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3 years ago

The GCF of 24 and 32 is

Mathematics

2 answers:

Harrizon [31]3 years ago

7 0

Answer:

Step-by-step explanation:

3 multiplied by 8 = 24

and 4 multiplied by 8 = 32

Oksana_A [137]3 years ago

4 0

Start by setting up a factor tree for each number.

Factor in anyway that you'd like.

At the end, circle all prime numbers.

Remember, prime numbers are numbers

with only 2 factors, 1 and the number itself.

Now write these factors in least to greatest

multiplying them separate rows.

Circle factors they have in common.

Since 3 pairs of two's match up, multiply by 2 three times to get 8.

So the GCF is 8.

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Marrrta [24]

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3 years ago

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Is -5^2 equal to (-5)^2

gtnhenbr [62]

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3 years ago

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What is the pattern to 1,2,4,7,11

Svetllana [295]

Answer:

1+1=2

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Step-by-step explanation:

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2 years ago

How do I do this and what’s the answers?

Iteru [2.4K]

Answer:

a.5years=300 rabbits

b. 50 years(multiply 50 by 300)

Step-by-step explanation:

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4 0

3 years ago

Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.

irina1246 [14]

Lagrange multipliers:

$L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)$

$L_x=y^2z^2+\lambda=0$
$L_y=2xyz^2+\lambda=0$
$L_z=2xy^2z+\lambda=0$
$L_\lambda=x+y+z-5=0$

$\lambda=-y^2z^2=-2xyz^2=-2xy^2z$

$-y^2z^2=-2xyz^2\implies y=2x$ (if $y,z\neq0$ )

$-y^2z^2=-2xy^2z\implies z=2x$ (if $y,z\neq0$ )

$-2xyz^2=-2xy^2z\implies z=y$ (if $x,y,z\neq0$ )

In the first octant, we assume $x,y,z>0$ , so we can ignore the caveats above. Now,

$x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2$

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of $f(1,2,2)=16$ .

We also need to check the boundary of the region, i.e. the intersection of $x+y+z=5$ with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force $f(x,y,z)=0$ , so the point we found is the only extremum.

4 0

3 years ago