What is 10^0 + 10^1 + 10^2 equal to? A. 10,201 B. 120 C. 111 D. 110 E. 100

A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded

Answer:

Step-by-step explanation:

Step 1:we should turn the “facts” into logical expressions.

Step 2:Assign variables

Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)

Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:

Check attachment

Step 4

We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.

Step 5

Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:

Check attachment

Step 6

Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:

If the butler is telling the truth, then by (a) the cook is telling the truth.

If the cook is telling the truth, then by (b) the gardener is lying.

If the gardener is lying, then by (c) the handyman is telling the truth.

If the handyman is telling the truth, they by (d) the cook is lying.

This leads to a contradiction (the cook can not be both telling the truth and lying)! Therefore the butler and cook must be lying. What about the gardener and the handyman? We don’t have enough information to figure out if they are lying. Since the cook is lying, we can’t use (b) to come to any conclusions about the gardener. Even if we are able to conclude that the gardener is telling the truth, we can’t use (c) to come to any conclusions about the handyman.

4 0

2 years ago

Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)

babunello [35]

$\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k$

We want to find $f(x,y,z)$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=x^2+y$

$\dfrac{\partial f}{\partial y}=y^2+x$

$\dfrac{\partial f}{\partial z}=ze^z$

Integrating both sides of the latter equation with respect to $z$ tells us

$f(x,y,z)=e^z(z-1)+g(x,y)$

and differentiating with respect to $x$ gives

$x^2+y=\dfrac{\partial g}{\partial x}$

Integrating both sides with respect to $x$ gives

$g(x,y)=\dfrac{x^3}3+xy+h(y)$

Then

$f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)$

and differentiating both sides with respect to $y$ gives

$y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C$

So the scalar potential function is

$\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}$

By the fundamental theorem of calculus, the work done by $\vec F$ along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it $L$ ) in part (a) is

$\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}$

and $\vec F$ does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them $L_1$ and $L_2$ ) of the given path. Using the fundamental theorem makes this trivial:

$\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3$

$\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4$

8 0

2 years ago

I need help with my homework please answer this correctly

Alla [95]

98,561

By following the rules for each digit, your answer should be 98,561

5 0

2 years ago

May runs around a 4 m track at a consistent speed of 250 m/min. how many minutes does it take me to complete for lapse of the tr

Nookie1986 [14]

Answer:

It takes May 6 minutes and 24 seconds to run 4 laps and 1 minute and 36 seconds per lap

Statement and question:

May runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take May to complete 4 laps of the track?

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Speed of May = 250 meters per minute

Length of the track = 400 meters

2. How many minutes does it take May to complete 4 laps of the track?

Let's answer the question calculating the total distance and the time it took Mary to run around the track, this way:

Total distance = 4 * 400 = 1,600 meters

Time it takes May to run 1,600 meters = 1,600/250

Time it takes May to run 1,600 meters = 6.4 minutes

6.4 minutes = 6 minutes + 0.4 * 60 seconds = 6 minutes and 24 seconds

Time it takes May to run one lap = 6.4/4 = 1.6

1.6 minutes = 1 minute + 0.6 * 60 seconds = 1 minute and 36 seconds

3 0

3 years ago

A company is setting up offices in two different cities. The number of employees hired by the company for its office in city A o

labwork [276]

For this case we have the following functions:
City A:
f (x) = 9x
City B:
g (x) = 3 (2) ^ x
The total number of employees will be:
h (x) = f (x) + g (x)
Substituting we have:
h (x) = 9x + 3 (2) ^ x
Rewriting we have:
h (x) = 3 (3x + (2) ^ x)
For 5 months we have:
h (5) = 3 * (3 * (5) + (2) ^ 5)
h (5) = 141
Answer:
the total number of employees in the company over x months and the total number of employees will be 141 when the function is:
h (x) = 3 (3x + (2)^x); 5 months

3 0

3 years ago

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