What is the square root of 196?

Find the absolute maximum and minimum values of f(x, y) = x+y+ p 1 − x 2 − y 2 on the quarter disc {(x, y) | x ≥ 0, y ≥ 0, x2 +

Andreas93 [3]

Answer:

absolute max: f(x,y)=1/2+p1 ; at P(1/2,1/2)

absolute min: f(x,y)=p1 ; at U(0,0), V(1,0) and W(0,1)

Step-by-step explanation:

In order to find the absolute max and min, we need to analyse the region inside the quarter disc and the region at the limit of the disc:

Region inside the quarter disc:

There could be Minimums and Maximums, if:

∇f(x,y)=(0,0) (gradient)

we develop:

(1-2x, 1-2y)=(0,0)

x=1/2

y=1/2

Critic point P(1/2,1/2) is inside the quarter disc.

f(P)=1/2+1/2+p1-1/4-1/4=1/2+p1

f(0,0)=p1

We see that:

f(P)>f(0,0), then P(1/2,1/2) is a maximum relative

Region at the limit of the disc:

We use the Method of Lagrange Multipliers, when we need to find a max o min from a f(x,y) subject to a constraint g(x,y); g(x,y)=K (constant). In our case the constraint are the curves of the quarter disc:

g1(x, y)=x^2+y^2=1

g2(x, y)=x=0

g3(x, y)=y=0

We can obtain the critical points (maximums and minimums) subject to the constraint by solving the system of equations:

∇f(x,y)=λ∇g(x,y) ; (gradient)

g(x,y)=K

Analyse in g2:

x=0;

1-2y=0;

y=1/2

Q(0,1/2) critical point

f(Q)=1/4+p1

We do the same reflexion as for P. Q is a maximum relative

Analyse in g3:

y=0;

1-2x=0;

x=1/2

R(1/2,0) critical point

f(R)=1/4+p1

We do the same reflexion as for P. R is a maximum relative

Analyse in g1:

(1-2x, 1-2y)=λ(2x,2y)

x^2+y^2=1

Developing:

x=1/(2λ+2)

y=1/(2λ+2)

x^2+y^2=1

So:

(1/(2λ+2))^2+(1/(2λ+2))^2=1

$\lambda_{1}=\sqrt{1/2}*-1 =-0.29$

$\lambda_{2}=-\sqrt{1/2}*-1 =-1.71$

$\lambda_{2}$ give us (x,y) values negatives, outside the region, so we do not take it in account

For $\lambda_{1}$ : S(x,y)=(0.70, 070)

and

f(S)=0.70+0.70+p1-0.70^2-0.70^2=0.42+p1

We do the same reflexion as for P. S is a maximum relative

Points limits between g1, g2 y g3

we need also to analyse the points limits between g1, g2 y g3, that means U(0,0), V(1,0), W(0,1)

f(U)=p1

f(V)=p1

f(W)=p1

We can see that this 3 points are minimums relatives.

Conclusion:

We compare all the critical points P,Q,R,S,T,U,V,W an their respective values f(x,y). We find that:

absolute max: f(x,y)=1/2+p1 ; at P(1/2,1/2)

absolute min: f(x,y)=p1 ; at U(0,0), V(1,0) and W(0,1)

4 0

3 years ago

How do I get the answer y= 2x^2+9x-5

guapka [62]

Answer:

Quadratic Formula

so

x = -5

and

x = 0.5

Step-by-step explanation:

Whenever you see a problem in this form, which you will see a lot of, you can try to factor it or use the "least squares" method or what have you, but those won't always work, unfortunately.

Fortunately, the quadratic formula will never fail you with quadratic expressions.

This is the Quadratic Formula

$x = \frac{-b \frac{+}{-} \sqrt{b^2-4ac} }{2a}$

a is the the number on the variable with the exponent ^2

b is the number on the variable with no exponent

c is the third number

a and b cannot be equal to 0; c can be

Since we're looking for a number with an equation that has a square root in it, we're going to get two answers. These two answers come from the radical being separately added AND subtracted from the radical. It's basically two problems.

Plugging in our numbers to this equation gives us x values of -5 and 0.5. This will always work with polynomials with factors of ^2 in them.

If you have a TI-84 calculator or newer, there's a tool on it that will factor polynomials like this one for you just by giving it the numbers.

7 0

3 years ago

What is the gif of nine and fifty two

Novosadov [1.4K]

I assume you mean 9+52,
If so you can add the 9 and the 2 together:
9+2 = 11

Then you can add the 11 on to the 50 to get the final answer:
50+11 = 61

Hope this helps! :)

4 0

3 years ago

The two-way table shows the distribution of book style to genre. Miguel claims that given that the book is paperback (PB) does n

Grace [21]

Answer:

Yes, the two events are independent because P(NF|PB)=P(NF).

Step-by-step explanation:

5 0

3 years ago

The slope of the line whose equation is 3x - 2y = 4 is 2/3 3/2 -2

7nadin3 [17]

Answer:

3/2

Step-by-step explanation:

The equation 3x-2y=4 can be written in the form of y=mx+c where m is the slope and c is the y intercept.

Therefore

2y=3x-4 and dividing both sides by 2 to have y at the LHS

y=3/2x-2

Therefore, 3/2 represents the gradient/slope

6 0

3 years ago