Solution: The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.
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:
9/5
Step-by-step explanation:
solve the original equation for x
-4× + 3 = 1x +(-6)
-1x
-5x + 3 = -6
-3
-5x = -9
/-5
x = 9/5
CHECK
-4(9/5) + 3 = 1(9/5) +(-6)
-21/5 = -21/5
Short Answer: g(x) = -3x This is a teaching question.
Remark
Define and describe f(x)
f(x) is read as y is dependent of x. The notation of f(x) with some exceptions is the same thing as y. What it stands for and what it can be used for is to tell you want value x can have if you want a specific value for x.
Suppose you are given
y = x + 2
Then suppose there is another statement above it
Let x = 5
y = x + 2
y = 5 + 2
y = 7
Instead of writing the top statement
Let x = 5
You use the shorthand
f(5) = x + 2
f(5) = 5 + 2
f(5) = 7.
So what does all this come down to. It is just a short way of writing Let x = ?
f(?) is what x will equal. x will become ?.
Your Question.
Remember that f(x) tells you what x becomes
f(5) means that x = 5.
Is that more than 4 or is that less than 4? It's a serious question.
Of course 5 is greater than 4. So that means that g(x) = - 3x. You don't have to do anything. Just read it.
If you’re trying to find how much more a RN makes compared to a dietitian, it would be 10,746. To find this, take the two salary’s and subtract. 64,690-53,944 = 10,746.
