Answer:
C
Step-by-step explanation:
HOPE THAT HELPSBDNQBDB
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Hi, the answer is "You pay $11 for a movie ticket and some amount at the concession stand for a total of $28". We know this because the key words "total" before $28 dollars - 'total' stands for an equal sign in equations.
The unknown, or x, is the "some amount at the concession stand". This is an unknown value, but we do know it is added to $11 dollars for the movie ticket (which is a known value.)
Therefore, we have 11 (the movie ticket) plus (key word: and) some amount (meaning x) = (key word: total) 28
Answer:
1320, permutation
Step-by-step explanation:
There are 12 members
Pick a president
We have 12 choices
Now there are 11 people left to pick from
now pick a vp
We have 11 choices
Now there are 10 people left to pick from
now pick a secretary
We have 10 choices
12*11*10 = 1320
This is a permutation since it matters who is president, vp and secretary
Answer:
Step-by-step explanation:
