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
An equation that relates the number of bags, x, to the cost, y is <u>y = 5x.</u>
<h3>What is an equation?</h3>
An equation is a mathematical statement that claims that the two sides are equal.
An equation involves two or more variables that require some mathematical operations to obtain their equivalent value.
Therefore, an equation contains numbers, variables, and operators, which show a value after the mathematical operations.
<h3>Data and Calculations:</h3>
Let the number of bags for the class = x (number of students)
Let the unit cost of a bag = $5
Let y = the total cost
Equation, <u>y = 5x</u>
Thus, an equation that relates the number of bags, x, to the cost, y is <u>y = 5x.</u>
Learn more about equations at brainly.com/question/2972832
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I tried my best to interpretate what you wrote. So I'm gonna attach a picture of what I came up with and my work. If you have any questions then just ask. :)
Answer:
A and B
Step-by-step explanation:
assuming the function should be
- 
+ 2, then
A
substitute the x value into f(x) and check the validity of the y- value
f(4) = - 
+ 2 = - 27 + 2 = - 25 ← agrees with y value
(4, - 25) lies on the graph
B f(1) = - 
+ 2 = - 1 + 2 = 1 ← agrees with y value
(1, 1) lies on the graph
C
f(- 1) = - 
+ 2 = - 
+ 2 ≠ 2
(- 1, 2) does not lie on the graph
D
f(0) = 
+ 2 = - 
+ 2 ≠ 0
(0, 0) does not lie on the graph
Answer:
4 minutes and 10 seconds.
Step-by-step explanation:
Time = Distance / Speed (or rate)
Time = 17.5 feet / 0.07 feet per second
Hence, time = 250 seconds.
250 seconds = 4 minutes 10 seconds.
