Answer:
(-1,1)(0,4)(2,7)(3,7)
Step-by-step explanation:
the arrows point from the x coordinate to the y coordinate in each in pair
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
It is wrong because the equation is missing parentheses around the sum
When it says "the quantity of..." it always means parentheses. The correct equation is 2(3x+4)
2(3+3) or 2(3)+6, so the answer is the third option. It’s just using the distributive property.
Answer:
<em>4(b) , 5(a)</em>
Step-by-step explanation:
(4). <em>(b)</em> Domain is {0, 1, 2, 3} and Range is { - 3, - 2, - 1, 0}
(5). <em>(a)</em> Domain is [ - 4, 2] and Range is [ - 4, 4]
or
domain: - 4 ≤ x ≤ 2 , range: - 4 ≤ y ≤ 4
