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2 years ago

What is the length of the interior diagonal, d, rounded to the nearest hundredth cm

Mathematics

1 answer:

inn [45]2 years ago

4 0

Answer:

The length of the diagonal, d is approximately 24.49 cm

Step-by-step explanation:

The question asks to find the length of the interior diagonal of a rectangular prism, also known as a cuboid;

The parameters of the prism are;

The height of the prism = 10 cm

The width of the prism = 10 cm

The length of the prim = 20 cm

The length of the given diagonal of the cuboid is found by Pythagoras's theorem from the height, 'h', of the cuboid and the diagonal of the base of the cuboid

Let 'l' represent the diagonal of the base of the cuboid, we have, by Pythagoras's theorem;

l² = ((20 cm)² + (10 cm)²) = 500 cm²

The length of the diagonal, 'd', by Pythagoras's theorem is given as follows;

d = √(l² + (²10 cm))

By plugging in the known value for 'l² = 500 cm²', we get;

d = √(500 cm² + (²10 cm)) = √(600 cm²) = 10·√6 cm

The length of the diagonal, d = 10·√6 cm ≈ 24.49 cm (by rounding to the nearest hundredth cm)

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20 points!!!!!!!

castortr0y [4]

See the attached figure to better understand the problem
let
L-----> length side of the cuboid
W----> width side of the cuboid
H----> height of the cuboid

we know that
One edge of the cuboid has length 2 cm-----> I'll assume it's L
so
L=2 cm
[volume of a cuboid]=L*W*H-----> 2*W*H
40=2*W*H------> 20=W*H-------> H=20/W------> equation 1

[surface area of a cuboid]=2*[L*W+L*H+W*H]----->2*[2*W+2*H+W*H]

100=2*[2*W+2*H+W*H]---> 50=2*W+2*H+W*H-----> equation 2
substitute 1 in 2
50=2*W+2*[20/W]+W*[20/W]----> 50=2w+(40/W)+20
multiply by W all expresion
50W=2W²+40+20W------> 2W²-30W+40=0

using a graph tool------> to resolve the second order equation
see the attached figure

the solutions are
13.52 cm x 1.48 cm
so the dimensions of the cuboid are
2 cm x 13.52 cm x 1.48 cm
or
2 cm x 1.48 cm x 13.52 cm

Find the length of a diagonal of the cuboid
diagonal=√[(W²+L²+H²)]------> √[(1.48²+2²+13.52²)]-----> 13.75 cm

the answer is
the length of a diagonal of the cuboid is 13.75 cm

4 0

3 years ago

If I ride 3 1/4 miles at 2/5 miles per minute how fast I’m going

Bogdan [553]

To get your answer, you would divide your distance by your speed. You should be going about 1.4 miles per hour.

3 0

3 years ago

The fourth term of an Arithmetic Sequence is equal to 3 times the first term, and the seventh term exceeds twice the third term

11Alexandr11 [23.1K]

Answer:

The first term is 3. The common difference is 2.

Step-by-step explanation:

The first term is x.

The common difference is d.

The second term is x + d.

3rd term: x + 2d

4th term: x + 3d

7th term: x + 6d

"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"

x + 3d = 3 * x Eq. 1

"the seventh term exceeds twice the third term by 1"

x + 6d = 2(x + 2d) + 1 Eq. 2

Simplify Eq. 1:

2x = 3d

Simplify Eq. 2:

x + 6d = 2x + 4d + 1

x = 2d - 1

Multiply both sides of the last equation by 2.

2x = 4d - 2

2x = 3d (simplified Eq. 1)

Since 2x = 2x, then the right sides are equal.

3d = 4d - 2

d = 2

2x = 3d

2x = 3(2)

2x = 6

x = 3

Answer: The first term is 3. The common difference is 2.

8 0

3 years ago

Some one plz help me 25 points

qaws [65]

C, a²+b²=c²

why does this have to be 20 characters long

5 0

3 years ago

Find a number in the sequence 1) 100, 400, 610, ?, 652 2) 342, 128, ?, 26

dsp73

Answer:

1. 460

2. 216

Step-by-step explanation:

From the series ,

100 , 400 , 610 , ? , 652

Writing the the digits in the revere order , i.e

001 , 004 , 016 , ? , 256

Now,

Now , getting the number in the form of the multiple of 4 as -

1 , 1 * 4 = 4 , 4 * 4 = 16 , ? , 64 * 4 = 4

Hence , the value for ? = 16 * 4 = 64 .

Again , reversing 64 to get the missing number of the series -

460 .

Hence ,

The value for ? is 460 .

From the series ,

342 , 128 , ? , 26

Now, multiplying the first digit with the second digit and merging it to the product of the second and third digit -

3 * 4 and 4 * 2 , 1 * 2 and 2 * 8 , ?

128 , 216 , ?

Hence ,

The value for question mark = 1 * 2 and 1 * 6 = 216

Hence ,

The value for ? is 216 .

4 0

3 years ago

What is the length of the interior diagonal, d, rounded to the nearest hundredth cm​

What is the length of the interior diagonal, d, rounded to the nearest hundredth cm