2000 - Monday
2000 - 0.10(2000) = 1800 -- Tuesday
1800 - .20(1800) = 1440 -- Wednesday
.25(2000) + 1440 = 1940 -- Thursday
net change = 2000 - 1940 = 60 <== net change
The square root of 72 lies between 8 and 9
First off, the underline underneath means plus or minus, since when you take the square root of something, the answer can be negative or positive at the same time
1. 64 is a perfect square. 8 x 8 = 64, therefore it is +- (plus or minus) 8.
2. 45 is not a perfect square, so you can pull out numbers or plug into a calculator and estimate.
Both answers: Since 45 is divisible by 9 and five, you can break a nine into two threes, therefore pull it out, and since the answer is negative, you get:
-3(5)^0.5 (an exponent of one-half or 0.5 means square root)
If you solve by calculator, the answer is ~= (approximately equal to) -6.72
3. Since 90 is not a perfect square, repeat the previous question. 9 can go into 90, therefore you can pull out two threes and are left with: +-3(10)^0.5
Using the calculator, you get ~= +-9.49
Answer:
Solution : Volume = 96/5π
Step-by-step explanation:
If we slice at an arbitrary height y, we get a circular disk with radius x, where x = y^(1/3). So the area of a cross section through y should be:
A(y) = πx^2 = π(y^(1/3))^2 = πy^(2/3)
And now since the solid lies between y = 0, and y = 8, it's volume should be:
V = ∫⁸₀ A(y)dy (in other words ∫ A(y)dy on the interval [0 to 8])
=> π ∫⁸₀ y^(2/3)dy
=> π[3/5 * y^(5/3)]⁸₀
=> 3/5π(³√8)⁵
=> 3/5π2^5
=> 96/5π ✓
