Answer:
Step-by-step explanation:
Let d be the number of days.
We have been that each day Katie finds 12 more seashells on beach, so after collecting shells for d days Katie will have 12d shells.
We are also told that Katie already has 34 seashells in her collection, so total number of shells in Katie collection after d days will be:
As Katie wants to collect over 100 seashells, so the total number of shells collected in d days will be greater than 100. We can represent this information in an inequality as:
Therefore, the inequality can be used to find the number of days, d, it will take Katie to collect over 100 seashells.
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
The length can be found using the Pythagorean Theorem...
c^2=a^2+b^2 and in this case:
d^2=(dx^2)+(dy^2)
d^2=(3-7)^2+(12-9)^2
d^2=-4^2+3^2
d^2=16+9
d^2=25
d=5
So the length of AB=5 units.
1/3 oranges were spoiled.....u threw away 4 oranges...
1/3 of what = 4....
1/3x = 4
x = 4 * 3
x = 12 oranges
1/4 grapefruits were spoiled....u threw away 7
1/4 of what = 7
1/4x = 7
x = 7 * 4
x = 28
so ur fruit basket contained 12 oranges and 28 grapefruits before u discarded the spoiled ones
6)a) XL = 13 cm
b) AC = 21 cm
c) PC = 13 cm
d) Angle L = 29°
e) Angle C = 29°
f) Angle X = 122°
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