For years of 1980 to 1990, the number of mountain owners m ( in millions ) in the US can be approximated by the model m=.377t^2 – 2.265t + 3.962,3 ≤ t ≤ 10 where t = 3 represents 1983. 1. In which year did 2.5 million people own mountain bikes? 2. In what year was the number of mountain bike owners at a minimum? I'll really appreciated if it's was posible to explain how did you got the answer. Thank you

The answers to the question are

1. 1985

2. 1983

Step-by-step explanation:

To solve the question we note that the equation is

To find the the year in which 2.5 milion people own mountain bikes we have

to equate to 2.5 million therefore

= 2.5 or 0.377·t² - 2.265·t + 3.962-2.5 = 0

0.377·t² - 2.265·t + 1.462 = 0 which gives (t-0.736)×(t-5.272)×0.377 =  0

That is t = 0.736 or 5.272 and the range is 3 ≤ t ≤ 10

the answer is 5.272 year or

1985

2. For the minimum mountain bike owners we have

0.377·t² - 2.265·t + 3.962 = minimum when  0.377·t² - 2.265·t + 3.962 = 0

Therefore we have

0.377·t² - 2.265·t + 3.962 = 0 or Solving with the quadratic formula we have

(2.265±√(2.265²-4×0.377×3.962))÷(2×0.377) Which is indeterminate

hence we differentiate the expression to get and equate to zero to get the minimum

0.754·t -2.265 =0 which gives t = 2.265/0.754 = 3.003979

or the 3rd year. That is

1983

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

answer: y=4000x+14000

step-by-step explanation: