The width of a rectangular box is 8in. The height is one fifth the length x. The volume is 640 in^3 (inches cubed). What is the
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Answer: The answer is 300 gallons.
Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.
To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ =
If a function is defined on the closed interval [a,b] and is any point in [
,
], then a Riemann Sum is defined as ∑f(
)Δ
.
For this question:
Δ =
= 1.4
Now, we have to find s(t) for each valor on the interval:
s(t) = 0.29 - t +25
s(0) = 25
s(1) = 24.29
s(2) = 24.16
s(3) = 24.61
s(4) = 25.64
s(5) = 27.25
s(6) = 29.44
s(7) = 32.21
Now, using the formula:
∑f()Δ
= 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)
∑f()Δ
= 1.4(212.6)
∑f()Δ
≅ 300
With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.
ANSWER
Find out the how much fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .
To proof
let us assume that the fluid should be drained and replaced with pure antifreeze be x .
As given
A radiator contains 10 quarts of fluid, 30% of which is antifreeze.
Now write 30% in the decimal form
Now write 60% in the decimal form
After drained and replaced the fluid with pure antifreeze than the quantity becomes = ( 10 - x )
The quantity of antifreeze is
The fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .
than the equation becomes
solyving
100x +300 - 30x = 600
70x = 300
x = 4.28 quarts (approx)
Hence 4.28 quarts (approx) fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .
Therefore the option (c.) is correct .