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2 years ago

Rachel runs 3.2 miles each weekday and 1.5 miles each day of the weekend how many miles will she have run in six weeks

Mathematics

1 answer:

navik [9.2K]2 years ago

5 0

3.2 x 5 + 1.5 x 2 = 19

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Use Lagrange multipliers to find the maximum and minimum values of

marusya05 [52]

The Lagrangian is

$L(x,y,\lambda)=x+8y+\lambda(x^2+y^2-4)$

It has critical points where the first order derivatives vanish:

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

$L_y=8+2\lambda y=0\implies\lambda=-\dfrac4y$

$L_\lambda=x^2+y^2-4=0$

From the first two equations we get

$-\dfrac1{2x}=-\dfrac4y\implies y=8x$

Then

$x^2+y^2=65x^2=4\implies x=\pm\dfrac2{\sqrt{65}}\implies y=\pm\dfrac{16}{\sqrt{65}}$

At these critical points, we have

$f\left(\dfrac2{\sqrt{65}},\dfrac{16}{\sqrt{65}}\right)=2\sqrt{65}\approx16.125$ (maximum)

$f\left(-\dfrac2{\sqrt{65}},-\dfrac{16}{\sqrt{65}}\right)=-2\sqrt{65}\approx-16.125$ (minimum)

5 0

3 years ago

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula bel

neonofarm [45]

Answer:

x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^2+bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^2-4ac} }{2a}$

in this problem we have

$4x^2 + 2x - 1=0$

$a=4$

$b=2$

$c=-1$

substitute in the formula

$x=\frac{-2(+/-)\sqrt{2^2-4(4)(-1)} }{2(4)}$

therefore

x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction

8 0

1 year ago

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THERE WAS A HALF CLASS OF WATER IN A FRACTION HOW MUCH WATER WOULD 3 PEOPLE GET?

kkurt [141]

Answer:

0.16

Step-by-step explanation:

you divide 1/2 by 3 to 0.16666666 but it would recuce to 0.16

6 0

3 years ago

Hira is rollerblading at 9 m/s. Danni is climbing at 7 m/s. Amelia is cartwheeling at 2 m/s.

anyanavicka [17]

Answer:

Hira

Step-by-step explanation:

They are going at the fastest speed as 9 is the most

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2 years ago

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Is 24.48 a interger

Sergio039 [100]

This is not an integer; an integer is a whole number that can be positive, negative, or zero such as -1, 0, and 1.

7 0

2 years ago

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