jose and two of his friends are collecting baseball cards. Their goal is for the three of them to collect at least 100 cards in
total. At the moment they have 43 cards. If they all plan to now collect the same number of cards,Which inequality can jose use to determine the minimum number of cards each person needs to collect to reach their goal?
2 answers:
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Answer:
20.823 nautical miles
S20°E
Step-by-step explanation:
I assume you mean ° (degrees), not ' (minutes). There are 60 minutes in 1 degree.
S52°E means "south, 52° east", or 52° east of south.
S50°W means "south, 50° west", or 50° west of south.
1 knots = 1 nautical mile / hour, so the boat first travels 8 nautical miles from A to B, then 4.5 nautical miles from B to C, then finally back to A.
If we say A is at the origin, then the coordinates of B are:
(8 sin 52°, -8 cos 52°)
And the coordinates of C are:
(8 sin 52° − 4.5 sin 50°, -8 cos 52° − 4.5 cos 50°)
(2.857, -7.818)
So the distance from A to C is:
x = √(2.857² + (-7.818)²)
x ≈ 8.323
And the total distance of the race is:
d = 8 + 4.5 + 8.323
d = 20.823
The compass bearing from A to C is:
θ = atan(2.857 / 7.818)
θ ≈ S20°E
Answer:
Step-by-step explanation:
Given , start by squaring both sides to work towards isolating
:
Recall and
:
Isolate the radical:
Square both sides:
Expand using FOIL and :
Move everything to one side to get a quadratic:
Solving using the quadratic formula:
A quadratic in has real solutions
. In
, assign values:
Solving yields:
Only works when plugged in the original equation. Therefore,
is extraneous and the only solution is