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AleksandrR [38]

3 years ago

10

Aziza has a triangle with two sides measuring 11 in. and 15 in. She claims that the third side can be any length as long as it i

s greater than 4 in. Which statement about Aziza’s claim is correct?

1 answer:

irina [24]3 years ago

4 0

Answer:

Aziza’s claim is incomplete. The third side must be between 4 in. and 26 in.

Step-by-step explanation:

With the Triangle Inequality Theorem, saying that the sum of lengths of any two sides of a triangle is greater than the length of the third side. With this we can develop two inequalities:

11 + 15 > x

26 > x

rewrite this as x < 26

11 + x > 15

x > 15 - 11 Subtract 11 from both sides

x > 4

Therefore, the third side can be anywhere greater than 4 inches and less than and less than 26 inches.

4 < x < 26

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3 years ago

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ZanzabumX [31]

Answer:

Inverse function is $f^{-1}(x)=\frac{3}{2}x+\frac{51}{2}$ .

Step-by-step explanation:

Given function is $f\left(x\right)=\frac{2}{3}x-17$ .

Now we need to find the inverse of the given function.

Step 1: replace f(x) with y

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Step 2: switch x and y

$x=\frac{2}{3}y-17$

Step 3: solve for y

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Hence required inverse function is $f^{-1}(x)=\frac{3}{2}x+\frac{51}{2}$ .

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3 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]

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)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

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

Differentiate w.r.t x

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

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

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

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

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

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

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

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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Answer:

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Step-by-step explanation:

I was working on this problem also.

Maybe my version will help, too.

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