Answer:
i)W = 2500 / T
ii) W = 500 Tons
iii) grad W(10°) = - 25î
iv) The formulation is not practical
Step-by-step explanation:
i) Write an equation describing the use of coal
As use of coal is inversely proportional to the average monthly temperature
if W is use of coal in tons/per month then
W(t) = k / T where k is a constant of proportionality and T is the average temperature in degrees. We have to determine k from given conditions
k = ?? we know that when T = 25° W = 100 tons the by subtitution
W = k/T 100 = k /25 k = 2500 Tons*degree
Then final equation is:
W = 2500 / T
ii) Find the amount of coal when T = 5 degrees
W = 2500 / 5
W = 500 Tons
iii)
The inverse proportionality implies that W will decrease as T increase.
The vector gradient of W function is:
grad W = DW(t)/dt î
grad W = - 2500/T² î
Wich agrees with the fact that W is decreasing.
And when T = 100°
grad W(10°) = - 2500/ 100 î ⇒ grad W(10°) = - 25î
iv) When T = 0 The quantity of coal tends to infinite and the previous formulation is not practical
Answer:
$6,506.51
Step-by-step explanation:
Recall that increasing an amount C in x% is equivalent to multiply it by (1+x/100)
As we have 4% APR, the monthly interest would be (4/12)% = 0.04/12
<u>Month 0</u> (first payment)
$250
Month 1
<u>Month 2</u>
<u>Month 3</u>
<u>Month 24 (2 years)</u>
The sum
is the sum of the first 24 terms of a geometric sequence with common ratio which is
so, after 2 years the saving balance is
250*26.02603071 = 6,506.50767= $6,506.51 rounded to the nearest cent.
Answer:
x = -33
Step-by-step explanation:
2x+7=?
X=6
2(6)+7=
12+7=19
In six years, the tree will be 19ft
2x+7=44
Minus seven on both sides
2x=37
Divide two from both sides
X=18.5
Thus, it will take 18 and a half years for the tree to reach 44ft
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Define x:
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Let x be the length of the pool.
Length of the pool and its border = x + 1 + 1
Length of the pool and its border = x + 2
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Given area = 361 ft², find x:
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(x+2)² = 361
x+ 2 = √361
x + 2 = 19
x = 19 - 2
x = 17
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Find Length of the pool:
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Length of the pool = x = 17 feet
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Find Area of the pool:
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Area = 17 x 17
Area = 289 ft²
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Answer: Area of the pool = 289 ft²
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