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Answer:
3. 7.2
4. 20
Step-by-step explanation:
Answer:
x-intercept =6/4=3/2
y -intercept= -6/3 = -2
Step-by-step explanation:
to find Y intercept assume the value of x as zero. to find X intercept assume the value of Y as zero.
Answer:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The minimum surface area is 173.55 ft²
Step-by-step explanation:
Surface area is given by:
![S(x) = x^2+\frac{880}{x}](https://tex.z-dn.net/?f=S%28x%29%20%3D%20x%5E2%2B%5Cfrac%7B880%7D%7Bx%7D)
The value of x for which the derivate of the surface area function is zero, is the length of the sides of the base that minimizes surface area:
![S(x) = x^2+\frac{880}{x} \\\frac{dS(x)}{dx}=0=2x-\frac{880}{x^2}\\x^3=440\\x=7.606\ ft](https://tex.z-dn.net/?f=S%28x%29%20%3D%20x%5E2%2B%5Cfrac%7B880%7D%7Bx%7D%20%5C%5C%5Cfrac%7BdS%28x%29%7D%7Bdx%7D%3D0%3D2x-%5Cfrac%7B880%7D%7Bx%5E2%7D%5C%5Cx%5E3%3D440%5C%5Cx%3D7.606%5C%20ft)
The height of the box is given by:
![V=hx^2\\220 =h*7.606^2\\h=3.802\ ft](https://tex.z-dn.net/?f=V%3Dhx%5E2%5C%5C220%20%3Dh%2A7.606%5E2%5C%5Ch%3D3.802%5C%20ft)
The dimensions of the box with minimum surface area are:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The absolute minimum is:
![S(x) = 7.606^2+\frac{880}{7.606}\\S_{min}=173.55\ ft^2](https://tex.z-dn.net/?f=S%28x%29%20%3D%207.606%5E2%2B%5Cfrac%7B880%7D%7B7.606%7D%5C%5CS_%7Bmin%7D%3D173.55%5C%20ft%5E2)
The minimum surface area is 173.55 ft²