If an relationship is proportional what is the missing value from the table?

Mathematics

1 answer:

Mariana [72]3 years ago

4 0

Answer : 12

Explanation :

In the first row of the table, we find that the -2 is the change, and in the third row -6 is the change.

Using this, we can find that the second row should have -4 subtracted from 16.

We know this because from looking at the changes from the first and second row, the differences multiply by two, as the rows increase. So -2 multiplied by 2 is -4, and 16 subtract 4 is 12.

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There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the outp

Mariana [72]

Answer:

<em> 15</em>
<em> 42,250</em>

Step-by-step explanation:

The given function is,

$P=40000+300x-10x^2$

where,

P = the total production of apples,

x = the number of trees added.

As the quadratic function has a negative leading coefficient, so it will open downward and at the vertex the value of function is maximum.

The vertex will be at $\left(-\dfrac{b}{2a},-f\left(\dfrac{b}{2a}\right )\right)$

The value of the function will be maximum at,

$x=-\dfrac{b}{2a}$

Putting the values,

$x=-\dfrac{300}{2\times (-10)}=\dfrac{300}{2\times 10}=\dfrac{300}{20}=15$

So at x=15 or for 15 number of trees the production will be ,maximum.

Putting x=15 in f(x) will yield the maximum production of apples.

$P=40000+300(15)-10(15)^2=42,250$

4 0

3 years ago

Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

Feliz [49]

$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have