Answer: 10 < x < 60, or x is from 10 to 60
Step-by-step explanation: A domain of a graph consists of all of the input values shown on the x-axis while the range consists of all of the output values shown on the y-axis. Since the question asks to find the domain, you should look at the values of the graph from left to right. The domain includes all real numbers. Notice the black horizontal line on the graph and match up the beginning of it and the end of it with the values on the x-axis. The line begins at an x-value of 10 and ends at an x-value of 60; therefore, the domain (x-values) is from 10 to 60.
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
First, we need to find 8% of 1,575. To do so we have to divide 8 by 100, then multiply the quotient by 1,575.
8% ⇒ 0.08
1,575 × 0.08 = 126
Now add the 8% increase to the original cost.
1,575 + 126 = 1,701
<h2>Answer:</h2>
<u>Option 1: </u><u>$1,701</u><u>.</u>
I hope this helps :)
