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Debora [2.8K]
3 years ago
12

Mr. Smith has 12 congruent boxes shaped like rectangular prisms in his office. If the length is 25 inches, the height is 2 feet,

and the volume is 9,000 cubic inches, what would the width of one of his boxes be?
Mathematics
1 answer:
Nana76 [90]3 years ago
4 0

Answer:

width of one box = 1.25 inches

Step-by-step explanation:

Given data:

12 congruent boxes

Length = 25 inches

height = 2 feet

Volume = 9000 cubic inches

First change the height into inches

1 foot = 12 inches

therefore 2 feet = 24 inches

Volume = Length * width * height

9000 = 25 * width * 24

9000 = 600 * width

width = 9000/600

width = 15 inches

width of one box = width of all boxes / number of boxes

width of one box = 15/12

width of one box = 1.25 inches

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Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose that one
olga_2 [115]

Answer:

Length = Width = Height = 64 ; Luggage Box is a CUBE

Step-by-step explanation:

Given : Length (L) + Width (W) + Height (H) ≤ 192 ; & Length = Width

Volume ( V )of luggage [Cuboid] = L.W.H

Since L = W :

V = L.L.H  → V = L^2H  

L + L + H = 192 →  2L + H = 192 → H = 192 - 2L

Putting value of 'H' in 'V'

V = L^2 (192 - 2L) → V = 192L^2 - 2L^3

Maximising volume function , differentiating it w.r.t 'L'

dV / dL = 2(192 L) - 3 (2L^2)  → = 384L - 6L^2

dV / dL = 384L - 6L^2  = 0

384L = 6L^2 → 384 = 6L

L = 384 / 6 → L = 64  ; W also = 64

Putting value of L in 1st given sum equation : 2L + H = 192

2 (64) + H = 192

128 + H = 192 → H = 192 - 128 → H = 64

Since L = W = H = 64 ; Luggage bag is a Cube

6 0
3 years ago
Determine the minimum value of the quadratic relation y=0.75(X+ 4)2 + 3.
Anestetic [448]
I think the answer is b but I am not for sure
6 0
3 years ago
PLEASE HELP VERY URGENT WILL GIVE BRAINILY PLEASE I BEG YOU PLEASE
yuradex [85]

Answer: 20.5 units

Step-by-step explanation:

P=Perimeter

JI=3-(-3)

JI=3+3

JI=6

IK=7-1

IK=6

JK=(6^2+6^2)^1/2   ==> Distance Formula

JK=(36+36)^1/2

JK=(2*36)^1/2

JK=6(2)^1/2

P=JI+IK+JK

P=6+6+6(2)^1/2

P=12+6(2)^1/2

P=20.485 units

P=20.5 units

5 0
1 year ago
How are these triangles congruent?
ICE Princess25 [194]

Answer:

\triangle PTY \cong \triangle PSQ by ASA

Step-by-step explanation:

In triangle PTU and triangle PSQ

\overline{PT} \cong \overline{PS}     [Side]             [Given]

\angle PTU \cong \angle PSQ          [Angle]

Vertical angles are those angles which are opposite to each other.

\angle TPU \cong \angle SPQ        {Angle]

ASA(Angle-Side-Angle) postulates states if two angles and one included  side of one triangle are congruent to two angles and the included side of the other triangle, then these triangle are congruent.

by ASA postulates;

\triangle PTY \cong \triangle PSQ


5 0
4 years ago
HELP ASAP!!!<br> Find the missing value.<br> V=758.16 L=13 W=? H=7.2
ella [17]

Answer:  8.1

Step-by-step explanation:

758.16 ÷ 13 =58.32

58.32 ÷ 7.2 = 8.1

Check: 8.1 ×13 ×7.2=758.16

6 0
3 years ago
Read 2 more answers
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