Answer:
Step-by-step explanation:
we know that
The smallest cube that could circumscribe the sphere has a length side equal to the diameter of the sphere
In this problem
The radius of the sphere is
The diameter of the sphere is two times the radius
so
The length side of the cube is
Remember that
The surface area of a cube is equal to the area of its six faces
so
substitute the value of b
Answer:
Step-by-step explanation:
49 - 16 = 33
= 5.74
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Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
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Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get
So the greatest integer possible for 'a' is a = 9.
------------------
Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
Answer:
X
Step-by-step explanation:
Let X is the number of hours Larry works a day
Given: Larry spends half of his workday teaching piano lessons.
=> Number of hours he teaches piano a day is: X
As we know that, he has 6 students, so the fraction of his workday is spent with each student is:
X : 6
= X
Hope it will find you well during the time of isolation.