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4 years ago

Find the multiplicative order of 5 and 7 in z16

1 answer:

3 0

$5\equiv5\mod{16}$
$5^2=25\equiv9\mod{16}$
$5^3\equiv5\cdot9\equiv45\equiv48-3\equiv-3\equiv13\mod{16}$
$5^4\equiv9^2\equiv81\equiv1\mod{16}$
$5^5\equiv5\cdot1\equiv5\mod{16}$

$7\equiv7\mod{16}$
$7^2\equiv49\equiv48+1\equiv1\mod{16}$
$7^3\equiv7\cdot1\equiv7\mod{16}$

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Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values

Vesnalui [34]

The Lagrangian is

$L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)$

with critical points where the partial derivatives vanish.

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$

$L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda$

$L_\lambda=x^2+y^2-9=0$

Substitute $x,y$ into the last equation and solve for $\lambda$ :

$\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6$

Then we get two critical points,

$(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)$

We get an absolute maximum of $3\sqrt{17}\approx12.369$ at the second point, and an absolute minimum of $-3\sqrt{17}\approx-12.369$ at the first point.

4 0

3 years ago

How do you solve the following problem: is (3,4) a solution to 2x+3y=10?

ale4655 [162]

The answer is C. plug 3 and 4 into the equation and see if it's true.

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3 years ago

The original price of a pair of shoes is $42. The sale price 20% off the orginal price. Sales tax of 7% is added to the sale pri

m_a_m_a [10]

Answer:

$8.40 is the amount to be subtracted from the $42.00. If you multiply 20% (.20) by $42.00 you get $8.40. To get your final price subtract $8.40 from $42.00 to get you final answer. I hope that helps.

Step-by-step explanation:

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3 years ago

Read 2 more answers

Which terms and 45p^4q have a GCF of 9p^3?

vredina [299]

Answer:

The answer is 18p^3r and 63p^3

Step-by-step explanation:

G.C.F of 18p^3 r and 45p^4q is = 9p^3

18p^3r = 2*3*3*p*p*p*r

45p^4q = 3*3*5*p*p*p*q

Thus the G.C.F is 3*3*p*p*p = 9p^3

G.C.F of 63p^3 and 45p^4q is = 9p^3

63p^3 = 3*3*7*p*p*p

45p^4q = 3*3*5*p*p*p*q

Thus the G.C.F is 3*3*p*p*p = 9p^3

Therefore the answer is 18p^3r and 63p^3....

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4 years ago

NEED HELP NOW!!!

Amiraneli [1.4K]

D.

Explanation:

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divide into two parts.

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