Tutor profile: Michael K.
Subject: Basic Math
Cleo wants to steal cookies from the cookie jar however she knows her parents would notice if she takes more than 10 percent of the cookies. Cleo has 3 friends and wants to divide the cookies evenly between her and her friends. If the cookie jar has 90 cookies, how many cookies should Cleo steal to maximize the amount of cookies she and her friends get without getting caught?
Cleo can steal up to 10% of 90 cookies without being caught, which equals 9 cookies. Since she has 3 friend, if you include Cleo that makes 4 people to divide the cookies amongst. However 9 doesn't divide equally by 4. Therefore, Cleo should only steal 8 cookies which she could then divide by 4 and each person would then get 2 cookies.
An airplane is tilted at a 45 degrees angle from the vertical while flying in a horizontal circle above the ground. Which type of force on the plane is generating the circular motion, which direction is this force pointing and which object is applying this force on the plane?
Lets start by stating that "centripetal force" is not the right answer. Centripetal force is not an actual force. When an object (like a plane) is moving in circular motion, some forces acting on the plane would be pointing towards the center of the circle - we call the sum of those forces the centripetal force however this doesn't tell us anything about the type of these forces. We don't know if those are gravity, electric, magnetic, normal, friction or tension forces. In our airplane problem it's relatively easy to identify the gravity force (exerted by the earth on the plane) as pointing downwards. This clearly cannot be the force generating the circular motion because it has no component pointing in the direction of the center of the circle made by the airplane's motion. The force that IS generating the circular motion is the LIFT FORCE exert by the AIR on the airplane. The direction of this lift force is 45 DEGREES FROM THE VERTICAL - it has a vertical component (balancing the gravity force so that the plan can stay horizontal) and a horizontal component pointing towards the center of the circle. It's the latter component that we call the centripetal force which is generating the circular motion. The lift force is a type of normal force by the way since it results from the air touching (and pushing up) the plane.
Pizza A has radius R and price X. Pizza B has smaller radius r and cheaper price Y. Use the variables above to express whether Pizza A is a smart use of your money.
When considering which pizza to buy, we should think about how much money we are spending per area of food (technically it should be per volume of food but it is safe to assume the thickness of the Pizzas are identical unless stated otherwise). Algebraically this becomes: (Pizza A price)/(Pizza A area) < (Pizza B price)/(Pizza B area) Area of pizza A: pi*R^2 Area of pizza B: pi*r^2 Therefore this becomes: (X)/(pi*R^2) < (Y)/(pi*r^2) We can cancel out pi from both sides of the inequality: X/R^2 < Y/r^2 That is our final answer :)