difficult rates of change question (1 Viewer)

[MC Squidge]

1. If you know two sides, a and b, of a triangle, and the angle, X, between them, you can calculate the area, A, by the formula A = (1/2)ab sin X. Suppose that at 2pm one of the sides is 6cm and is increasing at 2cm per second, another side is 10 cm and is increasing at 1cm per second, and the area is 15cm squared and is decreasing at 3cm squared per second. What is the angle between the two sides at 2pm, and at what rate is it changing?

2. At noon, a cylinder of variable dimensions has a radius of 13cm and a height of 12cm. The radius is increasing at a rate of 1cm per second, and the height is decreasing at the rate of 2cm per second. At what rate is the volume changing?

Question 2 has me stumped I made an attempt but it didn`t work out.

Question 1 I just can`t make sense of but I figure X is either pi/6 or 5pi/6

Thanks for everyone who helps in advance

 

[MC Squidge]

do i have to use implicit differenation for the second question?

 

[genius13]

fairly sure answer for question 2 is : -26pi cm^3 /second.

but im not going to tell u how I got it

Need everyone to remember how genius I am

 

[Absolutezero]

fairly sure answer for question 2 is : -26pi cm /second.

but im not going to tell u how I got it.

Need everyone to remember how genius I am

Have a heart matt, show your working.

 

[MC Squidge]

I know how to do the second one now, I just figured it out. I bet you cant do the first

 

[MC Squidge]

Here`s what I`ve got for the 1st one:

A=0.5absinX
A=15
a=6
b=10
dA/dt=-3
da/dt=2
db/dt=1

2dA/dt=bsinX.da/dt+asinX.db/dt+ab.cosC.dX/dt

dX/dt=-19(ROOT3)/90 if X=pi/6 from initial conditions
dX/dt=19(ROOT3)/90 if X=5pi/6 from initial conditions

the working is simple enough but I just don`t think the question makes sense based on the fact that if a and b increase how can A decrease?

 

[Deep Blue]

Because even though the side length are getting larger, if the angle is becoming narrower (or wider in the obtuse triangle) then the area is still going to decrease.

 

[MC Squidge]

thanks i see now

 

[hscishard]

Do you have solutions? For 1 I got -root3 / 6 and for 2 I got -52pi
While I was doing it, something didn't feel right. Is this harder 3unit? Because this definitely won't be 3unit.

 

[hscishard]

fairly sure answer for question 2 is : -26pi cm^3 /second.

but im not going to tell u how I got it , because ur a noob and I dont like you.

Need everyone to remember how genius I am

I got similar answers with this guy so...
dr/dt=1
dh/dt = -2
dV/dr = pir(2h+rdh/dr)
dh/dr = -2 ...from dt/dr x dh/dt
dV/dr=pir(2h-2r)
dV/dt = " "
So at r = 13, h=12 dV/dt=-26pi

 

[hscishard]

ffs product rule . Both answers are wrong