Homework Statement
You should shoot a basketball at the angle ##\theta## requiring minimum speed. Avoid line drives and rainbows. Shooting from (0, 0) with the basket at (a, b), minimize ##f(\theta)= 1/(a \sin (\theta) \cos (\theta) -b \cos^2 (\theta))##.
(a) If b =0 you are level with the...
You're absolutely right. I forgot the passengers in the plane. I fixed the solution and the end result equation will be ##y=\frac{2h}{L^3}x^3+\frac{3h}{L^2}x^2## and with this, the passenger will land safe and sound. :D https://www.desmos.com/calculator/5ah7z7cs11
Since I'm considering only the ##[-L,0]## interval, I would say that ##dy\over dx##(the limit is also one-sided) is negative for that point because the plane is going down to land. I think you're suggesting that the path of the plane before ##x=-L## is a straight horizontal line, then it starts...
The solution I typed however didn't assume ##dy\over dx## =0 at ##(-L, h)##. I'm only considering ##y =-\frac{h}{L^3}x^3## over the interval ##[-L, 0]## for the path of the plane.
Homework Statement
A plane starts its descent from height ##y =h## at ##x = -L## to land at ##(0,0)##. Choose ##a, b, c, d## so its landing path ##y =ax^3 + bx^2 + cx + d## is "smooth". With ##\frac{\mathrm {d}x}{\mathrm {d}t} = V =##constant, find ##\frac{\mathrm {d}y}{\mathrm {d}t}## and...
This one I understand as this is how ##p(x)## was defined.
I don't understand this one. I understand since my time is worth 10$/hour and that I want to get the $1000 scholarship, I wouldn't want to spend more than 100 hour writing for the scholarship. If I spend an extra hour on that...
Homework Statement
You are applying for a ##\$1000## scholarship and your time is worth ##\$10## an hour. If the chance of success is ##1 -(1/x)## from ##x## hours of writing, when should you stop?
Homework Equations
Let ##p(x)=1 -(1/x)## be the rate of success as a function of time, ##x##...
Forgive me for being inept at this but I don't understand what you said. Are you saying an example is enough to justify the current truth table of the conditional?
Why do we need to consider in the case(or even all of the cases from the truth table) where the antecedent and consequent of the statement are false to be a true statement so that our mathematical logic checks out? I've been seeing a lot of people trying to justify this by providing examples...
So if one knows the definition(truth values) of the conditional, one can deduce that it is true for any values of ##x##. But the author asserted this before he had completely determined the truth values of the conditional. How would one interpret what he meant given that the truth values hadn't...
I'm reading Velleman's book titled "How to Prove it" and I'm very confused when I'm reading about conditional statements. I understand that there exists some issue with the conditional connective and I accept that because that's the cost of espousing a truth-functional view. I came here to ask...