Baseball Cubes
How do you solve these math problems?
For all real numbers, f(x) = (x^2+ 1)/ 2. If f(a) = 25 and f(11) = b, which of the following could be the value of b – a?
a) -14
b) 36
c) 68
d) 77
e) 86
The number of baseball cards in Caleb’s collection doubles every three months.If after 9 months he has b baseball cards, then an expression for the number of baseball cards in his collection after y years is given by
a) (2^y)(b)
b) (2^4y – 3)(b)
c) (2^4y)(b)
d) (2b^4y-3)
e) (2^y)(b^y-3)
3 identical cubes,each with edges of length 8, are to be cut into a total of 384 identical rectangular solids of length 4. If the width and height of each solid are integers, what is the surface area of each solid?
a) 4
b) 8
c) 12
d)16
e) 18
c) 68
f(a) = 25
f(a) = (a^2 + 1)/2
a^2 + 1/2 = 25
a^2 + 1 = 50
a^2 = 49
a = ±7
f(11) = b
b = (11^2 + 1)/2
= 122/2
= 61
b – a = 61 – (+ 7) = 54 or 68
b – a = 61 – (1 7) = 68
The answer that fits is c) 68
b) (2^4y – 3)(b)
Set card 1 to t = 0
t = 3 there’s 2
t = 6 there’s 4
t = 9 there’s 8
And so on until at t = 24there’s 256
The only one that fits is b) (2^4y – 3)(b).
e) 18
V of the rectangles = V of the 3 cubes
e^3
= 8^3
= 512*3
= 1536
384 of them means each must have a volume of 4 (1536/384).
Length L = 4
W width and H height both = 1
2LW + 2WH + 2LH
= 2(4*1) + 2(1*1) + 2(4*1)=18
Ice Cube Baseball
