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OUIAE
communicate
conduplicate
conglutinate
conjunctivae
outdistance
outrivalled
cousinage
Hello Carly.
4. Write a counterexample for the converse of "Cats make great pets."
My answer: A tiger is a cat, and it’s not a great pet.
This is not correct. The sentence can be rewritten “All cats are great pets”; the converse is then “All great pets are cats”. Now give an example of an animal that is a great pet but not a cat.
6. Write a counterexample for the converse of "Cars have four wheels."
My answer: The aptera is a car, and it has three wheels.
Again, not correct. The converse is “All things with four wheels are cars”. Give an example of something that has four wheels but is not a car.
Today I learned the word thigmomorphogenesis, which is the way plants grow in response to touch.
Hi !nval!d_us3rnam3.
Another way you can do part (c) is to let
from which you get the system of linear equations
from which you can easily solve for x, y, z.
A geodesic on a smooth manifold M with an affine connection ∇ is defined as a curve γ(t) such that parallel transport along the curve preserves the tangent vector to the curve, i.e.
at each point along the curve, where
is the derivative with respect to t.
Using local coordinates on M, we can write the geodesic equation (using the summation convention) as the ordinary differential equation
where
are the coordinates of the curve γ(t) and
are the Christoffel symbols of the connection ∇.
[Source: Wikipedia]
If α is an automorphism of a finite field F, then
Is the above assertion true? If so, prove it; otherwise, give a counterexample.
#35. Did you know?
The first ship to circumnavigate the globe was the Victoria, one of the ships in a 16th-century expedition led by the Portuguese explorer Fernão de Magalhães – better known as Ferdinand Magellan – who was killed in the Philippines during the voyage.
Hi MKNB.
1.
The total number of combinations of balls drawn is
To draw three different colours, you need to draw a red ball (which can be done in 4 ways), a white ball (which can be done in 5 ways), and a green ball (which can be done in 6 ways); so the number of ways to draw three different-coloured balls is 4 × 5 × 6 = 120.
Hence the probability is 120 divided by N.
2.
There are
ways of choosing 3 balls from x of the same colour, i.e. c(4) = 4 ways of choosing 3 red balls, c(5) = 10 ways of choosing 3 white balls, and c(6) = 20 ways of choosing 3 green balls.
Add them up and divide by N to get the probability of drawing three balls of the same colour.
Hi Zeeshan.
1.
2.
3.
If f is a scalar function of the vector variable r = xi+yj+zk then
4.
Hint: Suppose A is the zero matrix.
5.
What do you think the value of
might be? Hint: If f(r) is twice differentiable and all derivatives are continuous, then
where s, t ∈ {x, y, z}.
6.
If they were simultaneous linear equations, how would you go about solving them? The method for solving simultaneous linear equations can be used to solve these.
7.
Use the definition given in Question 3.
#33. Did you know?
The most westerly point on the mainland of Africa is Cap-Vert, or Cabo Verde (not to be confused with the Cape Verde islands), in Senegal – so named by Dinis Dias, the Portuguese explorer who reached it in 1445.
#31. Did you know?
The first country in the world to abolish capital punishment was Venezuela (1863).
Ég er að hlusta á tónlist.
(I’m listening to music.)
Hi Amartyanil.
I should have mentioned that the numbers must be unequal.
That is still not enough: the original statement is still untrue. Take
then nx = mc but c = 3 is still prime.
I think the problem needs to be stated this way:
And here is the proof.
If gcd(m,n) = 1, then there are integers r, s such that
Multiplying this by c,
where k = rx+sc. Given that n > 1, c is positive and not equal to n, then k > 1 as well. Thus c = nk is composite.
Hi MKNB.
Start by trying factors of the constant term: ±1, ±2, ±4, ±8, ±16. Substitute one of these, say 2, for x in the polynomial expression and see if you get zero:
We don’t get 0, so (x−2) is not a factor. Try x = −2 instead:
This time we do get zero, so (x+2) is a factor.
Once you have a factor, you can factorize the polynomial and find other factors.
Thanks Bob!
My solution is entirely non-geometric.
Hi Jamus.
You got the right answer but you need to write your steps more clearly.
To verify that it is the right answer, substitute y = 5 back in the original equation:
The difference in price is $(20−15) = $5.
What percentage is $5 of $20 (the origial price)? You should be able to work this out.
Can you move this thread to that section? Thanks.
dab → bad
(Dab is a type of fish.)
feast
fluff
If
is a palindrome, when is a palindrome? By looking at this chart, it looks like the only values that work are . The values of are . Is it true that these are the only palindromes of the form , where is a palindrome? If true, prove why. Otherwise, find a counterexample.
Hi Anthony.
I’ve found another one:
Without using a calculator, prove that
No calculators, please. Well, you can’t use a calculator anyway; that value is irrational so a calculator won’t give you the exact result.
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