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2 years ago

8

Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possi

bilities exist for how the people could get off the elevator? (you can treat the people as indistinguishable for this problem, i.e., for example, if two people get off on the 4th floor, we don’t care which two people they are.)

1 answer:

Fittoniya [83]2 years ago

7 0

Answer:

140

Step-by-step explanation:

you multiply the amount of people by the amount of floors, 7x20=140

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Answer:

See diagram attached.

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Step-by-step explanation:

Given the two inequalities:

$y \ge 2x + 1\\ y \le 2x - 2$

To graph them, first of all, let us write their corresponding equations:

$y = 2x + 1 \\y = 2x - 2$

We now find at least 2 points each which satisfy the equations to plot the graph.

Equation $y = 2x + 1$ :

Putting x = 0, y = 1

Putting y = 0, x = $-\frac{1}2$ .

Two points are (0, 1) and ( $-\frac{1}2$ , 0).

Equation $y = 2x -2$ :

Putting x = 0, y = -2

Putting y = 0, x = 1.

Two points are (0, -2) and (1, 0).

Now, let us plot them.

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Which is true.

So, The shaded region will be <em>towards point (1,4).</em>

<em></em>

Let us take a point (1, 4) and check whether it satisfies the second inequality.

$4 \le 2 \times 1 -2\\\Rightarrow 4 \le 0\ [\bold{False}]$

So, The shaded region will be <em>opposite to point (1,4).</em>

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2 years ago

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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:

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

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

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:

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

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