Examples of Math Problems

Saturday, November 23, 2013

Please help me solve this equation : -1 - |-2(2)|

-1 - |-2(2)|
is the same as...

%0D%0A-1-abs%28-4%29=-1-4=-5%0D%0A

Notice that the absolute value "strips off" negative signs, but the result is still subtracted from -1

:)

The sum of ten distinct positive numbers is 100. The largest of the numbers is?

100-(1+2+3+4+5+6+7+8+9)=55
1%3C=x%3C=55

so the greatest possible number is 55

:)

the number of numbers less than 21 and relatively prime to 21 is

There is a famous function to compute this number, the euler totient function, when you get a chance you can look it up :)

For now we'll compute directly since 21 is relatively small
1, always
21/2=10 r 1 yes
21/3=7 r 0 no
21/4 => r 1 yes
21/5 yes
21/6 r 3 no
21/7 no
21/8 yes
21/9 no
21/10 yes
21/11 yes
21/12 no
21/13 yes
21/14 no
21/15 no
21/16 yes
21/17 yes
21/18 no
21/19 yes
21/20 yes
21/21 no
so the count is...12

:)

there is a three digit number one digit is prime another is a square number the last one is not prime or square. the number is not divisible by three. what is the greatest possible value of the number

we try the first digit as 9 because it is a perfect square and the greatest 3-digit numbers have 9 in their thousands place
the last one is not prime, so the middle number must be the prime so we choose 7 (greatest prime less than 9)
6 is not a prime, it is our only last digit possible if we require our number to not be a multiple of 3
so our number is 976

What is the logaritmic form of the equation 3^x= 12

We will use the inverse property of logs to help us

3%5Ex=+12

has a base of 3 so we use log base 3 which we'll denote by

log3

solve: x-5/3=x-3/5

This equation has no solution:
x-5/3=x-3/5
x-x-5/3=x-x-3/5

-5/3=-3/5 which is clearly not true. Whenever we can simplify an equation enough to determine that it will always be false, we know that the equation has no solution.

:)