15 second calculations
Solve for x.
x99999999 = x
x = 0, ±1
099999999 = 0
199999999 = 1
(-1)99999999 = -1
Let y = -4πi√5
Simplify in terms of x and x'
47{ln[sec3(x)+[(d/dx)(e2π-logx√y)]-cos4y[(d2/dx2)4y√π]-72y2x+(4/√y)}0
Where x≠(π/2)±πn, and n∈ℤ
Answer: 47
Anything to the power of zero is one.
47{x∼y}0
47(1)
47
Solve for x.
4x2 - 8 = 37 - x2
4x2 - 8 = 37 - x2
5x2 - 8 = 37
5x2 = 45
x2 = 9
x = 3 or -3
Solve:
1++-+-1--+-1--1-------0
Answer: 2
1++-+-1--+-1--1-------0
1 + 1 - 1 + 1
2 - 1 + 1
1 + 1
2
A cube's surface area is 24cm2.
What is its volume?
The volume is 8cm3.
A cube has 6 congruent faces, meaning each face is a square whose area is 24/6 or 4cm2.
Square root the area to find the side length, and since all side lengths are the same in a cube, the volume can be found with 2cm x 2cm x 2cm.
You have invented a new function, denoted by
pk(x)
where pk(2) = √5 and pk(5) = 19.5
Find the value of the following:
pk[ (15 - 5) / 5] - [ pk(2) ]2
pk[ (10) / 5 ] - [ (√5) ]2
pk(2) - 5
(√5) - 5
The answer is √5 - 5.
Multiple Choice:
What is the square root of 790321?
A) 905
B) 889
C) 866
D) 907
C) 889
The unit digit of the square is completely dependent on the unit digit of the square root.
Look at the last digit of 790321. For an integer to have its square end in 1, the unit digit (last digit) must be either 1 or 9 (as 12=1, 92=81)
For example, the square root could not end in 7 because when you multiply it out, the square would end in 9 (as 72=49)
Hence the answer must be 889.
The square root of a negative number is undefined, and is denoted by a real number multiplied by √(-1) or i.
Therefore, i2 = -1 and √(-9) = 3i
Solve the following in terms of i:
[ √(-100) ] [ i3 + i - 1/2 ] - 42i8 + 13i7
(10i) [ i2i + i - 1/2 ] - 42i2i2i2i2 + 13i2i2i2i
10ii(-1) + 10ii - 10i (1/2) - 42(-1)4 + 13(-1)3i
-10(-1) + 10(-1) - 5i - 42 + (-13)i
10 - 10 - 5i - 42 - 13i
The answer is -18i - 42 or -6 ( 3i + 7)
The default base system is base 10. In other number systems, such as base 2 (binary) or base 8, counting resets and another digit is added when a certain number is reached (similar to how after 9, the digits reset to 0 and a 1 is added to create 10).
Ex. In binary, 2 is denoted by 10, 3 by 11, and 4 by 100.
In a certain number system, the number 31 is denoted by "43".
What base system is this? Assume the base of the system is a natural number. (1, 2, 3, ...)
Base 7
Since the new number outside base 10 is larger, the base system must be of a number less than 10.
If we replace 43 with 40 (subtract 3 temporarily), this must be the fourth multiple of the base as the unit digit has been newly replaced with zero. In base 10, the base is evident when we divide 40 by 4 and end up with 10, but we can solve for this value in an unknown base by comparing it to its base 10 counterpart, being 31-3=28.
28/4=7
Base 7.