First, we determine the area of the piece of cardboard by multiplying its dimensions.
area of cardboard = (8.5 inches) x (11 inches) = 93.5 in²
Then, we solve for the area of the cut out square,
area of the square = (4 inches) x (4 inches) = 16 in²
Then, we subtract the areas giving us the area of the frame which is equal to,
77.5 in²
Step 1. Subtract 3/4 from both sides
x = 1/2 - 3/4
Step 2. Simplify 1/2 - 3/4 to -1/4
x = -1/4
Not of Bernoulli type, but still linear.
There's no need to find an integrating factor, since the left hand side already represents a derivative:
![\dfrac{\mathrm d}{\mathrm dx}[(1+x^2)y]=(1+x^2)\dfrac{\mathrm dy}{\mathrm dx}+2xy](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5B%281%2Bx%5E2%29y%5D%3D%281%2Bx%5E2%29%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%2B2xy)
So, you have
![\dfrac{\mathrm d}{\mathrm dx}[(1+x^2)y]=4x^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5B%281%2Bx%5E2%29y%5D%3D4x%5E2)
and integrating both sides with respect to
yields
Answer:
<u>2,365,200,000 times</u>
Step-by-step explanation:
<u>Given</u> :
- Average heartbeat rate = 60 times/minute
- Avg. human lifespan = 75 years
<u>To Find</u> :
- Number of heartbeats in lifetime of 75 years
<u>Solving</u> :
- Let the number we require be n
- n = average heartbeat rate x 60 x 24 x 365 x 75
- n = 60 x 60 x 24 x 365 x 75
- n = 3600 x 24 x 365 x 75
- n = 86400 x 365 x 75
- n = 31536000 x 75
- n = <u>2,365,200,000 times</u>
