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Ronch [10]
3 years ago
11

I dont understand it and I don't get what it's asking for

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
5 0
1/5 = 2/10
1/2 = 5/10

1/10 + 2/10 + 5/10 = 8/10.

8/10 = 4/5.

4/5 is your final answer.
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Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |
dsp73

Looks like f(x,y)=x^2+y^2-x^2y+7.

f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1

f_y=2y-x^2=0\implies2y=x^2

  • If x=0, then y=0 - critical point at (0, 0).
  • If y=1, then x=\pm\sqrt2 - two critical points at (-\sqrt2,1) and (\sqrt2,1)

The latter two critical points occur outside of D since |\pm\sqrt2|>1 so we ignore those points.

The Hessian matrix for this function is

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}

The value of its determinant at (0, 0) is \det H(0,0)=4>0, which means a minimum occurs at the point, and we have f(0,0)=7.

Now consider each boundary:

  • If x=1, then

f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4

which has 3 extreme values over the interval -1\le y\le1 of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

  • If x=-1, then

f(-1,y)=8-y+y^2

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

  • If y=1, then

f(x,1)=8

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

  • If y=-1, then

f(x,-1)=2x^2+8

which has 3 extreme values, but the previous cases already include them.

Hence f(x,y) has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

3 0
3 years ago
Celine's book club read 42 books over 14 months. How many total months will it take them to read 57 books? Solve using unit rate
miskamm [114]

Answer:

Step-by-step explanation:

42/14 = 57/x

42x = 57*14

42x = 798

x = 19 months

4 0
3 years ago
PLEASE HELP ME WITH THIS PROBLEM!!! I NEED TO TURN IT IN TODAY
Murrr4er [49]

Answer:

U=19

A=8

B=5

Step-by-step explanation:

Cardinality refers to the number of elements in a set.

8 0
3 years ago
30 POINTS please help me!
Stels [109]
To prove a similarity of a triangle, we use angles or sides.

In this case we use angles to prove

∠ACB = ∠AED (Corresponding ∠s)
∠AED = ∠FDE (Alternate ∠s)

∠ABC = ∠ADE (Corresponding ∠s)
∠ADE = ∠FED (Alternate ∠s)

∠BAC = ∠EFD (sum of ∠s in a triangle)

Now we know the similarity in the triangles.

But it is necessary to write the similar triangle according to how the question ask.

The question asks " ∆ABC is similar to ∆____. " So we find ∠ABC in the prove.

∠ABC corressponds to ∠FED as stated above.
∴ ∆ABC is similar to ∆FED

Similarly, if the question asks " ∆ACB is similar to ∆____. "
We answer as ∆ACB is similar to ∆FDE.

Answer is ∆ABC is similar to ∆FED.
7 0
3 years ago
Convert 7/11 to a percent. round the answer to the nearest hundredth
pychu [463]
<h3>Answer:</h3>

63.64%

<h3>Step-by-step explanation:</h3>

7/11 = 7/11 × 100% = (700/11)% ≈ 63.64%

_____

<em>Comment on fractions involving 11</em>

1/11 is the 2-digit repeating decimal 0.09090909...

So, any multiple of 1/11 is a 2-digit repeating decimal with the two digits being the numerator times 9.

Here, we have 7/11, so the 2-digit repeat is 7·9 = 63. That is ...

... 7/11 = 0.63636363...

3 0
3 years ago
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