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3 years ago

Determine if f(x, y) = 10 − x^2 − y^2

Mathematics

1 answer:

Eva8 [605]3 years ago

8 0

Answer:

Step-by-step explanation:

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. x is treat any other variable as a constant.

dz/dx=0-2x-0

dz/dx=-2x

Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.

Since this result is negative, it mrans as x increases z decreases.

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. y is treat any other variable as a constant.

dz/dx=0-0-2y

dz/dx=-2y

Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.

Since this result is positive it mrans as y increases z decreases.

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Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his sc

aivan3 [116]

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Step-by-step explanation:

The table containing the score and the relative probability of each score is:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Here we call

X = Miguel's score on the Water Hole

The expected value of a certain variable X is given by:

$E(X)=\sum x_i p_i$

where

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$p_i$ is the probability that $X=x_i$

Therefore in this problem, the expected value of MIguel's score is given by:

$E(X)=3\cdot 0.15 + 4\cdot 0.40 + 5\cdot 0.25 + 6\cdot 0.15 + 7\cdot 0.05=4.55$

In this problem, we call:

X = Miguel's score on the Water Hole

Here we have that:

- If the long hit is successfull, the expected value of X is

$E(X)=4.2$

- Instead, if the long hit fails, the expected value of X is

$E(X)=5.4$

Here we also know that the probability of a successfull long hit is

$p(L)=0.4$

Which means that the probabilty of an unsuccessfull long hit is

$p(L^c)=1-p(L)=1-0.4=0.6$

Therefore, the expected value of X if Miguel chooses the long hit approach is:

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In part 1) of the problem, we saw that the expected value for the short hit was instead

$E(X)=4.55$

Since the expected value for X is lower (=better) for the short hit approach, we can say that the short hit approach is better.

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3 years ago

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andrey2020 [161]

Answer:

The correct corresponding part is;

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Step-by-step explanation:

The information given symbolically in the diagram are;

ΔCAB is congruent to ΔCED (ΔCAB ≅ ΔCED)

Segment $\overline {CA}$ is congruent to $\overline {CE}$ ( $\overline {CA}$ ≅ $\overline {CE}$ )

Segment $\overline {CB}$ is congruent to $\overline {CD}$ ( $\overline {CB}$ ≅ $\overline {CD}$ )

From which, we have;

∠A ≅ ∠E by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

∠B ≅ ∠D by CPCTC

Segment $\overline {AB}$ is congruent to $\overline {DE}$ ( $\overline {AB}$ ≅ $\overline {DE}$ ) by CPCTC

Segment $\overline {AE}$ bisects $\overline {BD}$

Segment $\overline {BD}$ bisects $\overline {AE}$

Therefore, the correct option is $\overline {CB}$ ≅ $\overline {CD}$

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