Parameterize this surface (call it ) by
with and . The limits on should be obvious. We find the upper limit for by solving for where the sphere and cone intersect:
Take the normal vector to to be
(orientation does not matter here)
Then the area of is
Each basketball should cost $9.40
Answer:
Step-by-step explanation:
"78% of P" looks like this in an algebraic expression: .78P
"117% of Q" looks like this: 1.17Q
"...is 23.4 more than [above]" looks like this: [above] + 23.4
Putting that all together in one equation, knowing that the word "is" means "equals":
.78P = 1.17Q + 23.4
From there, we will now use the fact that Q is 40% of P, which looks like this:
Q = .4P
Now, using that substitution:
.78P = 1.17(.4P) + 23.4 and
.78P = .468P + 23.4 and
.312P = 23.4 so
P = 75
Going back up to what Q is equal to, we will sub in the value of P and solve for Q:
Q = .4P and P = 75, therefore,
Q = .4(75) so
Q = 30
Answer:
x = -4/5 or x = 71/8
Step-by-step explanation:
Solve for x:
(5 x + 4) (8 x - 71) = 0
Split into two equations:
5 x + 4 = 0 or 8 x - 71 = 0
Subtract 4 from both sides:
5 x = -4 or 8 x - 71 = 0
Divide both sides by 5:
x = -4/5 or 8 x - 71 = 0
Add 71 to both sides:
x = -4/5 or 8 x = 71
Divide both sides by 8:
Answer: x = -4/5 or x = 71/8