If they exist, find two numbers whose sum is 100 and whose product is a minimum. If such two numbers do not exist, explain why.
Second Derivative Test:
If f is a function defined on an interval I and f is twice differentiable function, then for critical value x
=
c
,
If f

(
c
)
=
0
and
f
′′
(
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<
0
, then f
(
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gives maximum value of f.
If f

(
c
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=
0
and
f
′′
(
c
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>
0
, then f
(
c
)
gives minimum value of f.

Answers

Answer 1

The two numbers whose sum is 100 and whose product is a minimum are: x= 50 and y= 50.

To find two numbers whose sum is 100 and whose product is a minimum, we can use the Second Derivative Test. Let's start by defining the two numbers as x and y. We know that:

x + y = 100

We want to find the minimum value of xy. So, let's define a function f(x) = xy. We can rewrite this function in terms of one variable:

f(x) = x(100 - x) = 100x - x^2

Now, let's find the critical point of this function by taking the derivative:

f'(x) = 100 - 2x

Setting f'(x) = 0 to find the critical point:

100 - 2x = 0
x = 50

So, the critical point is x = 50. To determine whether this is a minimum or maximum, we need to find the second derivative:

f''(x) = -2

Since f''(50) < 0, we know that the critical point x = 50 is a maximum. Therefore, to find the minimum value of f(x), we need to evaluate f at the endpoints of the interval [0, 100]:

f(0) = 0
f(100) = 0

Since f(x) is decreasing from x = 0 to x = 50, and increasing from x = 50 to x = 100, the minimum value of f(x) occurs at x = 50. Therefore, the two numbers whose sum is 100 and whose product is a minimum are:

x = 50
y = 100 - x = 50

So, the two numbers are 50 and 50.

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Answer:

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Answer:

D. 28,923

Step-by-step explanation:

We are given four numbers and are asked to find out which number is odd.

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Answers

Answer:

Each girl earned 2 points

Each boy earned 5 points

Step-by-step explanation:

Let x represent the number of points one girl earned

Let y represent the number of points one boy earned

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Answer:

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Step-by-step explanation:

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Answers

Answer:

f(n) = -6n - 10.

Step-by-step explanation:

This is arithmetic sequence with first term a1 = -16 and common difference d = -6.

So f(n) = a1 + d(n - 1)

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= -6n - 10.

Checking:

f(10) = -6(10) - 10 = -70.

The function that defines the sequence is f(n) = -6n - 10.

What is an Arithmetic Sequence ?

A sequence of numbers which have a relation between them and the consecutive numbers increase or decrease by a fixed amount is called as an Arithmetic Sequence.

The sequence given is -16,-22,-28,-34

This is arithmetic sequence

first term a1 = -16

common difference d = -6.

The nth term of an arithmetic sequence is given by

f(n) = a1 + d(n - 1)

f(n) = -16 - 6(n - 1)

f(n)= -16 - 6n + 6

f(n)= -6n - 10.

To verify this

f(10) = -6(10) - 10 = -70.

Therefore , The nth term is given by f(n)= -6n - 10.

To know more about Arithmetic Sequence

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Help due tonight

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Answers

Answer:

I have solved it in elimination method if you need it in another method let me know.

Step-by-step explanation:

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Answers

Answer:

1/15

Step-by-step explanation:

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 -------

 5 × 3

= 1/15

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The answer is 1/10

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1/5 divided by 2

1/5 times 1/2

1 x 1 = 1

5 x 2 = 10

1/10

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