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mixas84 [53]
2 years ago
9

What is the solution to 2(2x +1) = 0.5(2x - 14)?​

Mathematics
1 answer:
Leona [35]2 years ago
3 0
Where are the options
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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 23 in. by 13 in. by
faltersainse [42]

Answer:

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is 361.19 in^3.

Step-by-step explanation:

Given that the dimensions of a cardboard is 23 in by 13 in.

Let the side of the square be x in.

Then the length of the box= (23-2x) in

and the width of the box =(13-2x) in

and height = x in.

The volume of the box is = length ×width × height

                                         =[(23-2x)(13-2x)x] in^3

                                         =(299x-72x² +4x^3) in^3

∴V=299x-72x² +4x³

Differentiating with respect x

V'= 299-144x+12x²

Again differentiating with respect x

V''= -144+24x

To find the dimensions, we set V'=0

∴299-144x+12x²=0

Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here a=12, b=-144 , c=299

\therefore x=\frac{-(-144)\pm\sqrt{(-144)^2-4.12.299}}{2.12}

\Rightarrow x= 9.33, 2.67

If  we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.

∴x = 2.67 in

If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.

V''|_{x=2.67}=-144+(24\times 2.67)=-79.92

Therefore  at x = 2.67, the volume of the box maximum.

The length of the box =[23-(2×2.67)] in

                                    =17.66 in

The width of the box =[13-(2×2.67)] in

                                  =7.66 in

The height of the box= 2.67 in

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is =(17.66×7.66×2.67) in^3

                                                            =361.19 in^3

8 0
3 years ago
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Lata
Artist 52 [7]

Answer:

52/79

Step-by-step explanation:

One costume = 156 (This is our numerator.)

All visitors = 156 + 58 + 23 = 237 (This is our denominator.)

156/237

Find the GCF to simplify (sneak peek it's 3)

156/3 = 52

237/3 = 79

52/79 (tada!)

4 0
2 years ago
michael basketball team practice fir 2 hours and 40 minutes yesturday and 3 hours 15 minutes today.how much longer did team prac
Serjik [45]

Answer:

35 minutes

Step-by-step explanation:

2 hrs 4 min= 160 min

3 hrs 15 min= 195 min

195-160=35

6 0
3 years ago
X = 11 when y = 99. If y varies directly as x, find x when y = 144
goldenfox [79]

Answer:

99 is 9 times 11 144 divide by 9 is 16

4 0
2 years ago
Help!!! I really need this
anyanavicka [17]

Answer:

bruh

Step-by-step explanation:

maybe google works

6 0
3 years ago
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