If the cost see for manufacturing x units of a certain product is given by c=x squared +25x +40 find the number of units manufactured at a cost of 9390

  85 units

Step-by-step explanation:

Fill in the given value and solve for x.

  c = x² +25x +40

  9390 = x² +25x + 40

  x² +25x -9350 = 0 . . . . . . rearrange to standard form

  (x +110)(x -85) = 0 . . . . . . . factor the quadratic

The positive solution is the value of x that makes a factor be zero: x = 85.

The number of units manufactured at a cost of 9390 is 85 units.

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There are several ways you can solve the quadratic. There appear to be no restrictions here, so we used a graphing calculator to assist. It shows the zeros of the equation to be -110 and +85, so the factors are as shown above.

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The prime factorization of 9350 is ...

  9350 = 2 · 5² · 11 · 17

so there are 24 divisors:

  1, 2, 5, 10, 11, 17, 22, 25, 34, 50, 55, 85, 110, 170, 187, 275, 374, 425, 550, 850, 935, 1870, 4675, 9350

We're looking for two factors that differ by a relatively small amount, so we would start with the factors near the middle of this list:

  9350 = 85·110 . . . . . these differ by 25, so are the factors of interest

These let you rewrite the 25x term so you can factor by grouping:

  x² +110x -85x +9350 = 0 . . . . rewrite the middle term

  x(x +110) -85(x +110) = 0 . . . . . factor each pair of terms

  (x -85)(x +110) = 0 . . . . . . . . . . factor out the common factor

The solution of interest is x = 85.

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You can also "complete the square"

  x² +25x = 9350

  x² +25x + 156.25 = 9506.25

  (x² +12.5) = 97.5² . . . . . rewrite as squares

  x = 97.5 -12.5 = 85 . . . . take the positive square root

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2