ijeomaokoro9488
09.06.2021 •
Mathematics
2x - y = 7 find the x and y intercept of each equation. graph the equation using its intercepts.
Solved
Show answers
More tips
- H Health and Medicine Where is the appendix located?...
- S Style and Beauty How to Properly Tie a Tie: 5 Simple Steps...
- L Leisure and Entertainment How to Make a Crab Trap in Just a Few Minutes...
- H Health and Medicine How Much Does Abortion Cost? Expert Answers and Insights...
- S Sport How to Build Arm Muscles? Effective Exercises and Tips...
- H Health and Medicine When can it be said that a person has a normal pulse?...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
Answers on questions: Mathematics
- M Mathematics What are the slopes of the perpendicular lines? 1: y=-5/2x-8 2: y=5x 3: y=3x-8...
- M Mathematics Gillian had 76 dolphin stickers. she gave 4 stickers each to 7 friends. how many stickers does gillian have left...
- M Mathematics Easy for the right person! tons of points! write these functions as numbers instead of words a. this function adds 3 to the input number b. this function adds 3 to the input...
- M Mathematics The base of a cube is parallel to the horizon. if the cube is cut by a plane to form a cross section, under what circumstances would it be possible for the cross section to...
- M Mathematics Which of the following correctly describes the sum below? a. rational b. neither rational nor irrational c. a combination of both rational and irrational d. irrational...
- M Mathematics Acake has a circumference of 25 1/7 inches. what is the area of the cake? use 22/7 to approximate pi...
- M Mathematics A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function? y = –3x, y = equals StartFraction x Over 3 EndFraction. y =...
- M Mathematics Solve the equation for x. (x - 4) - (x + 7) = 8x a. -11/8 b -1/8 c -11/2 d -11/4...
- M Mathematics Y=-7x+10 in standard form...
- M Mathematics If 9x - 3 = 4, what does 9x - 2 = ?...
Ответ:
Ответ:
The times are t = 9, t = 10, t = 11 and t = 12
Step-by-step explanation:
For the train to be more than 16 km South and since south is taken as negative,
d(t) > -16
t³ - 9t² + 6t > -16
t³ - 9t² + 6t + 16 > 0
Since -1 is a factor of 16, inserting t = -1 into the d(t), we have
d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)
So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16
Factorizing t² - 10t + 16, we have
t² - 2t - 8t + 16
= t(t - 2) - 8(t - 2)
= (t -2)(t - 8)
So t - 2 and t - 8 are factors of d(t)
So (t + 1)(t -2)(t - 8) > 0
when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0
when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0
when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0
when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0
Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8
Since t ∈ (0, 12]
In the interval 0 < t < 2 the only value possible for t is t = 1
d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2
Since d(1) < -16 this is invalid
In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.
So,
d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km
d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km
d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km
d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km