Answer:
maximum height is 4.058 metres
Time in air = 0.033 second
Step-by-step explanation:
Given that the equation height h
h = -212t^2 + 7t + 4
What is the toy's maximum height?
Let us assume that the equation is a perfect parabola
Time t at Maximum height will be
t = -b/2a
Where b = 7 and a = - 212
t = -7/ - 212 ×2
t = 7/ 424 = 0.0165s
Substitute t in the main equation
h = - 212(7/424)^2 + 7(7/424) + 4
h = - 0.05778 + 0.115567 + 4
h = 4.058 metres
Therefore the maximum height is 4.058 metres
How long is the toy in the air?
The object will go up and return to the ground.
At ground level, h = 0
-212t^2 + 7t + 4 = 0
212t^2 - 7t - 4 = 0
You can factorize the above equation and pick the positive time t since time can't be negative
Or
Since we have assumed that it's a perfect parabola,
Total time in air = (-b/2a) × 2
Time in air = 0.0165 × 2 = 0.033 s
Answer:
The first choice is the one you want
Step-by-step explanation:
First thing you need to know about this greatest integer graph is that it is aptly called a step graph. It literally looks like stair steps on your calculator: short horizontal lines that are not connected vertically. Really cool graph.
Second thing you need to know is about transformations of functions. ANY side-to-side movement in ANY function will be in a set of parenthesis (or absolute value symbols, or under a radical sign, or inside the greatest integer brackets, etc.) and ANY up or down movement will be either added or subtracted. Added means you move the function up from its starting position, subtracting means you move the function down from its starting position. Since we have no numbers inside the greatest integer brackets, there is no side-to-side movement. Since there is a "-2" after the brackets, we are moving the whole function down.
If you do not know how to graph these without a calculator and you have no idea what this graph looks like, I recommend going to your calculator to see it. First, call up your "y = " window. Next, hit 2nd-->0 (catalog), then hit the x^2 button (this will take you to the letter I in the catalog). Scroll down til you see "int( " and hit that button. It will take you back to the "y = " window. Enter an x after that set of parenthesis and then close it, then hit " - 2 " and then "graph". Your steps should begin to appear. Notice that the horizontal line between x = 0 and x = 1 is at y = -2. The parent graph has this line between x = 0 and x = 1 on y = 0. The -2 in ours moved the graph down from y = 0 to y = -2
Summing up, the first choice is the one you want as your answer.
Answer:
this looks extremely hard im only in middle school and we have not learned this yet
Step-by-step explanation:
306 / 8.5 = 36 miles per hr
at 9.1 hrs....
36 * 9.1 = 327.6 miles <==
or this way...
306 / 8.5 = x / 9.1
cross multiply
8.5x = 2784.6
x = 2784.6 / 8.5
x = 327.6 miles
Answer:
Part 1) Descending Rate = -2,000 ft/min
Part 2) Starting altitude value is 33,000 ft
Part 3) The linear equation for the plane's altitude (y) as a function of time (x) is: 
Part 4) The information not used for the equation is that the plane was travelling for 4 hours to cover 1800 miles before starting the descent
Step-by-step explanation:
Part 1)
The rate at which the airplane descends is given by the difference between final and initial altitude (17,000 ft-33,000 ft) divided the elapsed time (8 minutes):
Part 2)
When graphing the descent (that is the plane's altitude as a function of time), the starting value for the altitude should be 33,000 ft
Part 3)
We can build the equation of the plane's altitude as a function of time in slope y-intercept form y = m x + b
by noticing that the slope "m" stands for the rate of descent that we found in part 1), and then using the information that at time zero (when the plane starts its descent), its altitude is 33000 ft:
with this information about the intercept "b", we can write the final expression for the plane's altitude as a function of time during its descent as:
Part 4)
The information that was not used to write the descent equation was the initial details about how long the plane traveled (4 hours) and for 1800 miles.
