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3 years ago

Pls help ASAP help pls

Mathematics

1 answer:

Savatey [412]3 years ago

4 0

Answer:

Angle Bisector

Step-by-step explanation:

The top angle is split into two equal sections

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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

$55 per gallon. 1 gallon covers 100sqft. What is the price per sqft?

marta [7]

the price is 0.55$ per square foot

Step-by-step explanation:

We can solve the problem by using the rule of three.

In fact, we know that:

1 gallon covers an area of $100 ft^2$

While the price per gallon is

$55 per gallon

This means that the price per $100 ft^2$ is $55, since 1 gallon cover $100 ft^2$

Therefore, to find the price per square foot, we can write

$\frac{55}{100}=\frac{x}{1}$

WHere x is the price per square foot. Solving for x,

$x=\frac{55}{100}=0.55\$$

So, the price is 0.55$ per square foot.

Learn more about problems with price:

brainly.com/question/4479991

#LearnwithBrainly

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3 years ago

The number of people estimated to vote in an election was 7,000. The actual number of people who voted was 5,600.

Inessa05 [86]

Answer:

20%

Step-by-step explanation:

7000-5600=1400

1400/7000×100=20

7 0

3 years ago

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(4x-1) = 6 2 How to solve rational equations

9966 [12]

Answer:

educated guess

Step-by-step explanation:

cos ( 390 ) sin ( 330 ) − 4 cot ( − 45 )

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2 years ago

Mrs. Alberts has two seventh grade math classes this year. They took their final exam, and Mrs. Alberts just finished grading th

goldfiish [28.3K]

Answer:

these are true = 1, 3, 5

Step-by-step explanation:

overall class a scored better than class b

they're more students in class a compared to class b

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3 years ago