Since 4 circles are circumscribed by a square, then the side length of the square is 8

So the area of the square is 8^2 = 64

The area of 4 squares is 4 * pi*2^2 = 16pi

So the answer will be 64 - 16pi

6 0

3 years ago

Read 2 more answers

Question 1 (5 points)

worty [1.4K]

Answer:

0.5 is the answer to this

5 0

3 years ago

Read 2 more answers

Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to f

tino4ka555 [31]

Answer:

The minimum value of the given function is f(0) = 0

Step-by-step explanation:

Explanation:-

Extreme value :- f(a, b) is said to be an extreme value of given function 'f' , if it is a maximum or minimum value.

i) the necessary and sufficient condition for f(x) to have a maximum or minimum at given point.

ii) find first derivative $f^{l} (x)$ and equating zero

iii) solve and find 'x' values

iv) Find second derivative $f^{ll}(x) >0$ then find the minimum value at x=a

v) Find second derivative $f^{ll}(x)$ then find the maximum value at x=a

Problem:-

Given function is f(x) = log ( x^2 +1)

step1:- find first derivative $f^{l} (x)$ and equating zero

$f^{l}(x) = \frac{1}{x^2+1} \frac{d}{dx}(x^2+1)$

$f^{l}(x) = \frac{1}{x^2+1} (2x)$ ……………(1)

$f^{l}(x) = \frac{1}{x^2+1} (2x)=0$

the point is x=0

step2:-

Again differentiating with respective to 'x', we get

$f^{ll}(x)=\frac{x^2+1(2)-2x(2x)}{(x^2+1)^2}$

on simplification , we get

$f^{ll}(x) = \frac{-2x^2+2}{(x^2+1)^2}$

put x= 0 we get $f^{ll}(0) = \frac{2}{(1)^2}$ > 0

$f^{ll}(x) >0$ then find the minimum value at x=0

Final answer:-

The minimum value of the given function is f(0) = 0

5 0

3 years ago

Identify the inverse g(x) of the given relation f(x).

Leno4ka [110]

Answer:

g(x) = {(3, 8), (1, 4), (-1,0), (-3, 4);

Step-by-step explanation:

Recall and use the fact that, the domain of a relation becomes the range of its inverse and vice-versa.

Base on the possible answers ,the given relation is f(x) = {(8,3), (4, 1), (0, -1), (4,-3)}

To find an inverse relation for f(x), we need to swap the x and y coordinates of f(x).

The inverse of f(x) will have the ordered pairs: (3,8),(1,4),(-1,0),(-3,-4)

Therefore the correct choice is g(x) = {(3, 8), (1, 4), (-1,0), (-3, 4);

8 0

3 years ago