3 years ago

Could someone help me? ASAP!!

Mathematics

1 answer:

Wewaii [24]3 years ago

8 0

Answer:

y=2x+3

Slope intercept form

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4 and 5 are complements, and 1 and 5 are complements. By the congruent complements theorem, which angle is congruent to 4? 1 2 3

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The angle congruent to 4 is 1.

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Claire has 0.5 juice left in her box and Ethan has 0.45 juice left in his juice box. Who has the most juice left

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Claire .5 is greater than .45

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Anna would like to purchase a new bike that costs $205. She already has $31 saved. If she saves a maximum of $12 a week, the fol

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It will take at least 15 weeks

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12w+31 ≥ 205

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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

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Answer:

$\frac{5}{3}$ 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.

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