Answer:
1. The answer of the radius of the cylinder is 1.127cm to produce the minimum surface area
2. The radius of the industrial tank is 1.465ft and the height is 662.396 ft
Step-by-step explanation:
<u>The first step</u> is to draw the shape and to determine the total surface area and the total volume of the shape. This is done by adding the total surface area of two hemispheres and the surface area of the cylinder and for the volume this is done by adding the volume of two hemispheres and the volume of the cylinder.
<u>The second step</u> is to make the total volume of the shape the constraint equation and the total surface area of the shape becomes the optimisation equation. From the constraint equation solve for h and make it in terms of r (you should advisable use V as a constant and finally substituting at the end). Thereafter, input the value of h in the optimisation equation and differentiate the equation with respect to r. Finally equate the equation to zero.
Third step involves solving for r
Now, for the second question, one has to double the total surface area of the hemispheres to provide the cost equation (this is done to take into account the higher costs of the hemispherical ends. Solve in the same way as the first and you will get the answer.
[KINDLY NOTE I TRIED TYPING THE SOLUTION BUT IT TOOK SO LONG THAT I GOT LOGGED OUT SO FIND ATTACHED PICTURES OF THE SOLUTION, if you follow the steps, it would serve as a guide]
I think it’s sampling error
Answer:
The equation of the cost is C = 50h + 15
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line ⇒ rate of change
- b is the y-intercept ⇒ constant value
∵ A plumber charges 15 per service call
→ That means there is a fixed amount of 15
∵ b is the constant amount
∴ b = 15
∵ It charges 50 per hour
→ That means, the rate of change is 50
∵ m is the rate of change
∴ m = 50
∵ C is the cost for h hours
→ Replace y by C and x by h in the form of the linear equation above
∴ C = m h + b
→ Substitute the values of m and b in the equation
∵ C = 50h + 15
∴ The equation of the cost is C = 50h + 15
3:1
,,,,,,,,,,,,,,hope this helps
Answer:
x =
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin30° = , then
sin30° = = = ( cross- multiply )
2x = 13 ( divide both sides by 2 )
x =