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2 years ago

Write a fraction that is greater than 1/3 and is less than 1/2.

Mathematics

2 answers:

julsineya [31]2 years ago

5 0

A fraction that works is 1/2.5

Sveta_85 [38]2 years ago

5 0

A fraction that works is 3/8

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I need help with this assignment.

Gelneren [198K]

2. Definition of supplementary angles
I’m not too good with proofs but hopefully at least one answer helped lol sorry

8 0

3 years ago

You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

2 years ago

A curve has equation y=x^3_6x+1.at the point where x=2

lisov135 [29]

Answer:2^3=8

6.2=12

Y=8-12+1= -3

Step-by-step explanation:

6 0

2 years ago

The distance between two points on a map varies directly with the actual

grigory [225]

Answer:

104 miles

Step-by-step explanation:

Step 1: 208/2.5

208/3.5= 59.4285714286

59.4285714286 times 1.75= 104

I Hope I am right and I hope this helps.

3 0

2 years ago

Each music class sings 8 songs a week.how many songs does each class sing in 5 weeks 6 weeks 7 weeks

love history [14]

The answer is fairly simple. Each week they sing 8 songs, and so in 5 weeks they would sing 8x5 songs (which is 40) in 6 weeks, they would sing 8x6 songs (which is 48) and in 7 weeks 7x8 songs (which is 56)

4 0

2 years ago