Answer:
is less than one, smaller
If
is the distance the runner travels between first and second base, then the distance between him and home plate
satisfies
![h^2=d^2+90^2](https://tex.z-dn.net/?f=h%5E2%3Dd%5E2%2B90%5E2)
(where the 90 here refers to the distance between first base and home)
Differentiating both sides with respect to time
gives
![2h\dfrac{\mathrm dh}{\mathrm dt}=2d\dfrac{\mathrm dd}{\mathrm dt}\implies\dfrac{\mathrm dh}{\mathrm dt}=\dfrac dh\dfrac{\mathrm dd}{\mathrm dt}](https://tex.z-dn.net/?f=2h%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dt%7D%3D2d%5Cdfrac%7B%5Cmathrm%20dd%7D%7B%5Cmathrm%20dt%7D%5Cimplies%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dt%7D%3D%5Cdfrac%20dh%5Cdfrac%7B%5Cmathrm%20dd%7D%7B%5Cmathrm%20dt%7D)
The runner's speed is
. When he is
away from first base, he is
![h=\sqrt{30^2+90^2}=30\sqrt{10}\,\mathrm{ft}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B30%5E2%2B90%5E2%7D%3D30%5Csqrt%7B10%7D%5C%2C%5Cmathrm%7Bft%7D)
away from home plate. So he is moving away from home plate at a rate of
![\dfrac{\mathrm dh}{\mathrm dt}=\dfrac{30\,\rm ft}{30\sqrt{10}\,\rm ft}\left(25\dfrac{\rm ft}{\rm s}\right)=5\sqrt{\dfrac52}\dfrac{\rm ft}{\rm s}\approx7.906\dfrac{\rm ft}{\rm s}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dt%7D%3D%5Cdfrac%7B30%5C%2C%5Crm%20ft%7D%7B30%5Csqrt%7B10%7D%5C%2C%5Crm%20ft%7D%5Cleft%2825%5Cdfrac%7B%5Crm%20ft%7D%7B%5Crm%20s%7D%5Cright%29%3D5%5Csqrt%7B%5Cdfrac52%7D%5Cdfrac%7B%5Crm%20ft%7D%7B%5Crm%20s%7D%5Capprox7.906%5Cdfrac%7B%5Crm%20ft%7D%7B%5Crm%20s%7D)
Answer:
26
Step-by-step explanation:
In a trapezoid, the length of a mid-segment is average of the two bases.
In this case, the bases are 12 and 40, the average of which is (40 + 12)/2 = 52/2 = 26
Answer: 100 ft^2
Step-by-step explanation:
Replace s with 5 in your equation and solve:
![4s^2](https://tex.z-dn.net/?f=4s%5E2)
![4(5)^2](https://tex.z-dn.net/?f=4%285%29%5E2)
![4(25)](https://tex.z-dn.net/?f=4%2825%29)
= ![100\\](https://tex.z-dn.net/?f=100%5C%5C)
There are no values of x that make the equation true so no solution.