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
Given that the recursive formula for a sequence is
The first term of the sequence is
We need to determine the first four terms of the sequence.
<u>Second term:</u>
The second term of the sequence can be determined by substituting n = 2 in the recursive formula.
Thus, we have;
Thus, the second term of the sequence is 8.
<u>Third term:</u>
The third term of the sequence can be determined by substituting n = 3 in the recursive formula.
Thus, we have;
Thus, the third term of the sequence is 14.
<u>Fourth term:</u>
The fourth term of the sequence can be determined by substituting n = 4 in the recursive formula.
Thus, we have;
Thus, the fourth term of the sequence is 22.
Hence, the first four terms of the sequence is 4, 8, 14, 22.
X = 4629 * tan(5) = 404.98 ≈ 405.
The correct answer would be 405.
Answer:
8.5
Step-by-step explanation:
Answer:
The answer is letter c.
Step-by-step explanation:
In order to know the answer, it is best to check what is given in the scenario above.
45 minutes = the time it takes for Betty and Dyan to pick 8 quarts of strawberries.
45x minutes= this refers to the time it takes for Dyan to pick 8 quarts of strawberries
In the rational expression, 45x-10, we've already known that 45x refers to minutes or the time it takes for Dyan to pick 8 quarts of strawberries, thus 10 here refers to minutes or time as well.
The mathematical operation used is<u> "subtraction,"</u> so this means that Betty takes a shorter time than Dyan when it comes to picking strawberries in the situation above.
Thus, the denominator represents the time it takes Betty to pick 8 quarts of strawberries if she takes 10 fewer minutes than Dyan.