1. the 24 students in Anne's class.
2. 1 of the 24 students is chosen at random.
3. 1/24 or 0.04166666666...
4. Unlikely, due to her small, but present, chances of 1/24.
They are traveling at right angles to each other so we can say one is traveling north to south and the other west to east. Then we can say that there positions, y and x are:
y=150-600t x=200-800t
By using the Pythagorean Theorem we can find the distance between these two planes as a function of time:
d^2=y^2+x^2, using y and x from above
d^2=(150-600t)^2+(200-800t)^2
d^2=22500-180000t+360000t^2+40000-320000t+640000t^2
d^2=1000000t^2-500000t+62500
d=√(1000000t^2-500000t+6250)
So the rate of change is the derivative of d
dd/dt=(1/2)(2000000t-500000)/√(1000000t^2-500000t+6250)
dd/dt=(1000000t-250000)/√(1000000t^2-500000t+6250)
So the rate depends upon t and is not a constant, so for the instantaneous rate you would plug in a specific value of t...
...
To find how much time the controller has to change the airplanes flight path, we only need to solve for when d=0, or even d^2=0...
1000000t^2-500000t+62500=0
6250(16t^2-8t+1)=0
6250(16^2-4t-4t+1)=0
6250(4t(4t-1)-1(4t-1))=0
6250(4t-1)(4t-1)=0
6250(4t-1)^2=0
4t-1=0
4t=1
t=1/4 hr
Well technically, the controller has t<1/4 because at t=1/4 impact will occur :)
Assuming that this problem is asking about a cylinder, the volume can be found using the formula (pi)(r)^2 * h (area of the circle * height) and the surface area can be found using the formula (2)(pi)(r)h (circumference of the circle * height).
Volume = (pi)(16)^2 * 27 = 21,714.688 in^3
Surface Area = (2)(pi)(16) * 27 = 2,714.336 in^2
Answer:
$179.20
Step-by-step explanation:
use the formula retail price = original price + markup
Step One: Convert 28% to a decimal
--> 0.28
Step two: Plug all the numbers into the equation
--> $140 + $140 x 0.28 = $179.20
Give brainliest if this was helpful! Thanks! Have an amazing day!
