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antoniya [11.8K]
3 years ago
5

Find the maximum rate of change off at the given point and the direction in which it occurs.

Mathematics
1 answer:
Alexeev081 [22]3 years ago
3 0

Answer:

Maximum rate change |\nablaf| = √65

Direction = ( 1, 8 ) / √65

i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )

Step-by-step explanation:

Given that;

f(x, y) = 4y √x, (4, 1)

{ x=4 and y=1 }

Maximum rate of change occurs with the gradient vector;

\nablaf = [ df/dx, df/dy ] = [ 2y/√x, 4√x ]

we substitute in our value of x and y

\nablaf =  2(1)/√4, 4√4

\nablaf = 2/√4, 4√4

\nablaf = ( 1, 8 )

Maximum rate change |\nablaf| = | ( 1, 8 ) | = √( 1² + 8² ) = √(1 + 64)

Maximum rate change |\nablaf| = √65

Direction = \nablaf / |\nablaf|

we substitute

Direction = ( 1, 8 ) / √65

i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )

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3 years ago
three different are rung at intervals of 36 minutes 40 minutes and 48 minutes if they were rung together at 9 a.m. at what time
Lena [83]

To find the time in which all the bells ring together, we need to find the LCM of 36,40,48.

Prime factorization of 36=2×2×3×3

Prime factorization of 40=2×2×2×5

Prime factorization of 48=2×2×2×2×3

Hence, LCM of 36,40,48=2×2×2×2×3×3×5=720 seconds.

 

720seconds=  

60

720

​

minutes=12minutes

Hence, all the bells will ring together after 12 mi

6 0
3 years ago
Read 2 more answers
Paula has buttons. she gives away 28 buttons. choose the expression that shows the number of buttons paula has left.
mamaluj [8]

Answer:

y = 28 - x

Step-by-step explanation:

The variable x represents how many buttons Paula had before giving 28 away and the variable y represents how many buttons she has now.

3 0
2 years ago
PLEASE HELP ME PLEASEEEEEEEEEEEEEEEEEEE!
mina [271]

Answer:

The most helpful representation would be option C.

Step-by-step explanation:

The horizontal distance traveled corresponds to one of the roots of the quadratic equation.

h(x) = -0.01(x-150)(x+4)

In this case, option c presents the roots of the polynomial, which answers are

x = -4

x = 150

Since we are talking about positive distances, the first option gets discarded.

So the horizontal distance is x = 150 feet

5 0
3 years ago
I NEED HELP PLEASE, THANKS! :)
Alenkasestr [34]

Answer:

Option A

Step-by-step explanation:

This is a great question!

The first thing we want to do here is to graph the system of " inequalities " -

\begin{bmatrix}2x+9y\le \:100\\ 9x+y\le \:54\end{bmatrix}

As x is ≥ 0, respectively y ≥ 0, it makes things a lot simpler, as it kind of restricts us to quadrant 1, but not entirely.

First change each inequality to " slope - intercept " form, as such -

2x + 10y \leq 100,\\10y \leq 100 - 2x,\\y \leq - 1 / 5x + 10\\----------\\9x + y \leq 54,\\y \leq - 9x + 54

The graphed solutions would be in the attachment. I have colored the region with which the two intersect, and the fact that we are limited to quadrant 1. In this colored region there are 3 major points, ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ). We have to determine which of these are are maximum points, as the minimum are the same. Substitute these values ( ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ) ) into the equation f( x, y ) = 10x + 4y,

f ( x, y ) = 10( 5 ) + 4( 9 ),\\f ( x, y ) = 86 -\\f ( x, y ) = 10( 0 ) + 4( 10 ),\\f ( x, y ) = 40 -\\f ( x, y ) = 10( 6 ) + 4( 0 ),\\f ( x, y ) = 60

( 5, 9 ) resulted in the greatest amount, 86. That would make it our maximum point -

<u><em>Solution = Option A</em></u>

3 0
3 years ago
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