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3 years ago

10

The greatest product of a 3 digit number and a 1 digit number is 8,891. is it correct?

2 answers:

xz_007 [3.2K]3 years ago

6 0

<span> no, 9 is the biggest single digit number and 999 is the biggest 3 digit number. 9x999 is 8991 <span> <span> </span></span></span>

KengaRu [80]3 years ago

3 0

The biggest 3 digit number is 999 since 9 is highest single digit number
highest singel digit numbe ris 9 so
9 times 999=8991
so you are incorrect unless you made a typo

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

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4 years ago

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Delvig [45]

Answer:

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Step-by-step explanation:

Side-spliting theorem

21/(x-4)=14/6

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21*6=14*(x-4)

distribute 14

126=14x-56

add 56 to both sides

126+56=14x-56+56

leaving you with

182=14x

Divide both sides by 14 to get x by itself

182/14=14x/14

13=x

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Solve the equation step by step in form of rational and irrational numbers<br>x^2=144

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X^2=144
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Answer:

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Step-by-step explanation:

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