Answer:
<em>There are 142 whole numbers less than 1000 and divisible by 7.</em>
Step-by-step explanation:
The multiples of 7 form an arithmetic sequence like shown:
7, 14, 21, ...
The last term of this sequence can be found by dividing 1000/7=142.9 and rounding down to the previous integer: 142*7= 994.
Thus, the sequence has:
a1=7, r=7, an=994. We need to find n and we'll do that by using the general term formula:
And solving for n:
n = 142
There are 142 whole numbers less than 1000 and divisible by 7.
The diagonal of a square is equal to the side x times square root of 2, xSqrt(2)
z = xSqrt(2), its rate of change is just Sqrt(2)
A linear approximation to the error in volume can be written as
... ∆V = (∂V/∂d)·∆d + (∂V/∂h)·∆h
For V=(π/4)·d²·h, this is
... ∆V = 2·(π/4)·d·h·∆d + (π/4)·d²·∆h
Using ∆d = 0.05d and ∆h = 0.05h, this becomes
... ∆V = (π/4)·d²·h·(2·0.05 + 0.05) = 0.15·V
The nominal volume is
... V = (π/4)·d²·h = (π/4)·(2.2 m)²·(6.8 m) = 25.849 m³
Then the maximum error in volume is
... 0.15V = 0.15·25.849 m³ ≈ 3.877 m³
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Essentially, the error percentage is multiplied by the exponent of the associated variable. Then these products are added to get the maximum error percentage.
Start by pulling out a three
y = 3(x^2 - x - 2) Now it is much easier.
y = 3(x - 2)(x + 1)
use the volume equation and add all the numbers to it
