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3 years ago

The surface area of a cube is 6(a/4)^2, where a is a positive constant. What is the perimeter of one face of the cube?

Mathematics

1 answer:

maksim [4K]3 years ago

7 0

Answer: The perimeter is $a$

Step-by-step explanation:

1. By definition, the formula for calculate the surface area of a cube is:

$SA=6s^{2}$

Where s is the lenght of any edge of the cube.

2. You know that the surface area of the cube of the problem is $6(a/4)^{2}$ , therefore the lenght of each edge of the cube is:

$s=a/4$

3. Each face of the cube is a square, therefore the perimeter of one face is:

$P=4s$

$P=4(a/4)$

$P=4a/4$

$P=a$

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Four streets enter a traffic circle at points A B C and D name six arcs formed by the streets.

lilavasa [31]

Arcs are just sections of the circle
so lets say you had a pizza

and you put some points on the crust, the legnth of the crust from point to point is that arc

example
if you put poins A and B, then arc AB is the crust between points A and B

arcs can include other points as well
and arc AB=arc BA

so
I wil name easy arcs first
arc AB
arc BC
arc CD
ard DA

now ones that include others
arc AC
arc BD

so the arcs you might want to list are

arc AB
arc BC
arc CD
ard DA
arc AC
arc DB

5 0

3 years ago

the cost of belonging to a gym can be modeled by by c(m)=50m+79.50 what is the meaning of the slope and y-intercept

Bess [88]

The slope is the relationship between the cost of the gym and how long you are there for.
the y-intercept is how much it costs to go to the gym for no hours ie the start-up cost.

5 0

3 years ago

Monday: 10 apples and 5 bananas cost £4.20 Friday: 8 apples and 10 bananas cost £5.40 Find the cost of each - with an explanatio

motikmotik

Answer:

An apple costs £0.25

A banana costs £0.34

Step-by-step explanation:

Let a be apples and b be bananas.

10a+5b=4.2

8a+10b=5.4

Solve for a:

10a+5b=4.2

Subtract 5b from both sides

10a=4.2-5b

Subtract 4.2 from both sides

10a-4.2= -5b

Multiply both sides by -1

-10a+4.2=5b

8a+10b=5.4

Subtract 10b from both sides

8a=5.4-10b

Subtract 5.4 from both sides

8a-5.4= -10b

Multiply both sides by -1

-8a+5.4= 10b

Divide both sides by 2

-4a+2.7=5b

Combine equations:

-4a+2.7= -10a+4.2

Add 10a to both sides

6a+2.7=4.2

Subtract 2.7 from both sides

6a=1.5

Divide both sides by 6

a=0.25

An apple costs £0.25

Solve for b:

10a+5b=4.2

Subtract 10a from both sides

5b= -10a+4.2

Subtract 4.2 from both sides

5b-4.2= -10a

Multiply both sides by -1

-5b+4.2=10a

8a+10b=5.4

Subtract 8a from both sides

10b= -8a+5.4

Subtract 5.4 from both sides

10b-5.4= -8a

Divide both sides by 4

2.5b-1.35= -2a

Multiply both sides by 5

12.5b-6.75= -10a

Multiply both sides by -1

-12.5b+6.75=10a

Combine equations:

-12.5b+6.75= -5b+4.2

Add 12.5b to both sides

6.75=7.5b+4.2

Subtract 4.2 from both sides

2.55=7.5b

7.5b=2.55

Divide both sides by 7.5

b=0.34

A banana costs £0.34

If you would like to check and see if it is true, (I already checked, it is) you can use the formulas I gave at the start of the explanation.

10a+5b=4.2

8a+10b=5.4

a=0.25

b=0.34

3 0

3 years ago

Simplify. (−5p4z6u)3

sineoko [7]

The rules of exponents tell you that you can distribute the exponent to each of the factors. When one already has an exponent, those exponents multiply.
$(-5p^{4}z^{6}u)^{3}=(-5)^{3}\cdot(p^{4})^{3}\cdot(z^{6})^{3}\cdot u^{3}\\\\=-125p^{4\cdot 3}z^{6\cdot 3}u^{3}\\\\=-125p^{12}z^{18}u^{3}$