As given he made 3/5 of basket he shot.
So we can find number of basket made by Everett equal to 3/5 of total number of shot .
So if total number of shot is 60.
Then the number of basket made by Everett =
of 60.
So the number of basket made by Everett in 60 shots = 36.
BY STUDYING THIS LECTURE, YOU MIGHT JUST ANSWER THIS PROBLEM ON YOUR OWN!
Any convergent sequence in any metric space is Cauchy. I think the easiest way to prove that this sequence is Cauchy is to show that it is convergent in C_b[-1,1], ie, to exhibit an element f in C_b[-1,1] and a proof that ||f_n - f|| goes to 0 as n goes to infinity (where || || denotes the supremum norm).
<span>It is clear that the pointwise limit of the f_n's is the function f(x) = (x^2 + 0)^(1/2) = |x|, so if the f_n's converge in the norm of C_b[-1,1] to anything it will have to be that. We just need to show that ||f_n - f|| does indeed go to 0. For this, note that for any x in [-1,1] we have </span>
<span>f_n(x) - f(x) = sqrt(x^2 + 1/n) - sqrt(x^2) </span>
<span>= [sqrt(x^2 + 1/n) - sqrt(x^2)] [sqrt(x^2 + 1/n) + sqrt(x^2)]/[sqrt(x^2 + 1/n) + sqrt(x^2)] </span>
<span>= [(x^2 + 1/n) - x^2]/[sqrt(x^2 + 1/n) + sqrt(x^2)] </span>
<span>= (1/n)/[sqrt(x^2 + 1/n) + sqrt(x^2)] </span>
<span>and since x^2 >= 0 for all x we have sqrt(x^2 + 1/n) + sqrt(x^2) >= sqrt(0 + 1/n) + sqrt(0) = sqrt(1/n) and therefore </span>
<span>|f_n(x) - f(x)| <= (1/n)/[sqrt(1/n)] = 1/sqrt(n) for all x in [-1,1], </span>
<span>and hence ||f_n - f|| <= 1/sqrt(n) holds for all n. [If you think about this argument for a moment you will see that it actually can be used to show that ||f_n - f|| = 1/sqrt(n) for all n, but this isn't important.] Since 1/sqrt(n) goes to 0 as n goes to infinity it follows that f_n converges to f in the norm of C_b[-1,1] and hence that the sequence f_n is Cauchy in C_b[-1,1]. </span>
<span>You may have noticed there is nothing special about [-1,1] here; for any closed interval [p,q] the same estimate could be used to show that f_n converges to f in the norm of C_b[p,q]. In fact the sequence f_n converges to f uniformly on all of R. [It is not easy to fit this into a metric space context because the most obvious choice of a metric space for discussing uniform convergence on R is the space C_b(R) of bounded functions on R, and while f_n - f is bounded, and hence in C_b(R), for any n, neither of the individual functions f or f_n is bounded, and hence neither f nor any of the f_n's is in C_b(R).] </span>
<span>In general, when asked to prove that a sequence is Cauchy, if you can identify its limit, as we could here, the easiest thing to do is to prove that it's convergent (which implies that it's Cauchy). Proving that a sequence is Cauchy straight from the definitions is more commonly done only when the limit of the sequence cannot be explicitly identified. This isn't as rare as it sounds, e.g. when you are proving general results about convergence you generally do not have 'formulas' for the limit and must proceed in this way. For example, the usual proof of the fact that an absolutely convergent series of real numbers must be convergent does this. One uses the hypothesis that sum |a_n| is convergent to show from the definition of "Cauchy sequence" that the sequence a_1, a_1 + a_2, ..., a_1 + a_2 + ... + a_k, ... is Cauchy, and therefore convergent, and therefore that sum a_n converges. This is done because there is no explicit formula for the sum of an arbitrarily given absolutely convergent series.</span>
Try graphing the 3 first (you know it's positive 3 because it has a + before it, and you know the line is going to go down (negative) because it has a - before it, after that you can find the slope if the line, in this case 1/2, and move one unit down (because it's negative) and 2 to the right
Hope this helped! :)
Answer:
Step-by-step explanation:
x² + 3x - 10 = 0
We have to find two numbers which multiply to -10 and have a sum of -3.
Two great numbers which match these conditions are 5 and -2!
5 + (-2) = 3
5 * (-2) = -10
So, now we can factor.
(x + 5)(x - 2) = x² + 3x - 10, right?
Now we know A and B are 5 and -2. (Please keep in mind these are not the solutions or the roots to the quadratic. When solving for the roots in a quadratic, you have to find numbers which make the equation equal to zero. Anything multiplied by zero is zero, so when you input a value into the parentheses which makes the value inside the parentheses zero, the whole equation becomes zero and this is why quadratics have up to two solutions because up to two values can make the equation equal to zero.)