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gizmo_the_mogwai [7]
3 years ago
10

Leave answer in exact form unless otherwise indicated.

Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
6 0

Answer:

Area segment = 32/3 π - 16√3 inches²

Step-by-step explanation:

∵ The length of the chord is 8"

∵ The length of the radius of the circle is 8"

∴ the central angle of the segment is π/3 (60° the chord and the radii

   formed an equilateral triangle)

∵ The area of the segment = area the sector - area Δ

∵ Area sector = 1/2 r²Ф

∵ r = 8" and Ф = π/3

∴ Area sector = 1/2 (8²) (π/3) = 32/3 π inches²

∵ Area Δ = 1/4 s²√3

∵ The length of the side is 8"

∴ Area Δ = 1/4 (8²) √3 = 16√3 inches²

∴ Area segment = 32/3 π - 16√3 inches²

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Answer: choice A. 40 liters

====================================

Explanation:

x = number of liters of the 50% alcohol solution

If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).

So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below

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6 0
3 years ago
Circle V is shown. Line segment T V is a radius with length 14 feet.
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We have been given graph of circle V with radius 14 feet. We are asked to find the area of the circle V.

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Upon substituting r=\text{14 ft} in above formula, we will get:

A=\pi(14\text{ ft})^2

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A=\pi\cdot 196\text{ ft}^2

A=196\pi\text{ ft}^2

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Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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