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Butoxors [25]
3 years ago
15

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

16
Mathematics
1 answer:
dexar [7]3 years ago
6 0
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.
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Which ordered pairs lie on the graph of the exponential function f(x) = 3 (1/4)x
sineoko [7]
The first two pairs.. just substitute the x-coordinate and find y
8 0
3 years ago
Which of the following would give the correct binomial expansion for the expression below?
12345 [234]
4x-8=0
4(x-2)=0
x-2=0
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3 0
3 years ago
Read 2 more answers
Find the volume of each sphere. Be sure to include appropriate units.<br> (Show your work)
babunello [35]

Answer:

2145.5m^3

679.2yard

Step-by-step explanation:

v

volume \: of \: a \: sphere =  \frac{4}{3}\pi \: r {}^{3}  \\ when \: r = 8 \\ volume =  \frac{4}{3}  \times  \frac{22}{7}  \times 8 {}^{3}  \\ volume =  \frac{4}{3}  \times  \frac{22}{7} \times 8 \times 8 \times 8 \\ volume =  \frac{4 \times 22 \times 512}{3 \times 7}   \\ volume =  \frac{45056}{21}  \\ volume = 2145.5m {}^{3}  \\  \\ for \: the \: second \: shape \\ volume =  \frac{4}{3}  \times  \frac{22}{7}  \times 5.5 {}^{3}  \\  =  \frac{4}{3}  \times  \frac{22}{7}  \times 166.373 \\  =  \frac{14641}{21}  \\  = 697.2yard

6 0
3 years ago
Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest fo
agasfer [191]

From the recursive rule

a_n = a_{n-1}-13

it follows that

a_{n-1}=a_{n-2}-13 \implies a_n = a_{n-2} - 2\times13

a_{n-2}=a_{n-3}-13 \implies a_n = a_{n-3} - 3\times13

and so on. Notice how the subscript on a on the right side and the coefficient multiplied by 13 add up to n (n - 2 + 2 = n; n - 3 + 3 = n; and so on). If we continue the pattern, we'll end up with

a_n = a_1 + (n-1)\times13

so that the explicit rule for the n-th term in the sequence is

a_n = -2 + 13(n-1) \implies a_n = \boxed{13n-15}

6 0
2 years ago
Is 56/7 a rational number or
Sati [7]

Answer:

Yes

Step-by-step explanation:

The definition of a rational number is a number that can be represented as a fraction. Since 56/7 is a fraction it must be a rational number. An irrational number is a number that cannot be represented as a fraction because it never ends and repeats without a pattern forever. An example of this is pi because pi can never exactly be represented as a fraction.

4 0
3 years ago
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