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.
V = sqrt (64h)
V = sqrt (64 * 23)
V = sqrt 1472
V = 38.366 rounds to 38.37 ft <==
Base on the question that ask to calculate the sine, cosine, and tangent of 5pi/3 radians and base on my further calculation, I would say that the answer would be <span>sin Θ = -sqrt 3/2; cos Θ = -1/2; tan Θ = -sqrt 3. I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification </span>
c =
using Pythagoras' identity on the right triangle
c = √( 4² + ( )² ) = √16 +
= =
Answer:
D. 20 quarts
Step-by-step explanation:
correct