(0,0)(1/3,7/3)
slope = (7/3 - 0) / (1/3 - 0) = (7/3) / (1/3) = 7/3 * 3 = 21/3 = 7 <==
<span>The maxima of a differential equation can be obtained by
getting the 1st derivate dx/dy and equating it to 0.</span>
<span>Given the equation h = - 2 t^2 + 12 t , taking the 1st derivative
result in:</span>
dh = - 4 t dt + 12 dt
<span>dh / dt = 0 = - 4 t + 12 calculating
for t:</span>
t = -12 / - 4
t = 3
s
Therefore the maximum height obtained is calculated by
plugging in the value of t in the given equation.
h = -2 (3)^2 + 12 (3)
h =
18 m
This problem can also be solved graphically by plotting t
(x-axis) against h (y-axis). Then assigning values to t and calculate for h and
plot it in the graph to see the point in which the peak is obtained. Therefore
the answer to this is:
<span>The ball reaches a maximum height of 18
meters. The maximum of h(t) can be found both graphically or algebraically, and
lies at (3,18). The x-coordinate, 3, is the time in seconds it takes the ball
to reach maximum height, and the y-coordinate, 18, is the max height in meters.</span>
Considering the given linear function, we have that:
- The change for each copy that he sells is of $120.
- If he sells no copies, he makes $2400.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
His payment for x copies bought is:
y = 120x + 2400.
Hence:
- The change for each copy that he sells is of $120, as the slope is of $120.
- If he sells no copies, he makes $2400, which is the y-intercept.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
2 real roots
Step-by-step explanation:
If the discriminant is >0 then the equation has 2 real roots
If the discriminant is =0 then the equation has 1 real roots
If the discriminant is <0 then the equation has 2 complex roots
since the discriminant is 4, it has 2 real roots
