Answer: 21.8
Step-by-step explanation:
The smallest amount of material needed is 54 square centimeters
<h3>How to determine the amount of material needed?</h3>
The given parameters are:
Volume = 36 cubic centimeters
Represent length with x, width with y and height with z.
So, we have
x = 3y
The volume is calculated as:
V = xyz
This gives
V = 3y²z
Substitute 36 for V
3y²z = 36
Divide by 3
y²z = 12
Make z the subject
z = 12/y²
The surface area is:
S = 2(xy + xz + yz)
This gives
S = 2(3y² + 3yz + yz)
Evaluate the like terms
S = 2(3y² + 4yz)
Expand
S = 6y² + 8yz
Substitute z = 12/y²
S = 6y² + 8y * 12/y²
This gives
S = 6y² + 96/y
Differentiate
S' = 12y - 96/y²
Set to 0
12y - 96/y² = 0
Multiply through by y²
12y³ - 96 = 0
Add 96 to both sides
12y³ = 96
Divide by 12
y³ = 8
Take the cube root of both sides
y = 2
Recall that:
x = 3y and z = 12/y²
This gives
x = 3 * 2 = 6
z = 12/2² = 3
Recall that:
S = 2(xy + xz + yz)
So, we have:
S = 2(6 * 2 + 3 * 3 + 2 * 3)
Evaluate
S = 54
Hence, the smallest amount of material needed is 54 square centimeters
Read more about surface areas at:
brainly.com/question/76387
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All you have to do to solve this problem is to put it into fraction form: if for every $4 Jo makes, Leila makes $3, then the fraction would be 3/4.
To solve this divide 60 by 4 to get 15 and then multiply 15 by 3 to get Leila's pay. 15*3=45
Check it by putting it into simplest form as a fraction to see if it checks:
45/60=3/4 and 3/4=3/4 so therefore Leila makes $45 in profit
Answer:
5 Miles
Step-by-step explanation:
Given, Height of the tower is 3 miles and the distance from the base is 4 miles.
According the Pythagoras Theorem, the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
So, putting the data in Pythagoras theorem, let's consider A= 3 and B= 4.
So C will be,
sqrt(A^2 + B^2 )= C
Or, sqrt( 3^2+ 4^2)= C
Or, sqrt( 9+ 16) = C
Or, sqrt(25) = C
Hence, C = 5
So, The distance would be 5 Miles.