Divide through everything by <em>b</em> :
![\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bc%7D%7Bb%2Bd%7D%20%3D%20%5Cdfrac%7B%5Cdfrac%20ab%20%2B%20%5Cdfrac%20cb%7D%7B1%20%2B%20%5Cdfrac%20db%7D)
Since <em>a/b</em> < <em>c/d</em>, it follows that
![\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bc%7D%7Bb%2Bd%7D%20%3C%20%5Cdfrac%7B%5Cdfrac%20cd%2B%5Cdfrac%20cb%7D%7B1%20%2B%20%5Cdfrac%20db%7D)
Multiply through everything on the right side by <em>b/d</em> to get
![\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bc%7D%7Bb%2Bd%7D%20%3C%20%5Cdfrac%7B%5Cdfrac%7Bbc%7D%7Bd%5E2%7D%2B%5Cdfrac%20cd%7D%7B%5Cdfrac%20bd%2B1%7D%20%3D%20%5Cdfrac%7B%5Cdfrac%20cd%5Cleft%28%5Cdfrac%20bd%2B1%5Cright%29%7D%7B%5Cdfrac%20bd%2B1%7D%20%3D%20%5Cdfrac%20cd)
and so (<em>a</em> + <em>c</em>)/(<em>b</em> + <em>d</em>) < <em>c/d</em>.
For the other side, you can do something similar and divide through everything by <em>d</em> :
![\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bc%7D%7Bb%2Bd%7D%20%3D%20%5Cdfrac%7B%5Cdfrac%20ad%20%2B%20%5Cdfrac%20cd%7D%7B%5Cdfrac%20bd%20%2B%201%7D)
and <em>a/b</em> < <em>c/d</em> tells us that
![\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bc%7D%7Bb%2Bd%7D%20%3E%20%5Cdfrac%7B%5Cdfrac%20ad%20%2B%20%5Cdfrac%20ab%7D%7B%5Cdfrac%20bd%20%2B%201%7D)
Then
![\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bc%7D%7Bb%2Bd%7D%20%3E%20%5Cdfrac%7B%5Cdfrac%20ab%20%2B%20%5Cdfrac%7Bad%7D%7Bb%5E2%7D%7D%7B1%20%2B%20%5Cdfrac%20db%7D%20%3D%20%5Cdfrac%7B%5Cdfrac%20ab%5Cleft%281%2B%5Cdfrac%20db%5Cright%29%7D%7B1%20%2B%20%5Cdfrac%20db%7D%20%3D%20%5Cdfrac%20ab)
and so (<em>a</em> + <em>c</em>)/(<em>b</em> + <em>d</em>) > <em>a/b</em>.
Then together we get the desired inequality.
I have no idea either sorry
Answer:
ED = 10
Step-by-step explanation:
CA is a radius perpendicular to AP
CA had length √(13² - 12²) = 5
ED is a diameter which is two radii.
Answer:
Step-by-step explanation:
- 4 assignments a week
- 3 weeks
- 46 minutes each assignment
<u>Total time spent</u>
- 4*3*46 = 552 min = 9 hours and 12 minutes
I = Prt
P = i / rt
P = 288 / (0.016 * 3)
P = 288 / 0.048
P = 6,000
answer
He should deposit $6,000