4 years ago

Draw a triangle with angles 60 degrees and 60 degrees and an included side length of 1 inch

Mathematics

1 answer:

timama [110]4 years ago

4 0

Answer:

draw it using a pencil and ruler :)

Step-by-step explanation:

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Kelly walks 1/5 mile to school every day. Jamie walks 1/2 as far as Kelly. How does Jamie walk to school every day?

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$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

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Substitute the values then we get

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

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Differentiate w.r.t x

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$V'(x)=0$

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

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

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

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

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

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

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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3 years ago

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