to divide the result by.

STEP 2

First, we need to calculate the value of each fraction. The general formula for a fraction isab\frac{a}{b}ba​where 'a' is the numerator and 'b' is the denominator.

STEP 3

Calculate the value of the first fraction.45.82 g(3.0 cm)3\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}(3.0 cm)345.82 g​

STEP 4

Calculate the cube of the denominator in the first fraction.(3.0 cm)3=27 cm3(3.0 \mathrm{~cm})^{3} =27 \mathrm{~cm}^{3}(3.0 cm)3=27 cm3

STEP 5

Now, divide the numerator by the calculated cube of the denominator in the first fraction.45.82 g27 cm3≈1.697 g/cm3\frac{45.82 \mathrm{~g}}{27 \mathrm{~cm}^{3}} \approx1.697 \mathrm{~g/cm}^{3}27 cm345.82 g​≈1.697 g/cm3

STEP 6

Calculate the value of the second fraction.0.64 g(0.859 cm)3\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}(0.859 cm)30.64 g​

STEP 7

Calculate the cube of the denominator in the second fraction.(0.859 cm)3≈0.633 cm3(0.859 \mathrm{~cm})^{3} \approx0.633 \mathrm{~cm}^{3}(0.859 cm)3≈0.633 cm3

STEP 8

Now, divide the numerator by the calculated cube of the denominator in the second fraction.0.64 g0.633 cm3≈1.011 g/cm3\frac{0.64 \mathrm{~g}}{0.633 \mathrm{~cm}^{3}} \approx1.011 \mathrm{~g/cm}^{3}0.633 cm30.64 g​≈1.011 g/cm3

STEP 9

Now that we have the values of both fractions, subtract the second fraction from the first..697 g/cm3−.011 g/cm3≈.686 g/cm3.697 \mathrm{~g/cm}^{3} -.011 \mathrm{~g/cm}^{3} \approx.686 \mathrm{~g/cm}^{3}.697 g/cm3−.011 g/cm3≈.686 g/cm3

STEP 10

Now that we have the result of the subtraction, divide this by2.0.686 g/cm32\frac{0.686 \mathrm{~g/cm}^{3}}{2}20.686 g/cm3​

STEP 11

Calculate the final result.0.686 g/cm3≈0.343 g/cm3\frac{0.686 \mathrm{~g/cm}^{3}}{} \approx0.343 \mathrm{~g/cm}^{3}0.686 g/cm3​≈0.343 g/cm3So, the solution to the problem is approximately 0.343 g/cm30.343 \mathrm{~g/cm}^{3}0.343 g/cm3.

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QuestionCalculate $\left[\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}-\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}\right] \div 2$ .

First, we need to calculate the value of each fraction. The general formula for a fraction is $\frac{a}{b}$ where 'a' is the numerator and 'b' is the denominator.

Calculate the value of the first fraction.
$\frac{45.82 \mathrm{~g}}{(3.0 \mathrm{~cm})^{3}}$

Calculate the cube of the denominator in the first fraction.
$(3.0 \mathrm{~cm})^{3} =27 \mathrm{~cm}^{3}$

Now, divide the numerator by the calculated cube of the denominator in the first fraction.
$\frac{45.82 \mathrm{~g}}{27 \mathrm{~cm}^{3}} \approx1.697 \mathrm{~g/cm}^{3}$

Calculate the value of the second fraction.
$\frac{0.64 \mathrm{~g}}{(0.859 \mathrm{~cm})^{3}}$

Calculate the cube of the denominator in the second fraction.
$(0.859 \mathrm{~cm})^{3} \approx0.633 \mathrm{~cm}^{3}$

Now, divide the numerator by the calculated cube of the denominator in the second fraction.
$\frac{0.64 \mathrm{~g}}{0.633 \mathrm{~cm}^{3}} \approx1.011 \mathrm{~g/cm}^{3}$

Now that we have the values of both fractions, subtract the second fraction from the first.
$.697 \mathrm{~g/cm}^{3} -.011 \mathrm{~g/cm}^{3} \approx.686 \mathrm{~g/cm}^{3}$

Now that we have the result of the subtraction, divide this by2.
$\frac{0.686 \mathrm{~g/cm}^{3}}{2}$

Calculate the final result.
$\frac{0.686 \mathrm{~g/cm}^{3}}{} \approx0.343 \mathrm{~g/cm}^{3}$ So, the solution to the problem is approximately $0.343 \mathrm{~g/cm}^{3}$ .