Amissile is launched from the ground. its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds. after 1 second, the missile is 130 feet in the air; after 2 seconds, it is 240 feet in the air. find the height, in feet, of the missile after 11 seconds in the air.

h(11) = 330 ft

Step-by-step explanation:

We have 2 points with which to find the equation of the projectile.  The standard form for the quadratic, which is the function that models parabolic motion, is

The problem tells us that the missile was launched from the ground, so c (the initial height of the missile) is 0, so we can literally disregard the c in the standard form and use the 2 points to solve for a and b:

At the point (1, 130) we fill in the standard form to get:

which gives us **130 = a + b**.  Now on to the second point, (2, 240):

which gives us **240 = 4a + 2b**

Solve the first **equation for a:

a = 130 - b

and sub that into the second **equation:

240 = 4(130 - b) + 2b and simplify to

140 = b

Now that we know b, we can sub it in to solve for a:

a = 130 - b so a = 130 - 140 so a = -10.  Therefore, the equation of the projectile's motion is

(If you knew your Physics, you'd know that -10x^2 is replacing the pull of gravity in the metric system which is -9.8x^2; that's how we know that this is the correct equation.)

Subbing in 11 for x:

gives us that h(11) = 330 feet

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560