Please answer all questions:

Explain why triangles are often used to build bridges, roofs, buildings, and other structures.

Which properties of a triangle make it a desirable geometric shape for these applications? Which type of triangle is best?

Why is the triangle preferred over other types of polygons? Explain.

Triangles and architecture

Step-by-step explanation:

Triangles are effective tools for architecture and are used in the design of buildings and other structures as they provide strength and stability. ... The most sturdy of the triangles are equilateral and isosceles; their symmetry aids in distributing weight.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

#12 the answer is the third option