HELP might fail class

Mathematics

1 answer:

sergiy2304 [10]3 years ago

7 0

By not using the digit 0, John has 9 digits left to choose from. By not using the letter m, John has 25 letters left to choose from.

The password pattern is <letter><letter><digit><digit><digit><digit>. Use the Multiplication Principle:

25 x 25 x 9 x 9 x 9 x 9 = 4,100,625

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In what ways can vertical, horizontal, and oblique asymptotes be identified

Wittaler [7]

They are all alike because they are all angles

8 0

3 years ago

a) Suppose f"(z) exists on an interval I and f(s) has a zero at three distinct points a < b< c on I. Show there is a pbint

Fynjy0 [20]

Answer:

We can find a root in the average point (a+b+c)/3

Step-By-Step Explanation:

We can use the Rolle Theorem. Since f is two times deribable on both [a,b] and [b,c], then there exists points x in (a,b) and y in (b,c) such that f'(x) = f'(y) = 0. Now, again by using Rolle Theorem, since f' is derivable in [x,y] (because it is a closed interval in I), then there exists s in [x,y] such that f''(s) = 0. This proves a.

The cube (x-a)(x-b)(x-c) has 3 roots, a, b and c and it is two times derivable because it is a polynomial. Hence we can use (a) to ensure that there is a root on I. Nevertheless, we can try to find the root manually:

f'(x) = (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)

f''(x) = (x-c)+(x-b)+(x-c)+(x-a)+(x-b)+(x-a) = 2(x-a)+2(x-b)+2(x-c) = 2( (x-a) + (x-b) + (x-c) ) = 6x - 2 (a+b+c).

We want x such that

6x - 2(a+b+c) = 0, or, equivalently,

3x - (a+b+c) = 0

Hence

x = (a+b+c)/3

Is a root of f'' in I.

3 0

3 years ago

Please help me itd mean alot

yan [13]