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
Heather runs 7 miles in 80 minutes.
At the same rate, how many miles would she run in 64 minutes?
Let x represent miles would she run in 64 minutes?
Question Sets Up the Proportion
7/80= x/63 |Cross Multiplying to solve for x
x = 7*64/80
x = 5.6mi
Hope this helps!
880
Underline the number in the tens place
look to the right
if number is greater than 5
add 1 to the underlined number
leave the numbers behind the underlined number zero
Answer:
A. 9.8 ft
Step-by-step explanation:
first convert the degrees to radians:
80° x (pi/180) ≈ 1.396
arc length = r x θ (always in radians)
= 7 x 1.396
= 9.772 ≈ 9.8 ft
