who can do these two very hard calculus questions? (1 Viewer)

[chrisk]

1) a and b are variables related by the equation ab^3 = 40.
At the instant when a = 5, b is increasing at 1 unit per second.
What is happening to a at this instant?

2) A right angled triangle ABC has a fixed hypotenuse AC of length 10cm, and side AB increases at 0.1cm per second. At what rate is angle CAB increasing at
the instant when the triangle is isosceles?

I need working so that i can understand pz ^^

Answers
1) a is decreasing at 7.5 units per second

2) decreasing at (root 2)/ 100 radians per second


my head is completely out right now -_-...

i call you genius if you can do those stuff
give me ur facebook. ill add you
cheers

 

[Mark576]

ab³ = 40
a = 5, b = +/-2
differentiating implicitly: a'b³ + 3b²b'.a = 0
rearrange for a': da/dt = -[3b².db/dt.a]/b³ = -7.5, after substituting for given values.

 

[3unitz]

2) A right angled triangle ABC has a fixed hypotenuse AC of length 10cm, and side AB increases at 0.1cm per second. At what rate is angle CAB increasing at
the instant when the triangle is isosceles?

let AB = x, BC = y, angle CAB = @

dx/dt = 0.1 -----(1)

from trig:

x/10 = cos@

x = 10cos@

dx/d@ = -10sin@ -----(2)

using (1) and (2):

dx/dt . d@/dx = 0.1 (-1/10sin@)

d@/dt = -1/(100sin@)

when triangle is isosceles, @ = pi/4:

d@/dt = -1/[100sin(pi/4)]

d@/dt = - sqrt(2) / 100

ie. @ is decreasing at a rate of sqrt(2) / 100 radians per second

 

[chrisk]

thank you guys >.<