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Montano1993 [528]
3 years ago
8

T+2/3t-1/3 I really need this question to be answered

Mathematics
1 answer:
Murrr4er [49]3 years ago
5 0

<u> Equation:</u>

x(x      -     5)     +     3(x     +     5)

<u>Steps:</u>

x(x      -     5)     +     3(x     +     5)

<u>Expand:</u>

x(x     -     5 ):           x^2      -    5x

x^2    -    5x     +   3(x      +     5)

<u>Expand:</u>

3(x     +    5):        3x   +    15

x^2     -     5x     +     3x       +     15

<u>Add Similar Elements:   </u>  

-5x      +    3x    

=         -2x

Answer        x^2    -     2x      +    15    Doesn't Factor






Hope that helps!!!                                  : )


         


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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

Solve by quadratic formula,

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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