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Zigmanuir [339]

2 years ago

10

several friends each had 2/5 of a bag of peanuts left over from the baseball game. They realized that they could have bought 2 f

ewer bags of peanuts between them. How many friends went to the game?

1 answer:

djyliett [7]2 years ago

6 0

I think it is 3 friends that went to the game.

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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

2 years ago

A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of t

skad [1K]

Answer:

3876

Step-by-step explanation:

Given the following :

Fraternity members = 20

They are to attend 5 different parties in groups of 4

Meaning a group = 4 persons

Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).

Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.

Group members are in 4's

19C4

From: nCr = n! /(n-r)! r!

19C4 = 19! / (19 - 4)! 4!

= 19! / 15! 4!

= (19 * 18 * 17 * 16) / (4 * 3 * 2)

= 93024 / 24

= 3876

3 0

2 years ago

Sean pays £10 for 24 chocolate bars. He sells all 24 chocolate bars for 50p each.

VladimirAG [237]

Answer:

the percentage profit is 20%

Step-by-step explanation:

Given that

Sean paid £10 for 24 chocolate bars

He sold all 24 chocolate bars for 50p each

we need to find out the percentage profit

Since he paid £10 and sale value is (24 × 0.50) i.e. £12

So, the percentage profit is

= (£12 - £10) ÷ (£10)

= 20%

Hence, the percentage profit is 20%

4 0

2 years ago

The championship record in baseball in a certain year was 52 games won, and 14 lost. What percent of the games were won?

slamgirl [31]

Number of games won/Number of total games played x 100%

52/66 x 100% = 78.79%

Hope u understood! :)

5 0

2 years ago

Suppose that a person's birthday is a uniformly random choice from the 365 days of a year (leap years are ignored), and one pers

maxonik [38]

P ( A ∩ B ∩ C) = 1/365
P(A) = 1/365, P(B)= 1/365, P(C) = 365
If events A,B and C are independed then P (A ∩ B ∩ C) = P (A) P(B) P(C) must be true,
From the probabilities we have
1/365≠ 1/365 * 1/365 * 1/365
Thus, events A,B, C are not independent.

3 0

2 years ago