(1.) 35-3m
m= 4
35-3m
= 35-3(4)
= 35-12 (do the multiple/division first before doing the addition/subtraction)
= 23
C. 23
(2.) 1 + x ÷ 5
x = 80
1 + x ÷ 5
= 1+80÷5
= 1+16
= 17
(3.) mx-y
m=5, x=3, and y=8
mx-y
= 5(3)-8
= 15-8
= 7
(4.) 3a+15+bc−6
a=7, b=3, and c=15
3a+15+bc-6
= 3(7)+15+3(15)-6
= 21+15+45-6
= 75
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
#SPJ1
Area of rectangle= Width x Length
600= 20x Length
Length= 600÷20= 30
Ans: The floor is 30 feet long.
.
Answer:
49/83 = m
Step-by-step explanation:
49=83m
Divide each side by 83
49/83 = 83m/83
49/83 = m
