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cestrela7 [59]
2 years ago
10

A manufacturer wants to double the volume of a 3 in.×2 in.×6 in. 3 i n . × 2 i n . × 6 i n . box, while using as little extra ca

rdboard as possible. Which statement is true?
Mathematics
1 answer:
viktelen [127]2 years ago
6 0

Answer: 2 inch dimension will give smallest increase.


Step-by-step explanation:

Length = 3 in

width = 2 in

height = 6 in

Extra cardboard  means to find surface area

on doubling the length

length = 6 In

width = 2 In

Height = 6In

Surface area for the above dimensions = 2 [ 6x2+2x6+6x6] = 120 sq in

On doubling the width

length = 3 in

width = 4 in

Height = 6 inch

Surface area for the above dimensions= 2 [ 3x4+4x6+6x3] = 2[54] = 108 sq inches

On doubling height

Length =3 in

width = 2 in

Height = 12 in

Surface area for above dimensions = 2 [ 3x2+2x12+12x3] = 2[6+24+36] = 132 sq inch

On doubling width surface area is minimum.

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it takes max 1.8 hours to walk home from work at a rate of 3.5km/h. how long would it take max to cover the same distance walkin
NikAS [45]

Time taken by Max to cover the same distance walking at 4.2 km/h is 1.5 hours

<h3><u>Solution:</u></h3>

Given it takes Max 1.8 hours to walk home from work at a rate of 3.5km/h

We have to find time taken by Max to cover the same distance walking at 4.2 km/h

<em><u>The relation between speed and time is given as:</u></em>

speed = \frac{distance}{time}

<em><u>CASE 1:</u></em>

It takes Max 1.8 hours to walk home from work at a rate of 3.5km/h

Let us first find the distance covered

Time taken = 1.8 hours and speed = 3.5 km/hr

3.5 = \frac{distance}{1.8}\\\\distance = 3.5 \times 1.8 = 6.3

Hence distance covered is 6.3 km

<em><u>Now we have to find the time taken to cover same 6.3 km walking at 4.2 km\hr</u></em>

4.2 = \frac{6.3}{time taken}\\\\time taken = \frac{6.3}{4.2} = 1.5

So time taken by Max to cover the same distance walking at 4.2 km/h is 1.5 hours

3 0
2 years ago
Jim Ryan, an owner of a Burger King restaurant, assumes that his restaurant will need a new roof in 7 years. He estimates the ro
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PSYCHO15rus [73]
We can start solving this problem by first identifying what the elements of the sets really are.

R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.

Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).

W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.

W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.

R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.

0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.

∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are <u>not</u> an element of R).

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-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.
3 0
2 years ago
Read 2 more answers
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Answer:

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Step-by-step explanation:

In the figure attached AB is the light house of height 200 feet.

Angle of depression of the boat from the top of a lighthouse = angle of elevation of the lighthouse from the boat = 14°52'

so 1' = \frac{1}{60} degree

so angle of elevation at point C = 14 + \frac{52}{60}

So angle of elevation from C = (14 + 0.87) = 14.87°

Similarly, when boat arrives at point D angle of elevation = 45°10' = 45 + \frac{10}{60} = 45.17°

Now we have to calculate the distance CD, traveled by the boat.

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Similarly in ΔABD

tan45.17 = \frac{200}{BD}

1 = \frac{200}{BD}

BD = 200 feet

So distance CD = BC - BD

CD = 753.239 - 200

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Therefore, Boat traveled 553.24 feet towards the lighthouse.

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2 years ago
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jeka94
Daniel because 3/4 is larger than 5/12 if you cross multiply.
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