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3 years ago

Determine if 0.4744335042096347... is rational or irrational and give a reason for your answer.

Mathematics

1 answer:

Marina86 [1]3 years ago

7 0

Answer: Irrational

Explanation:

Based on what is shown so far, there isn't any clear pattern of the digits. And the digits don't seem to repeat. Because of this, it's very likely that the number is irrational.

If in contrast we had something like 0.47474747, where the "47"s repeat forever", then it would be rational. We would be able to use algebra to show that 47/99 = 0.4747474747...

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Classwork 12.1 surface area

s344n2d4d5 [400]

Answer:

6) LA = 90 units² and SA = 202 units²

7) LA = 377 units² and SA = 477.5 units²

8) LA = 208 units² and SA = 232 units²

9) LA = 455 units² and SA = 591 units²

Step-by-step explanation:

* Lets revise the rules of lateral area and surface area

- Lateral area of the solid = perimeter of its base × its height

- Surface area = lateral area + 2 × area of its base

* Now lets solve the problems

6) The solid is a rectangular prism

- Its base is a rectangle with dimensions 8 units and 7 units

- Its height is 3 units

∵ Perimeter of the rectangle = 2(L + W)

∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units

∴ LA = 30 × 3 = 90 units²

∵ Area of the rectangle = L × W

∴ Area of the base = 8 × 7 = 56 units²

∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²

7) The solid is a cylinder

- Its base is a circle with diameter 8 units

∴ Its radius = 8 ÷ 2 = 4 units

- Its height is 15 units

∵ The perimeter of the circle is 2πr

∴ The perimeter of the base = 2π(4) = 8π

∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π

∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²

6) The solid is a triangular prism

- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units

- Its height is 13 units

∵ Perimeter of the triangle is the sum of the 3 sides

∴ Perimeter of the base = 5 + 5 + 6 = 16 units

∴ LA = 16 × 13 = 208 units²

∵ Area of the triangle = 1/2 × base × height

∴ Area of the base = 1/2 × 6 × 4 = 12 units²

∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²

9) The solid is a prism

- Its base is an isosceles trapezium with parallel bases 7 units and 10

units, 2 non-parallel bases 9 units and height 8 units

- Its height is 13 units

∵ Perimeter of the trapezium is the sum of its sides

∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units

∴ LA = 35 × 13 = 455 units²

∵ Area of the trapezium = 1/2(b1 + b2) × h

∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²

∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²

6 0

3 years ago

Suppose ABCD is a rhombus with AB = 12 inches. The midpoints of its sides are joined to form a quadrilateral. What type of quadr

MrRissso [65]

Answer:

A rectangle

Step-by-step explanation:

The given parameters are;

The quadrilateral ABCD is a rhombus;

The length of the sides of the rhombus = 12 inches

The lengths of the sides of a rhombus are equal

The opposite interior angles of the rhombus are equal

The length of each midpoint from the vertex = 12 in./2 = 6 in.

Therefore, we have;

The line joining the midpoints form a quadrilateral with the length of the opposite sides equal

The sum of the interior angles of the rhombus = 180°

From the diagram created with Microsoft Visio, we have;

4·a + 4·b + 360 = 4 × 180 = 360 + 360

4·a + 4·b = 360

a + b = 90°

We have;

The interior angles of the quadrilateral formed = x

a + b + x = 180° Sum of angles on a straight line

∴ x = 180° - (a + b) = 180° - 90° = 90°

x = 90°

Therefore, the interior angles of the quadrilateral formed = 90°

The quadrilateral formed having equal opposite sides, and all interior angle of 90° each is a rectangle

6 0

2 years ago

What is the midpoint of the segment shown below?

I am Lyosha [343]

Answer:

Step-by-step explanation:

Because the number between 10 is 5 going across and the one that goes up and down you can count 3 down and thats where your point it

5 0

3 years ago

Find the PERIMETER of this triangle

olga2289 [7]

First we need to find the missing side, use

$a = \sqrt{ {c}^{2} - {b}^{2} }$
So the missing leg = the sqrt of the hypotenuse squared minus the other leg squared.

Let's substitute the numbers,

$a = \sqrt{ {10}^{2} - {6}^{2} }$
Solve for the squares,

$a = \sqrt{100 - 36}$
Subtract,

$a = \sqrt{64}$
Solve for the root,

$a = 8$
~~

So our missing length is 8.

To find the perimeter of the triangle, simply add all the sides....

~~

$8 + 10 + 6 = 24$

~~

Answer : 24

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

4 0

3 years ago

Read 2 more answers

How many groups of Two-thirds are in Three-fifths?

cestrela7 [59]

Answer:

9/10 of a group

Step-by-step explanation:

Take 3/5 and divide by 2/3

3/5 ÷ 2/3

Copy dot flip

3/5 * 3/2

9/10

3 0

3 years ago

Read 2 more answers