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4 years ago

We want to find the maximum and minimum values of f(x, y) = 10x2 + 11y on the disk D: x2 + y2 < 1.

1 answer:

8 0

If you're just focusing on the boundary, it's the circle $x^2+y^2=1$ . Parameterize it by taking $x=\cos t$ and $y=\sin t$ , with $0\le t\le2\pi$ . Then $f(x,y)$ reduces to a univariate function $g(t)$ :

$f(x,y)=10x^2+11y\iff g(t)=f(\cos t,\sin t)=10\cos^2t+11\sin t$

Then you can find any extrema on the boundary by checking the critical points of $g$ .

You might be interested in

Given: ∠N ≅ ∠S, line ℓ bisects at Q.

bixtya [17]

Answer:

angle NQT equals angle STR

Step-by-step explanation:

You already have two angLes, you just need a side to be able to say the AAS Theorem. The answer is the remaining side to figure that out

5 0

3 years ago

A counselor records the number of disagreements (per session) among couples during group counseling sessions. If the number of d

Shalnov [3]

Answer:

$P(X>4)=P(\frac{X-\mu}{\sigma}>\frac{4-\mu}{\sigma})=P(Z>\frac{4-4.4}{0.4})=P(z>-1)$

And we can find this probability with the complement rule:

$P(z>-1)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the disagreements of a population, and for this case we know the distribution for X is given by:

$X \sim N(4.4,0.4)$

Where $\mu=4.4$ and $\sigma=0.4$

We are interested on this probability

$P(X>4)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>4)=P(\frac{X-\mu}{\sigma}>\frac{4-\mu}{\sigma})=P(Z>\frac{4-4.4}{0.4})=P(z>-1)$

And we can find this probability with the complement rule:

$P(z>-1)=1-P(z$

3 0

3 years ago

What is the answer to this question ? Pls help!!

sammy [17]

The answer is B when you subtract every like term

6 0

3 years ago

Read 2 more answers

How many 10-digit ternary strings are there that contain exactly two 0s, three 1s, and five 2s?

Svet_ta [14]

There are $\dbinom{10}2$ ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are $\dbinom83$ ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's $\dbinom55=1$ way of doing that.

So we have

$\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520$

The last expression has a more compact form in terms of the so-called multinomial coefficient,

$\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520$

5 0

3 years ago

What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2, –14)?

vichka [17]

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a = determines whether the graph opens up or down, and it also makes the parent function wider or narrower.

positive value of a = opens upward
negative value of a = opens downward
a is between 0 and 1, (0 < a < 1) the graph is wider than the parent function.
a > 1, the graph is narrower than the parent function.

h = determines how far left or right the parent function is translated.

h = positive, the function is translated h units to the right.
h = negative, the function is translated |h| units to the left.

k determines how far up or down the parent function is translated.

k = positive: translate k units up.
k = negative, translate k units down.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)² -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)

8 0

3 years ago