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sesenic [268]
3 years ago
13

what types of problems can be solved using the greatest common factors? What types of problems can be solved using the least com

mon multiple
Mathematics
2 answers:
gayaneshka [121]3 years ago
7 0
What types of problems can be solved using the greatest common factor? What types of problems can be solved using the least common multiple? Complete the explanation. 
<span>*** Use the words 'same' and 'different' to complete the following sentences.*** </span>

<span>Problems in which two different amounts must be split into (the same) number of groups can be solved using the GCF. Problems with events that occur on (different) schedules can be solved using the LCM.</span>
Lorico [155]3 years ago
4 0

Answer:

The greatest common factor or GCF is the greatest factor any two numbers share or we can say that GCF is the greatest factor that divides two different numbers.

Like the greatest common factor of 12 and 8 is 4.

There can be problems like - Kesha has 8 cans of normal soda and 16 cans of diet soda. She wants to create few refreshment tables that will operate during the basketball game soon to be held. She does not want any sodas left over. What is the greatest number of refreshment tables that she can stock?

-------------------------------------------------------------------------------------

The least common multiple or the LCM is the smallest common number or multiple of any two numbers.

Like the least common multiple of 3 and 5 is 15.

There can be problem like - Brian has painting lessons every fifth day and swimming lessons every third day. If he had both the lessons on May 7, when will be the next date on which he has both lessons?

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Step-by-step explanation:

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If a cylinder has a height of 12 cm and a radius of 4 cm, what do you do to find the volume of the cylinder?
jenyasd209 [6]

Answer:

V = 603.43 cm³

Step-by-step explanation:

V = πr²h

Where r = 4 cm, h = 12 cm

V = 22/7 × 4² × 12

V = 22/7 × 4 × 4 × 12

V = 4224/7

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A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides
ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

                                                         =(15-2x)(10-2x)x cubic inches

                                                         =(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=12, b= -100 and c=15

x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}

\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}

\Rightarrow x=0.1528,8.18

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, V''|_{x=0.1528}=24(0.1528)-100

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

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