11/15 + 7 ⇒ rational ⇒ the sum of two rationals is always rational
√14+13 ⇒ irrational ⇒ the sum of a rational and an irrational is always irrational
30×√6 ⇒ irrational ⇒ the product of a nonzero rational and an irrational is always irrational
11/12 × 7/15 ⇒ rational ⇒ the product of two rationals is always rational
<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>
The answer is between $175 and $295. The standard deviation rule tells us that for distributions that have the normal shape, approximately 99.7% of the observations fall within 3 standard deviations of the mean. Indeed, 175 = 235 − 3 * 20 and 295 = 235 + 3 * 20 are exactly 3 standard deviations below and above the mean, respectively.
$4225 first year
$2746.25 second year
$1785.0625 third year
