Question

#1 The area of a rectangular deck, in square meters, is given by the polynomial 40p^2 + 24p.

Answer 1

Answer:

1.

a. 5p + 3

b. 26p + 6

2.

a r = (v ÷(pi)h)½

b. r = 3.74 to the nearest hundredth

Step-by-step explanation:

1.

Area of deck = 40p² + 24p

Width of deck = 8p

Area = length × width(breadth)

a. Area = length × width

40p² + 24p = length × 8p

Factorise out 8p from the left hand side

8p(5p + 3) = length × 8p

Divide both sides by 8p

5p + 3 = length

b Perimeter of deck = 2 (length + width)

"" = 2(5p+3 + 8p)

"" = 2 (13p + 3)

"" = 26p + 6

2.

Volume = 200 mm³

Height = 17mm

a. isolate the r in the equation v = (pi)r²h

v = (pi)r²h

Divide both sides by (pi)h

v ÷ (pi)h = r²

Take the square roots of both sides

(v ÷ (pi)h)½ = r

b. find r using your answer in a.

r = (v ÷ (pi)h)½

r = (200 ÷ ( 22/7 × 17))½

r = (200 ÷ 53.4286)

r = 3.7433

r = 3.74 to the nearest hundredth