5 3/7<span> = 5.428571428571429 or 5.43</span>
Answer:
$450
Step-by-step explanation:
Answer: 2, 2, 2, 5, 13, 13.
Step-by-step explanation:
Here is the math in order to find the prime factorization
6760 ÷ 2 = 3380
3380 ÷ 2 = 1690
1690 ÷ 2 = 845
845 ÷ 5 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
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:
m = 18
Step-by-step explanation:
Step 1: Write out equation
-1/2m = -9
Step 2: Multiply both sides by -2
m = 18
