Y^-5
x^-5
because you have to put together all the x and then put all the y's together
b is correct! good job :)
Answer:
If I'm doing the problem correctly, the radius should be 4 yards.
Step-by-step explanation:
You work the problem backwards. Multiply 200.96 by 3, since it's a cone, so you're working with the volume of what a cylinder would be with the same dimensions. Then divide by the height (12 yd), then divide by pi. You should end up with 16, and 4 squared equals 16. Work the problem forwards from there to check.
4 squared is 16. 16 times 3.14 is 50.24. 50.24 times 12 is 602.88. 602.88 divided by 3 is 200.96.
Answer:
C. Yes, because the ratios are equivalent between each pair of values.
Step-by-step explanation:
A relationship between two quantities is proportional if the ratio of the two quantities are the same for all the given possible pairs of values.
In the table given, the ratio of block to mins in the first given pair of values is 3/6 = 3/6 = ½.
In the second given pair, it is 7 to 14 = 7/14 = ½. The same ratio is gotten for the others as well.
Therefore, the table represents a proportional relationship.
The answer is: "C. Yes, because the ratios are equivalent between each pair of values."
You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.
