Can anyone help me w/ this problem...i cant seem to get the right answer?

Question

A point is moving on the graph of xy=7. When the point is at (4, 7/4), its x –coordinate is increasing at a rate of 1 units per sec. What is the speed of the y-coordinate at that moment and in which direction is it moving?

Answer 1

Implicitly differentiate the equation with respect to time (you will have to use the product rule).

xy' + yx' = 0
4*y' + (7/4)*1 = 0
4y' = -7/4
y' = -7/16 units/sec

The point is moving towards the 4th quadrant since you are in the 1st quadrant and dx/dt is positive while dy/dt is negative.

Answer 2

Hi! I'm an older mom now - my daughters are 11 and 13, but I remember being where you are! My hubby would come home with that dreaded question "what did you do today" and I was ready to deck him - I mean, my oldest at 4 months was nursing every hour and a half for 40 minutes at a time - she never slept for longer than 1/2 hour - probably no more than 10 hours out of 24. I was exhausted all the time as well. Best advice I can give is first and foremost, try to get rid of the guilt and just enjoy your baby. This will pass - as others said, the difference between 4 months and 8 months is huge. As a SAHM still, I know all about lack of money! The main things I tried to do were: 1) Always get up and get dressed - make yourself presentable whether you expect to see anyone or not - it's just a great habit to get into - you'll feel better about yourself. 2) As soon as you get up, make up your bed. It goes a long way to restoring the order of your household - and an unmade bed sets you up for disorder. 3) Talk to your daughter constantly as though she understands you - you'll be surprised later just how much she really does! 4) (and this was most difficult for me) Try to plan your dinner meal and have things all ready for a nice dinner - does wonders for your marriage, too. Wishing you all the best!

Answer 3

xy=7 f(x)=7/x
f'(x)=-7/(x^2) f'(4)=-7/16, the point is moving parallel to the line y=-7/16

the speed of the point is distance covered over time. The instantaneous slope of the line is -7/16, so for every unit the point moves parallel to he x-axis, it moves -7/16 units down, parallel to the y-axis. The distance covered is the hypotenuse of the right triangle formed by over 1, and down 7/16.
So use the pythagorean theorem: 1^2+(-7/16)^2=h^2 where h is the hypotenuse
1+49/256=h^2
h=sqrt[1+49/256]
h=sqrt[305/256]
h=sqrt[305]/16 or 1.0915, so the point moves 1.0915 units every second

Answer 4

What happens in one second? The x-coordinate goes from 4 to 5. The y-coordinate must then go from 7/4 to 7/5, so that the original condition of xy=7 is preserved.

7/5 - 7/4 = 28/20 - 35/20 = -7/20.

So the y-coordinate is decreasing at the rate of 7/20 units per second.

Answer 5

Given: x = 4, y = 7/4, dx/dt = 1

xy = 7
x(dy/dt) + y(dx/dt) = 0

solve for dy/dt:
x(dy/dt) = -y(dx/dt)
dy/dt = (-y/x)(dx/dt)

plug in the numbers
dy/dt = (-y/x)(dx/dt)
dy/dt = (-(7/4)/4)(1)
dy/dt = -7/16 units per second
-the negative sign indicates the y coordinate is moving downward

Answer 6

xy = 7

y = x/7

dy/dx = 1/7
since dy/dx is positive, it is increasing. If x is moving at 1 unit / sec, y = (1/7) units / sec

Answer 7

OMG what?!

Answer 8

65mph ... toward your mama's house.