Answer:
Step-by-step explanation:
Understanding the problem:
x -----> number of munchkins
y -----> number of yema
Devise a plan:
x + y ≥ 10
3x + 2y ≥ 50
Carry out:
y ≥ -x + 10 ------------(I)
3x + 2y ≥ 50
2y ≥ -3x + 50
y ≥ ![\frac{-3}{2}+\frac{50}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B2%7D%2B%5Cfrac%7B50%7D%7B2%7D)
![y \geq \frac{-3}{2}x + 25](https://tex.z-dn.net/?f=y%20%5Cgeq%20%5Cfrac%7B-3%7D%7B2%7Dx%20%2B%2025)
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849381 - 9 = 849372
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Step-by-step explanation:
hypotenuse =
![\sqrt{a {}^{2} + b {}^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%7Ba%20%7B%7D%5E%7B2%7D%20%2B%20b%20%7B%7D%5E%7B2%7D%20%20%7D%20)
Answer:
W=2001.24 newton meters
Caution: check units and arithmetic - I often make errors.
Step-by-step explanation:
Work is force times distance.
Denote height by h where h=0 is at ground level.
Denote the mass of the bucket and rope at height h by m(h).
The rate at which the bucket loses mass with height is (20-16)/10=0.4 kg/m
The rate at which the rope between the bucket and the top of the building loses mass is 0.4 kg/m
The initial mass of the bucket and rope is
![m_{0}=20+0.4+0.4(10)=24.4](https://tex.z-dn.net/?f=m_%7B0%7D%3D20%2B0.4%2B0.4%2810%29%3D24.4)
The mass at height h is
![m(h)=24.4-0.8h](https://tex.z-dn.net/?f=m%28h%29%3D24.4-0.8h)
The force required at height h is
m(h)g
where g is the gravitational acceleration.
g=9.81 meters/sec/sec
The work required is
![\int\limits^b_a {m(h)g} \, dh](https://tex.z-dn.net/?f=%5Cint%5Climits%5Eb_a%20%7Bm%28h%29g%7D%20%5C%2C%20dh)
Where a=0 and b=10
![g\int\limits^b_a {(24.4-0.8h)} \, dh=g(24.4h-0.4h^2)\left \{ {{10} \atop {0}} \right.](https://tex.z-dn.net/?f=g%5Cint%5Climits%5Eb_a%20%7B%2824.4-0.8h%29%7D%20%5C%2C%20dh%3Dg%2824.4h-0.4h%5E2%29%5Cleft%20%5C%7B%20%7B%7B10%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
g(244-40)=204g
W=2001.24 newton meters
Answer:
b
Step-by-step explanation:
![\frac{x^4}{x^7} =x^4 \times x^{-7} =x^{4-7} =x^{-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E4%7D%7Bx%5E7%7D%20%3Dx%5E4%20%5Ctimes%20x%5E%7B-7%7D%20%3Dx%5E%7B4-7%7D%20%3Dx%5E%7B-3%7D)