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Pie
3 years ago
12

The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves w

ho always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
6 0

Answer:

A is a knave

B is a knight

Step-by-step explanation:

If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.

If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y 2 ( y 2 − 4 ) = x 2 ( x
yawa3891 [41]

Answer:

y = -2

Step-by-step explanation:

To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx

The equation is

y^2(y^2-4)=x^2(x^2-5)

implicit differentiation give us

\frac{d}{dx}[y^2(y^2-4)=x^2(x^2-5)]\\\\2y\frac{dy}{dx}(y^2-4)+y^2(2y\frac{dy}{dx})=2x(x^2-5)+x^2(2x)\\\\4y^3\frac{dy}{dx}-8y\frac{dy}{dx}=2x^3-10x+2x^3\\\\\frac{dy}{dx}=\frac{4x^3-10x}{4y^3-8y}

But we know that

m=\frac{dy}{dx}\\y=mx+b

Hence, for the point (0,-2) and by replacing for dy/dx

m=\frac{dy}{dx}_{(0,-2)}=\frac{4(0)+10(0)}{4(-2)^3-8(-2)}=0

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:

y=(0)x+b = -2

HOPE  THIS HELPS!!

4 0
4 years ago
Simplify radicals problems attached please help!
Finger [1]

Answer:

  G7.  (2√3)/3

  G8.  -2+√7

  G9.  (6 +2√2 -3√3 -√6)/7

Step-by-step explanation:

G7.

\dfrac{2}{\sqrt{3}}=\dfrac{2}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}

__

G8.

\dfrac{3}{2 +\sqrt{7}}=\dfrac{3}{2+\sqrt{7}}\cdot\dfrac{2-\sqrt{7}}{2-\sqrt{7}}=\dfrac{6-3\sqrt{7}}{2^2-(\sqrt{7})^2}\\\\=\dfrac{6-3\sqrt{7}}{-3}=\sqrt{7}-2

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G9.

\dfrac{2-\sqrt{3}}{3-\sqrt{2}}=\dfrac{2-\sqrt{3}}{3-\sqrt{2}}\cdot\dfrac{3+\sqrt{2}}{3+\sqrt{2}}=\dfrac{(2-\sqrt{3})(3+\sqrt{2})}{9-2}\\\\=\dfrac{6+2\sqrt{2}-3\sqrt{3}-\sqrt{6}}{7}

_____

<em>Comment on the problems</em>

In most cases, these expressions are the simplest possible (take the least amount of ink to draw, and take the fewest math operations to evaluate). What seems to be intended is that the denominator be made a rational number. This is done by multiplying the given fraction by a fraction equal to 1 that has the same denominator but with the sign of the radical reversed (unless, as in the first case, the radical is by itself).

The purpose of doing this is to take advantage of the fact that (a-b)(a+b) = a²-b², so if "a" or "b" is a square root, that root will not be seen in the product. In problem G9, we see this can make the numerator quite messy--not exactly a simpler form--but all the irrational numbers are in the numerator.

8 0
4 years ago
As part of a quality-control study aimed at improving a production line, the weights (in ounces) of 50 bars of soaps are measure
grin007 [14]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is the weight in ounces of a soap bar.

Attached is a QQplot diagram.

A Q-Q plot is a diagram that compares two probability distributions, in this case, the probability distribution of the data set against the theoretical normal distribution. If the observed data matches the theoretical sets, you can say that that population follows said distribution.

As you can see in the graphic the observed values (blue dots) fit the normal theoretical quantiles, so we can say that the data appear to come from a normal distribution.

I hope it helps.

4 0
3 years ago
5(a + 2b)<br><br> Please help me on this problem
just olya [345]
If you are looking to get it into standard form, you distribute the 5 to get 5a+10b
3 0
3 years ago
Read 2 more answers
H(x)=2x-6 find the value. -2[h(3)]
defon

Answer:

-2[h(3)] = 0

Step-by-step explanation:

Step 1: Define

h(x) = 2x - 6

Step 2: Find h(3)

h(3) = 2(3) - 6

h(3) = 6 - 6

h(3) = 0

Step 3: Find -2[h(3)]

-2(0)

0

3 0
3 years ago
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