Pls answer 1 and 2 will give brainliest to who is right

Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 =

dexar [7]

Given $f(x,\ y)=x^2-y^2-2$ subject to the constraint $x^2+y^2=16$

Let $g(x,\ y)=x^2+y^2$ .

The gradient vectors of $f$ and $g$ are:

$\nabla f(x,\ y)=\langle2x,-2y\rangle$ and $\nabla g(x,\ y)=\langle2x,2y\rangle$

By Lagrange's theorem, there is a number $\lambda$ , such that

$\langle2x,-2y\rangle=\lambda\langle2x,2y\rangle=\langle2\lambda x,2\lambda y\rangle$

$\lambda=\pm1$

It can be seen that $f(x,\ y)=x^2-y^2-2$ has local extreme values at the given region.

6 0

3 years ago

Jared drove a distance of 165 miles to billings last weekend, which used 11 gallons of gas. How many gallons of gas will he need

blondinia [14]

Answer:

8550

Step-by-step explanation:

1. you need to figure out how many time 11 goes into 165 which is 15 then you need to get the 15 and multiply it by 570.

3 0

3 years ago

Sketch the region that is common to the graphs of x ≥ 2,

Oliga [24]

a. Find the graph of their common region in the attachment

b. The area of the common region of the graphs is 8 units²

<h3>a. How to sketch the region common to the graphs?</h3>

Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.

The graph of x ≥ 2 is the region right of the line x = 2.

The graph of y ≥ 0 is the region above the line y = 0 or x-axis.

To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.

So, the graph of x + y ≤ 6 is the region below the line y = - x + 6

From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)

Find the graph of their common region in the attachment

<h3>b. The area of the common region</h3>

From the graph, we see that the common region is a right angled triangle with

height = 4 units and
base = 4 units

So, its area = 1/2 × height × base

= 1/2 × 4 units × 4 units

= 1/2 × 16 units²

= 8 units²

So, the area of the common region of the graphs is 8 units²

Learn more about region common to graphs here:

brainly.com/question/27932405

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6 0

1 year ago

A set of piano prices distributed at a mean of 3000 and a standard deviation of 200 dollars. An electric piano has a price of 25

lana [24]

Answer:

The proportion of piano prices higher than the electric piano is 98.3%

Step-by-step explanation:

The first thing to do here is to calculate the standard score of the price of the electric piano given.

Mathematically, this is

z-score = (x-mean)/SD

where mean is 3000 and SD is 200, x is 2576

z-score = (2576-3000)/200 = -2.12

Now we proceed to calculate the probability of this z-score

The probability we are trying to calculate is

P( x > $2576) or simply P ( z > -2.12)

Using standard score probability calculator or table, we have

P(x>2576) = 1 - P(x<2576)

But, P(x<2576) = 0.017003

P(x>2576) = 1 - P(x<2576) = 0.983

This is same as 98.3%

4 0

3 years ago

Write the fraction as a percent. 6/25

Eduardwww [97]

Answer:

0.0417

Step-by-step explanation:

6 0

3 years ago