math (combination)
There are 2 friends who won't come together. (2C1)(9C4) only counts the times in which one of those 2 friends are invited. There are 9C5 ways to invite neither of those 2 friends.
math (combination)
Denote n choose k by nCk. nCk = n!/(k!(n-k)!) a. 9 of the friends can attend separately 2 must attend together There are 9C5 ways to not invite the married couple. There are 9C3 ways to invite the married couple and 3 other friends. Total: 9C5 + 9C3 b. 9 of the friends will at...
Math (combination/permutation)
The book solution undercounts because there are 12 ways to fix the first member of A, and 8 ways to fix the first member of B. However, computing 12*C(11,3)*8*C(7,3) overcounts by making the first member of A and B distinctive. The correct solution is the same as the first pro...
calculus
For a cone, V = (1/3)(pi)(r^2)(h). But h=3r, so V = (pi)r^3. Differentiate with respect to time. dV/dt = (3pi)(r^2)(dr/dt) dr/dt = (3pi)(r^2)/(dV/dt)
related rates problem-calculus
Edit: actually we're given dr/dt and SA. Since dV/dt = 4(pi)r^2(dr/dt) and SA = 4(pi)r^2, dV/dt = SA(dr/dt).
related rates problem-calculus
The balloon is spherical, so V = (4/3)(pi)r^3 SA = 4(pi)r^2 Differentiate both with respect to time. dV/dt = 4(pi)r^2(dr/dt) dSA/dt = 8(pi)r(dr/dt) We're given the rate of change in SA and need to find the rate of change in volume. Let's write an equation for it. (dV/d...
Math
The ladder is the hypotenuse of a right triangle, with the sides being the ground and the wall. By Pythagorean Theorem, a^2 + b^2 = c^2. c, the length of the ladder, is constant. Take b to be the ladder's height on the wall, and a the distance on the ground from the wall. ...
geometry
search for cylinder on wikipedia; select cylinder (geometry)
math
You can simplify log((a^3)sqrt(ab)/(ab^2)) to log((a^2.5)/(b^1.5)). = 2.5log(a) - 1.5log(b) But you cannot evaluate this without knowing log(a) and log(b).
logarithms
You posted an expression, but no question.
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