For real numbers a and b, define a%b=sqrt(a^2+b^2). What is the value of (5%12)%((-12)%(-5))?
The percentage is just a random sign the problem had a diamond instead, I just couldn't find any other symbol.Thank you!
a%b = √(a^2+b^2)
so, just plug in your numbers:
5%12 = (-5)%(-12) = 13
so, you have
(13)%(13) = 13√2
Ah, the clown is ready to perform some math tricks! Let's get cracking!
To find the value of (5%12)%((-12)%(-5)), we'll replace the percentage sign with the symbol '+-' just for clarity.
First, let's evaluate (-12)%(-5):
((-12)%(-5)) = sqrt((-12)^2 + (-5)^2)
= sqrt(144 + 25)
= sqrt(169)
= 13
Now we substitute the value into the original expression:
(5%12)%((-12)%(-5)) = (5%12)%13
Next, let's calculate 5%12:
(5%12) = sqrt(5^2 + 12^2)
= sqrt(25 + 144)
= sqrt(169)
= 13
So, (5%12)%13 is equal to 13. The answer to the expression (5%12)%((-12)%(-5)) is 13.
Why was the math book sad? Because it had too many problems!
To find the value of (5%12)%((-12)%(-5)), let's break it down step-by-step:
Step 1: Evaluate (-12)%(-5)
Plug the values into the given formula:
(-12)%(-5) = sqrt((-12)^2 + (-5)^2)
= sqrt(144 + 25)
= sqrt(169)
= 13
Step 2: Evaluate (5%12)%((-12)%(-5))
Plug the previously evaluated values into the given formula:
(5%12)%((-12)%(-5)) = (5%12)%13
Step 3: Evaluate (5%12)%13
Plug the values into the given formula:
(5%12)%13 = sqrt((5%12)^2 + 13^2)
= sqrt((5^2 + 12^2) + 13^2)
= sqrt((25 + 144) + 169)
= sqrt(338 + 169)
= sqrt(507)
≈ 22.53
Therefore, the value of (5%12)%((-12)%(-5)) is approximately 22.53.
To find the value of (5%12)%((-12)%(-5)), we need to first evaluate (-12)%(-5) and then substitute the result into the expression 5%12.
Let's start by evaluating (-12)%(-5) using the given definition a%b = sqrt(a^2 + b^2):
(-12)%(-5) = sqrt((-12)^2 + (-5)^2)
= sqrt(144 + 25)
= sqrt(169)
= 13
Now, we can substitute the result back into the expression 5%12:
(5%12)%((-12)%(-5)) = (5%12)%13
To evaluate (5%12)%13, we need to once again use the definition a%b = sqrt(a^2 + b^2):
(5%12)%13 = sqrt((5%12)^2 + 13^2)
= sqrt((5^2 % 12^2) + 169)
= sqrt((25 % 144) + 169)
= sqrt(25 + 169)
= sqrt(194)
≈ 13.928
Therefore, the value of (5%12)%((-12)%(-5)) is approximately 13.928.