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3 years ago

The diagonal of a square measured 10 cm. Find the length of a side of the square to the nearest tenth.

Mathematics

1 answer:

Naddika [18.5K]3 years ago

6 0

Answer:

7.1 cm

Step-by-step explanation:

Let s represent the side length of the square. The Pythagorean theorem tells you the relationship to the diagonal length is ...

(10 cm)² = s² +s² . . . . the sum of the squares of the legs is the square of the hypotenuse

100 cm² = 2s² . . . . . . simplify

50 cm² = s² . . . . . . . . divide by 2

√(50) cm = s ≈ 7.1 cm . . . . . take the square root

The length of a side of the square to the nearest tenth is 7.1 cm.

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You are working for a company that designs boxes, bottles and other containers. You are currently working on a design for a milk

ra1l [238]

Volume is a measure of the quantity of substance a given object can contain. The required answers are:

1.1 The volume of each milk carton is 360 $cm^{3}$ .

1.2 The area of cardboard required to make a single milk carton is 332.6 $cm^{2}$ .

1.3 Each carton can hold 0.36 liters of milk.

1.4 The cost of filling the 200 cartons is R 86.40.

The volume of a given shape is the amount of substance that it can contain in a 3-dimensional plane. Examples of shapes with volume include cubes, cuboids, spheres, etc.

The area of a given shape is the amount of space that it would cover on a 2-dimensional plane. Examples of shapes to be considered when dealing with the area include triangle, square, rectangle, trapezium, etc.

The box to be considered in the question is a cuboid. So that;

Volume of cuboid = length x width x height

Thus,

1.1 The volume of each milk carton = length x width x height

= 6 x 6 x 10

= 360

The volume of each milk carton is 360 $cm^{3}$ .

1.2 The total area of cardboard required to make a single milk carton can be determined as follows:

i. Area of the rectangular surface = length x width

= 6 x 10

= 60

Total area of the rectangular surfaces = 4 x 60

= 240 $cm^{2}$

ii. Area of the square surface = side x side = s²

= 6 x 6

Area of the square surface = 36 $cm^{2}$

iii. There are four semicircular surfaces, this implies a total of 2 circles.

Area of a circle = $\pi r^{2}$

where r is the radius of the circle.

Total area of the semicircular surfaces = 2 $\pi r^{2}$

= 2 x $\frac{22}{7}$ x $(3)^{2}$

= 56.57

Total area of the semicircular surfaces = 56.6 $cm^{2}$

Therefore, total area of cardboard required = 240 + 36 + 56.6

= 332.6 $cm^{2}$

The area of cardboard required to make a single milk carton is 332.6 $cm^{2}$ .

1.3 Since,

1 $cm^{3}$ = 0.001 Liter

Then,

360 $cm^{3}$ = x

x = 360 x 0.001

= 0.36 Liters

Thus each carton can hold 0.36 liters of milk.

1.4 total cartons = 200

Total volume of milk required = 200 x 0.36

= 72 litres

But, 1 kiloliter costs R1 200. Thus

Total volume in kiloliters = $\frac{72}{1000}$

= 0.072 kiloliters

The cost of filling the 200 cartons = R1200 x 0.072

= R 86.40

The cost of filling the 200 cartons is R 86.40.

For more clarifications on the volume of a cuboid, visit: brainly.com/question/20463446

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4 0

2 years ago

What is the series in Expanded Form?

tangare [24]

Answer:

∴ ∑₁⁸i = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8

Step-by-step explanation:

Given:

To Find:

∑₁⁸i =?

Solution:

Σ This symbol called Sigma means "summation up"

∴ ∑ n mean sum for all n

But if ∑₁³n means Sum for n=1 , 2 ,and 3 ADD

∴ ∑₁³n = 1 + 2 + 3

∴ ∑₁⁸i = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8

7 0

3 years ago

Solve x and y x/2 + y/3 = 4 7x - y = 12

Anestetic [448]

Answer: here the answer

Step-by-step explanation:

3 0

3 years ago

Which unit would use used to measure the capacity? Milliliter or liters For a bucket

frozen [14]

Answer:

Liters

Step-by-step explanation:

Milliliters are used to measure smaller amount of liquids while liters are used for bigger. If you were to use a bucket, you would need to measure the capacity with bigger measurements.

7 0

2 years ago

First person to help gets brainliest

lions [1.4K]

The solution of the given equation w.r.t m is m = 3 ,i.e., option A

<h3>What are Algebraic equations?</h3>

With one exception, algebraic equations are essentially algebraic expressions.

An = sign is required in all algebraic equations.

No matter what kind of equation it is, all equations use the = sign.

The next topic is algebraic expression, which lacks the operators =,,, >, and.

To put it simply, there is no comparison between two terms in an algebraic statement.

Algebraic expressions frequently use terms like polynomial and square root.

So you now recognize the distinction between the two?

1) An algebraic equation has the symbol =, and 2) an algebraic expression lacks any comparison symbols (such as > and =).

As per the question:

$6\frac{1}{9} + 3\frac{1}{3} =28\frac{1}{3}$

55/9 + 10/3 = 85/3

(55m+30m)/9 = 85/3

85m/9 = 85/3

85m = (85*9)/3

85m = 85*3

m = (85*3)/85

∴ m = 3

To now more about algebraic equations, visit

brainly.com/question/953809

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5 0

1 year ago