Aphotograph has a length that is 3 inches longer than its width, x. so its area is given by the expression x(x+3) square inches. if the area of the photograph is 70 square inches, what is the length of the photograph?
the length of the photograph ?

The length of the photograph is     10     inches.

Explanation:

Given, Width of a photograph is x.  

Length of the photograph is 3 inches longer than its width. i.e. x + 3.

Area of the photograph = x(x+3)

If its area is 70 square inches, then  

x(x+3)=70

x(x-7)+10(x-7)=0

(x+10)(x-7) =0

x+10=0; x-7 = 0

x = -10 and x = 7

Width of the photograph must not be in negative value. So, we can ignore –10.

Therefore, width of the photograph, x = 7 inches.

Now, the length of the photograph = 7 + 3 = 10 inches.

Thus, the required length of the photograph is 10 inches.

(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.