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
Answer:
56 groups of 5 Fabergé eggs can be taken.
Step-by-step explanation:
It is given that Ashley is packing her bags for her vacation. She has 8 unique Fabergé eggs, but only 5 fit in her bag. In order to find how many different groups of 5 Faberge' eggs can she take, we apply the combination formula:
Thus, 56 groups of 5 Fabergé eggs can be taken.
Step-by-step explanation:
The answer is C
We can easily eliminate B and D since Ms. Macdonald isn't starting with 3 rabbits.
We can also eliminate choice A, because 5 to the 3rd power isn't 15.
5 to the 3rd power is 125, therefore the choice is C
Answer:
Superficie de un prisma rectangular fórmula
Área de un prisma rectangular = 2la + 2ah + 2lh.
Step-by-step explanation:
A collection of nickels and dimes is worth $4.40. There are 53 coins in all. How many nickels are there?
Nickel is a US coin worth 5 cents or 0.05.
Dime is a US coin worth 10 cents or 0.10
n + d = 53
0.05n + 0.10d = 4.40
n = 53 - d
0.05(53 - d) + 0.10d = 4.40
2.65 - 0.05d + 0.10d = 4.40
0.05d = 4.40 - 2.65
0.05d = 1.75
d = 1.75 / 0.05
d = 35
n = 53 - d
n = 53 - 35
n = 18
There are 18 nickels and 35 dimes.
0.05n + 0.10d = 4.40
0.05(18) + 0.10(35) = 4.40
0.90 + 3.5 = 4.40
4.40 = 4.40
