(1 pt) The altitude of a triangle is increasing at a rate of 1.000 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.500 centimeters and the area is 80 square centimeters? i got 2.551 which seems to be wrong

Question

(1 pt) The altitude of a triangle is increasing at a rate of  1.000 centimeters/minute while the area of the triangle is increasing at a rate of  4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.500  centimeters and the area is 80  square centimeters?  i got 2.551 which seems to be wrong

mani_jha · Answer

Area=Altitude*Base
$$A=bh/2$$
$$dA/dt=d(bh)/dt2$$
=$$2(dA/dt)=b(dh/dt)+h(db/dt)$$
dA/dt=4.5 dh/dt=1 h =8.5 A=80 find b using A=bh/2
Then find db/dt using the differential equation

anonymous · Answer

so i got 2(4.5)/4.25 which equals 2.118

anonymous · Answer

wait no matter what i do i get 2.551

anonymous · Answer

maybe 1.155?

anonymous · Answer

A = 1/2 ( b *h) 
 -> b = 2A/ h = 2 * 80/ 8.5 = 18.8 cm

A' = 1/2 ( b' h + bh')
=> b' = (2A' - bh' ) / h = ( 2 * 4.5 - 18.8 * 1) / 8.5 = 6.79 cm/min

anonymous · Answer

that was also incorrect

anonymous · Answer

How?

anonymous · Answer

i entered 6.79 and it says it was wrong

anonymous · Answer

enter exactly 6.785467128

mani_jha · Answer

Hey, is it -1.15?

anonymous · Answer

the rate is increasing?

anonymous · Answer

-1.15 was correct but i dont know how

mani_jha · Answer

h=(2*4.5-18.8)/8.5
isnt 2*4.5=9 and 9-18.8=-9.8?
So, it suggests that the base is decreasing
You made a calculation mistake!

anonymous · Answer

Oh yes, somehow I enter wrong :")

anonymous · Answer

oh thats sucks i ran out of attempts right before i get to the right answer

anonymous · Answer

You got that anyway, AJ!

anonymous · Answer

@Mani, thanks again pointing out my error!

anonymous · Answer

I guess I'm so sleepy when punching into my calculator!!!

anonymous · Answer

ya was pluggin in 4.5^2 instead of 4.5 for the da/dt

mani_jha · Answer

Dont worry, I have done those kind of mistakes a thousand times, and have suffered because of it!

anonymous · Answer

thanks both of you

mani_jha · Answer

De rien!(you are welcome in french)

anonymous · Answer

As long as it works out, I'm happy and so lucky that some one as Mani be here to help out :)

mani_jha · Answer

Thanks chlorophyll. Hey, where are u from?

anonymous · Answer

Virginia!

anonymous · Answer

And you? your major?

mani_jha · Answer

I am from India. Nice to meet you!

anonymous · Answer

Wow! I'm in school with most of intelligent Indian, Chinese and Korean! I need to work extremly much harder :(

anonymous · Answer

Oh, there's also have an asker pre - algebra, smart and nice!  Should you take a look at his question!

mani_jha · Answer

Ya, why not

anonymous · Answer

Most of Indian excel at language programming. I bet you'll find a buddy since pre -algebra also passionate in language! I wish I can understand it but it's tough with all kind of sorts and arrays, link list!