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2 years ago

Solve for x 6x - 19 = 13x - 5

Mathematics

2 answers:

xenn [34]2 years ago

6 0

Answer:

6x-19=13x-5

We move all terms to the left:

6x-19-(13x-5)=0

We get rid of parentheses

6x-13x+5-19=0

We add all the numbers together, and all the variables

-7x-14=0

We move all terms containing x to the left, all other terms to the right

-7x=14

x=14/-7

x=-2

Step-by-step explanation:

stira [4]2 years ago

4 0

Answer:

x = -2

Step-by-step explanation:

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2 years ago

A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

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$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

2 years ago

Solve for x 6x - 19 = 13x - 5​

Solve for x 6x - 19 = 13x - 5