I literally need help.
1 answer:
Answer:
Step-by-step explanation:
Given in the question:
a) A family paid $96 for 4 pool passes and 2 gym memberships.
b) Later that day, an individual bought pool passes for herself and 2 of her friends , and 1 gym membership for her . She paid $60.
Let's write the system of equation for each purchase that happened in the scenario.
Let,
P= Price of each pool passes
G= Price of each gym membership
We get,
a) A family paid $96 for 4 pool passes and 2 gym memberships:
b) Later that day, an individual bought pool passes for herself and 2 of her friends , and 1 gym membership for her . She paid $60:
Therefore, the equations generated in the scenario were:
Where,
P=Price of each pool passes
G=Price of each gym membership
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Answer:
(√6)/2 square units
Step-by-step explanation:
The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.
QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)
QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)
The cross product is the determinant ...
The magnitude of this is ...
|QR × QS| = √((-2)² +1² +(-1)²) = √6
The area of the triangle is half this value:
Area = (1/2)√6 . . . . square units
To demonstrate a method for computing the limit itself, let's pick a small value of n. If n = 3, then our limit is
Let a = 1 and b the cosine product, and write them as
with
Now we use the identity
to rationalize the numerator. This gives
As x approaches 0, both a and b approach 1, so the polynomial in a and b in the denominator approaches 6, and our original limit reduces to
For the remaining limit, use the Taylor expansion for cos(x) :
where essentially means that all the other terms in the expansion grow as quickly as or faster than x⁴; in other words, the expansion behaves asymptotically like x⁴. As x approaches 0, all these terms go to 0 as well.
Then
so in our limit, the constant terms cancel, and the asymptotic terms go to 0, and we end up with
Unfortunately, this doesn't agree with the limit we want, so n ≠ 3. But you can try applying this method for larger n, or computing a more general result.
Edit: some scratch work suggests the limit is 10 for n = 6.