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3 years ago

If Martha and Howard are 5 hours into the marathon, how far has each person run?

Mathematics

1 answer:

vova2212 [387]3 years ago

8 0

Answer: The Answer is 10

Step-by-step explanation:

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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

When two probabilities

Ivenika [448]

Answer: True

Step-by-step explanation: Because if we have two independent events and want to know the probability of their happening at the same time, we multiply the two probabilities together. "Two events happening at the same time" is a compound event. We more often see this as "P(xy)," the probability of x AND y.

7 0

3 years ago

3250-1250=1500+2(1250-500) is this true

exis [7]

Answer:

Its false because

Step-by-step explanation:

3250-1250=1500+2.(1250-500)

2000 = 1500 + 2 . 750

2000 = 1500 + 1500

2000 != 3000

Obviously 2000 isnt the same of 3000

5 0

3 years ago

Read 2 more answers

Write an equation of the line with a slope of<br> 3 and y-intercept of -8

Yuki888 [10]

Answer:

3x-8=y

Step-by-step explanation:

3 0

3 years ago

PLZ HELP GUYS I RLLY NEED HELPPP!<br> i rlly rlly rlly need help, i am not good at mathh! :(((((((((

Kisachek [45]

Answer:

1`. y = 4x+6

2. y = -6x + 29

3. y= 3x+1

4. y = x -2

5. y = 11.5x+ 3

6. y = -2x -4

Step-by-step explanation:

5 0

3 years ago