Answer:
If the non-zero whole number is even, then there are 3 zeroes
If the non-zero whole number is odd, then there are 2 zeroes
Step-by-step explanation:
* <em>Lets explain the information in the problem</em>
- Whole numbers are positive numbers, including zero, without
any decimal or fractional
- Nonzero whole numbers are positive numbers, not including zero
- The non-zero whole numbers less then 10 are:
1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9
- The product of any nonzero whole number less than 10 and 500
means multiply any of nonzero number above by 500
- The number of zeros in the product is equal to the sum of the
number of zeros at the end of each of the factors.
# 1 × 500 = 5 × 100 ⇒ 2 zeros
# 2 × 500 = 2 × 5 × 100 = 10 × 100 ⇒ 3 zeros
# 3 × 500 = 3 × 5 × 100 = 15 × 100 ⇒ 2 zeros
# 4 × 500 = 2 × 2 × 5 × 100 = 2 × 10 × 100 ⇒ 3 zeros
# 5 × 500 = 5 × 5 × 100 = 25 × 100 ⇒ 2 zeroes
# 6 × 500 = 2 × 3 × 5 × 100 = 3 × 10 × 100 ⇒ 3 zeros
# 7 × 500 = 7 × 5 × 100 = 35 × 100 ⇒ 2 zeroes
# 8 × 500 = 2 × 2 × 2 × 5 × 100 = 4 × 10 × 100 ⇒ 3 zeros
# 9 × 500 = 3 × 3 × 5 × 100 = 45 × 100 ⇒ 2 zeros
- From all answers above:
# If the non-zero whole number is even (2 , 4 , 6 , 8), then there are
3 zeros in the product
# If the non-zero whole number is odd (1 , 3 , 5 , 7 , 9), then there are
2 zeros in the product
and differentiating both sides with respect to 
yields![\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B3x%5E2%2By%5E2%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B7%5Cbigg%5D%5Cimplies%206x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D0)
![\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B6x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B0%5Cbigg%5D%5Cimplies%206%2B2%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%2B2y%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D0)
and 
, we have