Answer:
0.5 < t < 2
Step-by-step explanation:
The function reaches its maximum height at ...
t = -b/(2a) = -16/(2(-16)) = 1/2 . . . . . . where a=-16, b=16, c=32 are the coefficients of f(t)
The function can be factored to find the zeros.
f(t) = -16(t^2 -1 -2) = -16(t -2)(t +1)
The factors are zero for ...
x = -1 and x = +2
The ball is falling from its maximum height during the period (0.5, 2), so that is a reasonable domain if you're only interested in the period when the ball is falling.
Answer:
x = 45
Step-by-step explanation:
180 = (2x + 45) + x
135 = 2x + x
135/3 = 3x/3
45 = x
Answer:
will be inequality which shows the times there will be more than 10 gallons in the barrel.
Step-by-step explanation:
To determine:
Write an inequality showing the times there will be more than 10 gallons in the barrel.
Information Fetching and Solution Steps:
- Skylar is filling a barrel with water.
- The graph shows the relationship between time in minutes and the gallons of water in the barrel.
As the questions asks to determine the inequality showing the times there will be more than 10 gallons in the barrel.
For inequalities with 'more than', we use the 'greater than' symbol.
The graph shows that at time 15 minutes, the number of gallons of water is being shown as 10. As we have to determine the inequality for the time there will be more than 10 gallons in the barrel. So, time must be greater than 15 when there will be more than 10 gallons in the barrel.
If time is represented by 't', then the inequality showing the times there will be more than 10 gallons in the barrel will be:
Therefore, will be inequality which shows the times there will be more than 10 gallons in the barrel.
<h3>
Answer: 658.3</h3>
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Explanation:
The adjacent complementary angle to that 28 degree angle is 62 degrees because 62+28 = 90.
If the reference angle is the upper acute angle 62 degrees, then the y is the opposite leg and the side 350 is the adjacent leg.
Use the tangent ratio
tan(angle) = opposite/adjacent
tan(62) = y/350
350*tan(62) = y
y = 350*tan(62)
y = 658.254262871217
y = 658.3
Note that the 2nd equation can be re-written as y=8x-10.
According to the second equation, y=x^2+12x+30.
Equate these two equations to eliminate y:
8x-10 = x^2+12x+30
Group all terms together on the right side. To do this, add -8x+10 to both sides. Then 0 = x^2 +4x +40. You must now solve this quadratic equation for x, if possible. I found that this equation has NO REAL SOLUTIONS, so we must conclude that the given system of equations has NO REAL SOLUTIONS.
If you have a graphing calculator, please graph 8x-10 and x^2+12x+30 on the same screen. You will see two separate graphs that do NOT intersect. This is another way in which to see / conclude that there is NO REAL SOLUTION to this system of equations.
