Part A
4 < 5 < 9 is given to us. Apply the square root to each term to end up with this inequality: sqrt(4) < sqrt(5) < sqrt(9)
So sqrt(5) is between <u>sqrt(4)</u> and <u>sqrt(9)</u>
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Part B
Simplify those two mentioned square roots
sqrt(4) = sqrt(2^2) = 2
sqrt(9) = sqrt(3^2) = 3
Therefore, sqrt(5) is also between <u>2</u> and <u>3</u>
We can see this through using a calculator: sqrt(5) = 2.23607 approximately
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Part C
We can now say:
2 < sqrt(5) < 3
Multiply all three sides by 6
6*2 < 6*sqrt(5) < 6*3
So the expression 6*sqrt(5) is between <u>6 x 2</u> and <u>6 x 3</u>
Sure enough, a calculator confirms this
6*sqrt(5) = 13.416408
since 6*2 = 12 and 6*3 = 18. We see that 13.416 is between 12 and 18.
Yes he will have enough 1.35+0.12 is 1.47 he will have .03 left after that
Answer:
16 < w < 21
Step-by-step explanation:
Given that :
Width if mirror = w
Length of mirror = l
L = 6 + w
Perimeter of mirror < 96 and > 76
Possible width of the mirror
Perimeter of a rectangle :
2(l + w)
2(6 + w + w)
= 2(6 + 2w)
= 12 + 4w
Hence,
76 < perimeter < 96
76 < 12 + 4w < 96
76 - 12 < 4w < 96 - 12
64 < 4w < 84
16 < w < 21
The word inscribed means that the sphere is inside the cylinder and its diameter is equal to the height and diameter of the cylinder. The surface area of the sphere is equal to
SA (sphere) = πd²
where d is the diameter.
That of the cylinder is,
SA (cylinder) = πd(h + d/2)
Since h is also equal to d
SA (cylinder) = πd(d + d/2) = 3πd²/2
Therefore, the surface area of the cylinder is approximately 1.5 times that of the sphere.
