Answer:
$ 2330
Step-by-step explanation:
a = $240
Earning at the end of fifth week = $ 680
increase in earnings per weak = ( 680 -240)/2 = 440/2 =110
d =110
l = a + (n-1)d
a20 = 240 + (19 * 110 ) = 240 + 2090 = 2330
I think you would multiply 4 and 10 and that equals 40.
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
<h3>
Answer:</h3>
1
<h3>
Step-by-step explanation:</h3>
The given angle is opposite the longest given side, so there will be exactly one solution.
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The number of solutions may be 0, 1, or 2 when the given angle is opposite the shortest given side.
