Awater trough is 7 feet long, and its cross section is an equilateral triangle with sides 4 feet long. water is pumped into the trough at a rate of 4 cubic feet per second. how fast is the water level rising when the depth of the water is 1/2 foot?
( hint: first, what is the height h of an equilateral triangle of side length s? next, what is the area of an equilateral triangle in terms of the side length s? then write the area in terms of h. the volume of the water in the trough at time t is the product of the cross-sectional area with water and the length of the trough. )
a) what is the height h of an equilateral triangle of side length s?
b) the water level is rising at a rate of

a. An equilateral triangle main characteristic is that all the sides lenght are the same (s). To find the height (h), we could divide the triangle (as seen in the picture) and apply Pytagorean theorem.

Clearing the expression, we obtain:

b. Knowing the rate at which the volume is changing 4 , we can find the relation between the change in the volume and the height.

As we want to express the volume in terms of the height, we have to find the area in terms of height

Base=s=

Therefore,

Therefore the change in the volume with the height, will be the derivate of this expression

Knowing dV/dt=4 cubic feet per second, and h=1/2 foot, we can know dh/dt

Step-by-step explanation:

idk

step-by-step explanation:

payback

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages