Question

The altitude of a triangle is increasing at a rate of 3.0 centimeters/minute while the area of the triangle is increasing at a rate of 2.0 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 11.5 centimeters and the area is 91.0 square centimeters?

Answer 1

area of a triangle = 1/2 base* height

Answer 2

differentiate this equation wrt time

Answer 3

u can write
A= 1/2 b* h

Answer 4

can u differentiate this equation wrt time?

Answer 5

what will the equation that i have to differentiate be? what numbers would i sub in?

Answer 6

differentiate this equation
A= 1/2 b * h
A= area o the triangle
b= base
h= height

Answer 7

supposes u have been given
x= 2t^2 and i ask u to differentiate this wrt t(time)

Answer 8

x is the distance traversed..and if u differentiate it then u'll get the speed...right?

Answer 9

forget the substitution part for now...that will come later

Answer 10

x= 2t^2
differentiate x wrt time

Answer 11

x=4t?

Answer 12

it'll be dx/dt= 4t

Answer 13

differentiation of x wrt t= dx/dt

Answer 14

im confused

Answer 15

what's ur confusion?

Answer 16

I gave u an equation x=t^2 and asked u to differentiate wrt t

Answer 17

i got the equation for my problem to equal 2=(1/2)dB/dT * 11.5+dH/dT*(1/2)b

Answer 18

is that correct?

Answer 19

A= 1/2 b * h
dA/ dt = 1/2( db/dt *h + b * dh/dt)
2= 1/2 ( db/dt *h + b*3)

Answer 20

u have been given dh/dt= 3cm/minute

Answer 21

now u have to find db/dt when h=11.5 and A=91 cm^2

Answer 22

see this equation
2= 1/2 ( db/dt *h + b*3)
for finding db/dt u need to know b and h..but u know h only
so find b

Answer 23

for finding b,use A= 91 cm^2

Answer 24

b=.063107 ?

Answer 25

A=91, h=11.5 then b=?

Answer 26

b=15.82 cm

Answer 27

2=1/2(db/dt) *11.5+15.82*3 ?

Answer 28

2=1/2(db/dt) *11.5+1/2 * 15.82*3

Answer 29

u left 1/2 in the 2nd term of RHS

Answer 30

so find db/dt that will be the answer.

Answer 31

i got -.778223
but its telling me its the wrong answer

Answer 32

how did u come to know that it's wrong answer?

Answer 33

due to -ve sign?

Answer 34

the retriceinment is online to i entered the answer, and its telling me its wrong

Answer 35

let me check

Answer 36

assignment*

Answer 37

enter this value
db/dt=-3.77

Answer 38

is it right?

Answer 39

no its coming up incorrect