Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
Answer:
18 and 335
Step-by-step explanation:
y = 18x + 11
x * y = 6030
x * (18x + 11) = 6030
18x^2 + 11x = 6030
18x^2 + 11x - 6030 = 0
(18x + 335)(x - 18) = 0
18x + 335 = 0 x - 18 = 0
18x = -335 x = 18
x = -335/18
x is gonna have to be a positive number...so x = 18
y = 18x + 11
y = 18(18) + 11
y = 324 + 11
y = 335
so ur numbers are 18 and 335
Answer:
x=11
Step-by-step explanation:
-11=x/-1
x=-11×-1
x=11
Answer:did u ever find the answer i need it
Step-by-step explanation:
I'm not sure if you're already given the length of the rectangle, but the width is either (x + 3) or (x + 15).
We can find this by factoring x² + 18x + 45, as the area of a rectangle is found by multiplying the length and width together, so if we factor this expression we can find what was multiplied together.
Factoring x² + 18x + 45, we get (x + 3)(x + 15), which then tells us the two sides of the rectangle. Again, I'm not sure if you were already told the length, but if you were then the width is the other side. For example, if you were told the length was (x + 3), then the width would be (x + 15).
I hope this helps!
