If Bert had 3 cents more he would have twice as much as Georgia. If he had 4 cents less, he would have the same amount.

The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 88/(2 + x2 + y2), where T is measured in °C and x,

-Dominant- [34]

Answer:

$D_uT(3,1)=-\frac{44}{9}*\frac{1}{\sqrt{2} } \approx-3.46$

Step-by-step explanation:

To find the rate of change of temperature with respect to distance at the point (3, 1) in the x-direction and the y-direction we need to find the Directional Derivative of T(x,y). The definition of the directional derivative is given by:

$D_uT(x,y)=T_x(x,y)i+T_y(x,y)j$

Where i and j are the rectangular components of a unit vector. In this case, the problem don't give us additional information, so let's asume:

$i=\frac{1}{\sqrt{2} }$

$j=\frac{1}{\sqrt{2} }$

So, we need to find the partial derivative with respect to x and y:

In order to do the things easier let's make the next substitution:

$u=2+x^2+y^2$

and express T(x,y) as:

$T(x,y)=88*u^{-1}$

The partial derivative with respect to x is:

Using the chain rule:

$\frac{\partial u}{\partial x}=2x$

Hence:

$T_x(x,y)=88*(u^{-2})*\frac{\partial u}{\partial x}$

Symplying the expression and replacing the value of u:

$T_x(x,y)=\frac{-176x}{(2+x^2+y^2)^2}$

The partial derivative with respect to y is:

Using the chain rule:

$\frac{\partial u}{\partial y}=2y$

Hence:

$T_y(x,y)=88*(u^{-2})*\frac{\partial u}{\partial y}$

Symplying the expression and replacing the value of u:

$T_y(x,y)=\frac{-176y}{(2+x^2+y^2)^2}$

Therefore:

$D_uT(x,y)=(\frac{1}{\sqrt{2} } )*(\frac{-176x}{(2+x^2+y^2)^2} -\frac{176y}{(2+x^2+y^2)^2})$

Evaluating the point (3,1)

$D_uT(3,1)=(\frac{1}{\sqrt{2} } )*(\frac{-176(3)-176(1)}{(2+3^2+1^2)^2})=(\frac{1}{\sqrt{2} })* (-\frac{704}{144})=(\frac{1}{\sqrt{2} }) ( - \frac{44}{9})\approx -3.46$

6 0

1 year ago

Which is the domain of the function f(x) = Negative five-sixths (three-fifths) Superscript x?

amm1812

Answer:

All real numbers less than 0

Step-by-step explanation:

I think it's this one because greater than 0 is wrong

8 0

1 year ago

Person A buys 10 granola bars and 6 cups of yogurt for 518 Person B buys 5 granola bars and 4 cups of yogurt for $9.50. Find the

Alja [10]

Person A buys 10 granola bars and 6 cups of yogurt for $18

Person B buys 5 granola bars and 4 cups of yogurt for $9.50

Let x represent the granola bars

Let y represent the yogurt

10x + 6y = 18 << ( Divide both sides by 2 )

The second equation is 5x + 4y = 9.50. Now subtract the two equations.

5x + 4y = 9.50

-5x - 3y = -9

y = $.50

5x + 3(.50) = 9

5x + 1.50 = 9

5x = 7.5

x = $1.50

I hope this answered your question

Please remember to rate my answer and comment bellow if you have any questions

4 0

1 year ago

Chris wonders whether the planes that fly over his house follow any sort of pattern. For two months, he

KatRina [158]

Answer:

Kindly check explanation

Step-by-step explanation:

From the relative frequency below:

For NORTH - SOUTH:

Monday - Thursday = 115 ; has a relative frequency of 75.16%,

Hence, we can obtain the row total since it amounts to 100% thus;

75.16% of row total = 115

0.7516× row total = 115

Row total = 115 / 0.7516 = 153.00

Hence, Friday - sunday:

Row total - (Monday-Thursday)

153 - 115 = 38

FOR EAST - WEST:

Monday - Thursday = 21 ; has a relative frequency of 25.30%,

Hence, we can obtain the row total since it amounts to 100% thus;

25.30% of row total = 21

0. 253 × row total = 21

Row total = 21 / 0.253 = 83.00

Hence, Friday - sunday:

Row total - (Monday-Thursday)

83 - 21 = 62

x = (38 / 100) × 100%

x = 0.38 × 100%

x = 38.00 %

5 0

2 years ago

Approximately what is the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertica

Lera25 [3.4K]

Answer:

212m

Step-by-step explanation:

The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.

Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;

Since we have the angle theta = 45° and opposite = 150m

According to SOH;

Sin theta = opposite/hypotenuse.

Sin45° = 150/hyp

hyp = 150/sin45°

hyp = 150/(1/√2)

hyp = 150×√2

hyp = 150√2 m

hyp = 212.13m

Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m

8 0

1 year ago