The population, P in thousands of a resort community is shown by P(t)= 500t/2t^2+9'

where t is the time in months since city council raised property taxes.

Find the interval on which the population was 40,000 or greater

t ≤ 4.24

Step-by-step explanation:

P(t) ≥ 40000 implies

500t/(2t²+9) ≥ 40000

Multiplying through by t², we have

500t ≥ 40000(2t²+9)

500t/40000 ≥ 2t²+9

Collecting like terms

0.0125t  ≥ 2t²+9

0  ≥ 2t²+ 9 - 0.0125t

2t²+ 9 - 0.0125t  ≤ 0

2t²- 0.0125t + 9 ≤ 0

Using the quadratic formula,

The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)

So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0

(t - 0.00313)² - 4.24² ≤ 0

(t - 0.00313)² ≤ 4.24²

taking square-root of both sides,

√(t - 0.00313)² ≤ √4.24²  

t - 0.00313 ≤ 4.24

t ≤ 4.24 + 0.00313

t ≤ 4.24313 ≅ 4.24

t ≤ 4.24

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5