1. Find the exact value for area of the triangle with the side lengths 5, 9, and 10.

area = 6  units²

Step-by-step explanation:

Given the 3 sides of a triangle, we can use Hero's formula to calculate the area (A)

A =

where s s the semi perimeter and a, b , c the sides of the triangle

let a = 5, b = 9 and c = 10

s = = = = 12

A =

   =

   =

   =

   =  6 units²

Step-by-step explanation:

a = 5 units ; b = 9units ; c = 10 units

Semi perimeter = (a+b+c)/2 = (5+9+10)/2 = 24/2 = 12 units

s-a = 12 -5 = 7 units

s -b = 12 - 9 = 3 units

s-c = 12- 10 =2 units

=6*3.742 = 22.452

= 22.45 square units

(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.