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nevsk [136]
3 years ago
11

An isosceles triangle has sides of length x, x, and y. in addition, assume the triangle has perimeter 24. (a) find the rule for

a function that computes the area of the triangle as a function of x.
Mathematics
1 answer:
ser-zykov [4K]3 years ago
8 0

Answer:

  A(x) = (24 -2x)√(6(x -6))

Step-by-step explanation:

Heron's formula for the area of a triangle in terms of sides a, b, and c is ...

  A = √(s(s -a)(s -b)(s -c))

where s is the semi-perimeter.

Here, we have s = 24/2 = 12, and a = b = x, c = 24-2x. So, the area is ...

  A = √(12(12 -x)(12 -x)(12 -(24 -2x)) = (12 -x)√(12(2x -12))

  A = 2(12 -x)√(6(x -6))

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il63 [147K]

A) The center of gravity of the two joined beams is;

<u><em>(x, y) = (25/44), (19/88)</em></u>

B) The gravitational torque on the joined beams about an axis through the corner is;

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We are given;

Mass of vertical beam; m₂ = 19 kg

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Length of vertical beam; L₂ = 1 m

A) Formula for center of gravity of the two joined beams is;

(x, y) = [(m₁x₁ + m₂x₂)/(m₁ + m₂)],  [(m₁y₁ + m₂y₂)/(m₁ + m₂)]

Where;

(x₁, y₁) is the <em>center of gravity</em> on the <em>horizontal beam</em>

(x₂, y₂) is the <em>center of gravity</em> on the <em>vertical beam</em>

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Plugging in the relevant values gives;

(x₁, y₁) = (2/2, 0)

(x₁, y₁) = (1, 0)

(x₂, y₂) = (0, L₂/2)

Plugging in the relevant values gives;

(x₂, y₂) = (0, 1/2)

(x₂, y₂) = (0, 0.5)

Thus, center of gravity of the 2 joined beams is;

(x, y) = [((25 × 1) + (19 × 0))/(25 + 19)],  [((25 × 0)  + (19 × 0.5)))/(25 + 19)]

(x, y) = (25/44), (19/88)

B) Formula for the gravitational torque on the joined beams about an axis through the corner is given as;

τ = (m₁g)x₁ + (m₂g)x₂

Plugging in the relevant values;

τ = (25 × 9.8)1 + (19 × 9.8)0

τ = 245 N.m

Read more at; brainly.com/question/14825257

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