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2 years ago

4. Separate 77 into two parts so that one part is 4 less than twice as much as the other. Find each part.

Mathematics

1 answer:

Igoryamba2 years ago

8 0

Answer:

50,27

Step-by-step explanation:

let the parts be x and y

x+y=77

x=2y-4

substitute

2y-4+y=77

3y=77+4

3y=81

y=81/3=27

x=2×27-4=54-4=50

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

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$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

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3 years ago

a rectangular prism has a volume of 300 cm squared if the scale factor of the second rectangular prism is 3.5 what is the volume

velikii [3]

Volume of rectangular prism= 30 cm³
Formula for volume of rectangular prism:
V=whl
Scale factor of second prism= 3.5
Which is 3 and a half times greater than the 1st one.
So volume of 2nd prism = 3. 5 x 300
V= 1050 cm³

Answer: Volume of second Rectangular Prism is 1050 cm³

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4. Separate 77 into two parts so that one part is 4 less than twice as much as the other. Find each part.​

4. Separate 77 into two parts so that one part is 4 less than twice as much as the other. Find each part.