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rosijanka [135]

3 years ago

5

Complete the following problems.

1 answer:

Nadusha1986 [10]3 years ago

5 0

To find the answer, see if the point is going to the left or to the right. If it is going to the left, it is less than. If it is going to the right it is greater than. Next find if the point is closed (shaded in) or open (not shaded in). If it is closed, it is equal to, if it is open, it is not equal to. Ex: Closed to the right - Greater than or equal to.

1) x is less than -7

2) x is less than or equal to 4.5

3) x is greater than -5

4) x is greater than 1.5

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Answer:

4/10

Step-by-step explanation:

There are 10 items and 4 chocolates, therefore it is 4/10

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A

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Laura has 45 buttons. She gives away b buttons. Write an expression that shows the number of buttons Laura has left.

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State if the triangle in each pair are similar. If so, state the reason they are similar and complete the similarity statement.

leva [86]

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

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

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

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

3 years ago