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marta [7]
3 years ago
7

what is the approximate area of a regular pentagon with a side lenghtt of 6 feet and a distance from the center to a vertex of 6

feet
Chemistry
1 answer:
Degger [83]3 years ago
6 0
A regular pentagon may be divided into 5 congruent triangles.


If the side of the pentagon is 6 feet, each base of the triangles will be 6 feet.


If the distance from the center to a vertex is 6 feet, all the sides of the triangles will 6 feet.


So there are 5 congruent, equilateral triangles each with side equal to 6 feet.


The area one of those triangles is calculateb by:


base * height / 2


height ^2 = (side length) ^2 - (side length /2)^2 = 6^2 - 3^2 = 36 - 9 = 27


=> height = √(27) ≈ 5.2 feet


And, using area = base * height / 2 ,


area of a triangle = 6 feet * 5.2 feet / 2 = 15.6 feet^2


And the area of the entire pentagon equals 5 triangles ≈ 5 * 15.6 feet^2 = 78 feet^2


Answer: 78 feet^2
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If a solid line represents a covalent bond and a dotted line represents intermolecular attraction, which of these choices shows
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4 0
3 years ago
2000 minutes to hours dimensional analysis
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Answer:

33.33 h

Explanation:

You know that

1 h = 60 min

If you divide both sides by 60 min, you get the conversion factor: 1 h/60 min = 1.

If you divide both sides by 1 h, you get the conversion factor: 1 = 60 min/1 h.

Both are conversion factors because they both equal one and multiplying a measurement by one does not change its value.

You choose the conversion factor that gives you the correct dimensions for your answer. It must have the correct dimensions on top (in the numerator),

Thus, to convert 2000 min to hours, you use the conversion factor with “h” on the top.

\text{Time} = \text{2000 min} \times \dfrac{\text{1 h}}{\text{60 min}} = \textbf{33.33 h}

5 0
3 years ago
The daily output of stomach acid (gastric juice) is 1000 to 2000 mL. Prior to a meal, stomach acid (HCl) typically has a pH of 1
Semmy [17]

Answer:

B.) 2 HCl(aq) + CaCO₃(s) → CaCl₂(aq) + H₂O(l) + CO₂(g)

C.) 7.4 × 10² mL

D.) 2 HCl(aq) + Mg(OH)₂(aq) → MgCl₂(aq) + H₂O(l)

E.) 1.3 × 10³ mL

Explanation:

<em>The daily output of stomach acid (gastric juice) is 1000 to 2000 mL. Prior to a meal, stomach acid (HCl) typically has a pH of 1.49.</em>

We can calculate the concentration of H⁺ using the definition of pH.

pH = -log [H⁺]

[H⁺] = antilog -pH = antilog (-1.49) = 0.0324 M

Since HCl is a strong monoprotic acid, we can consider this to be the concentration of HCl as well.

<em>B.) One chewable tablet of the antacid Maalox contains 600 mg of CaCO₃. Enter the neutralization equation. Express your answer as a molecular equation including phases.</em>

The neutralization equation is:

2 HCl(aq) + CaCO₃(s) → CaCl₂(aq) + H₂O(l) + CO₂(g)

<em>C.) Given that one chewable tablet of the antacid Maalox contains 600 mg of CaCO₃, calculate the milliliters of stomach acid neutralized by two tablets of Maalox. Express the volume in milliliters to two significant figures.</em>

We can establish the following relations:

  • Each tablet has 600 mg (0.600 g) of CaCO₃.
  • The molar mass of CaCO₃ is 100.09 g/mol.
  • The molar ratio of HCl to CaCO₃ is 2:1.
  • The concentration of HCl is 0.0324 mol/L.

The mililiters of HCl that neutralize 2 tablets of Maalox are:

2Tablet.\frac{0.600gCaCO_{3}}{1Tablet} .\frac{1molCaCO_{3}}{100.09gCaCO_{3}} .\frac{2molHCl}{1molCaCO_{3}} .\frac{1000mLHCl}{0.0324molHCl} =7.4 \times 10^{2} mLHCl

<em>D.) The antacid milk of magnesia contains 400 mg of Mg(OH)₂ per teaspoon. Enter the neutralization equation. Express your answer as a molecular equation including phases.</em>

The neutralization equation is:

2 HCl(aq) + Mg(OH)₂(aq) → MgCl₂(aq) + H₂O(l)

<em>E.) Given that the antacid milk of magnesia contains 400 mg of Mg(OH)₂ per teaspoon, calculate the number of milliliters of stomach acid that are neutralized by 1 tablespoon of milk of magnesia. (1 tablespoon = 3 teaspoons.)Express the volume in milliliters to two significant figures.</em>

We can establish the following relations:

  • 1 tablespoon = 3 teaspoons
  • 1 teaspoon contains 400 mg (0.400 g) of Mg(OH)₂
  • The molar mass of Mg(OH)₂ is 58.32 g/mol.
  • The molar ratio of HCl to Mg(OH)₂ is 2:1.
  • The concentration of HCl is 0.0324 mol/L.

The mililiters of HCl that neutralize 1 tablespoon of milf of magnesia are:

1Tablespoon.\frac{3Teaspoon}{1Tablespoon} .\frac{0.400gMg(OH)_{2}}{1Teaspoon} .\frac{1molMg(OH)_{2}}{58.32gMg(OH)_{2}} .\frac{2molHCl}{1molMg(OH)_{2}} .\frac{1000mLHCl}{0.0324molHCl} =1.3 \times 10^{3} mLHCl

4 0
3 years ago
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