expressing a number with products of prime number
The number gives the exact value of one and seven thirtieths is (c) One and twenty three hundredths with the three repeating
<h3>How to determine the number gives the exact value of one and seven thirtieths? </h3>
The number is given as:
One and seven thirtieths
This can be represented as:
One + seven thirtieths
Express seven thirtieths as 7/30
One + 7/30
Express One as 1
1 + 7/30
Evaluate the quotient 7/30
1 + 0.2333
Evaluate the sum
1.2333
This can be rewritten as:
One and twenty three hundredths with the three repeating
Hence, the number gives the exact value of one and seven thirtieths is (c) One and twenty three hundredths with the three repeating
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Answer:
41
Step-by-step explanation:
10=15
24=x
cross multiply
24×15=410
410÷10=41
The formula for volume of cone is:
V = π
r^2 h / 3
or
π r^2
h / 3 = 36 cm^3
Simplfying in terms of r:
r^2 = 108 / π h
To find for the smallest amount of paper that can create
this cone, we call for the formula for the surface area of cone:
S = π
r sqrt (h^2 + r^2)
S = π
sqrt(108 / π h) * sqrt(h^2 + 108 / π h)
S = π sqrt(108 / π h) * sqrt[(π h^3 + 108) / π h]
Surface area = sqrt (108) * sqrt[(π h + 108
/ h^2)]
<span>Getting the 1st derivative dS / dh then
equating to 0 to get the maxima value:</span>
dS/dh = sqrt (108) ((π – 216
/ h^3) * [(π h + 108/h^2)^-1/2]
Let dS/dh = 0 so,
π – 216
/ h^3 = 0
h^3 = 216 / π
h = 4.10
cm
Calculating
for r:
r^2 = 108 / π (4.10)
r = 2.90 cm
Answers:
h = 4.10 cm
<span>r = 2.90 cm</span>
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