(a) The "average value" of a function over an interval [a,b] is defined to be
(1/(b-a)) times the integral of f from the limits x= a to x = b.
Now S = 200(5 - 9/(2+t))
The average value of S during the first year (from t = 0 months to t = 12 months) is then:
(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12
or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12
This equals 200/12 * (5t -9ln(2+t))
Evaluating this with the limits t= 0 to t = 12 gives:
708.113 units., which is the average value of S(t) during the first year.
(b). We need to find S'(t), and then equate this with the average value.
Now S'(t) = 1800/(t+2)^2
So you're left with solving 1800/(t+2)^2 = 708.113
<span>I'll leave that to you</span>
Answer:
option-B
Step-by-step explanation:
we know that
Sum rule of logarithm:
which is same as
the log of a product (ab) is equal to the addition of log a nad log b
Subtraction rule of logarithm:
which is same as
the log of the quotient of a and b is equal to the log of a minus the log of b
Exponent rule of logarithm:
which is same as
the log of the quantity a raised to b is equal to the product of b and the log of a
so,
option-B is not correct
Answer:
36 feet.
Step-by-step explanation:
We have been given that a ball is thrown upward from ground level. Its height h, in feet, above the ground after t seconds is 
. We are asked to find the maximum height of the ball.
We can see that our given equation is a downward opening parabola, so its maximum height will be the vertex of the parabola.
To find the maximum height of the ball, we need to find y-coordinate of vertex of parabola.
Let us find x-coordinate of parabola using formula 
.
So, the x-coordinate of the parabola is 
. Now, we will substitute in our given equation to find y-coordinate of parabola.
Therefore, the maximum height of the ball is 36 feet.
Answer:
2, 10, 50, 250
Step-by-step explanation:
Using the formula with a₁ = 2 , then
a₂ = 5a₁ = 5 × 2 = 10
a₃ = 5a₂ = 5 × 10 = 50
a₄ = 5a₃ = 5 × 50 = 250
The first 4 terms are 2, 10, 50, 250
Answer:
41.6 centimeters
Step-by-step explanation:
The right triangle formula: c^2 = a^2 + b^2
c is the hypotenuse side of the triangle
a and b are the legs of the triangle.
Find the hypotenuse : c^2 = (24)^2 + (34)^2
c = square root of ( (24)^2 + (34)^2)
c = square root of ( 576 + 1,156)
c = 41.6173
