The equation of the line that passes through the point (4,-4) and has a slope of -3 is y = -3x + 8.
<h3>How to find the equation of a line?</h3>
The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
Therefore, the equation of the line that passes through the point (4,-4) and has a slope of -3 can be found as follows;
m = -3
Hence,
y = -3x + b
using (4, -4) let's find the y-intercept.
-4 = -3(4) + b
-4 = - 12 + b
b = -4 + 12
b = 8
Therefore, the equation is y = -3x + 8
learn more on equation of a line here: brainly.com/question/29472392
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Answer:
Step-by-step explanation:
The height of the triangle is the height of the base
Height of the base = 16 m
Height of the prism = 20 m
Pattie runs at 5 ft/sec
She has got a head start of 15 feet.
So after 1 second, Pattie runs = (5+15) ft
<span>
= 20 </span>
ft
After 2 second Pattie runs = (20+5)ft
= 25 ft
After 3 second Pattie runs = (25+5) ft
= 30 ft
After 4 seconds Pattie runs = (30+5) ft
= 35 ft
After 5 seconds Pattie runs = (35+5) ft
= 40 ft
After 6 seconds Pattie runs = (40+5) ft
= 45 ft
Now Keith runs at 8 ft/sec
After 1 second Keith runs = 8 ft
After 2 second Keith runs = (8+8) ft
= 16 ft
After 3 second Keith runs = (16+8) ft
= 24 ft
After 4 second Keith runs = (24+8) ft
= 32 ft
After 5 second Keith runs = (32+8) ft
= 40 ft
After 6 second Keith runs = (40+8) ft
= 48 ft
So Pattie will stay ahead of Keith upto 4 seconds. In the 5th second Pattie and Keith will be level and in the 6th second Pattie will be overtaken by Keith.
Answer:
The rate of change of the distance between the cars at that instant is 5.46 meters per second
Step-by-step explanation:
Speed of first car = 7 m/s
Speed of second car = 3 m/s
At instant, distance of first car from intersection = 5 meters
distance of second car from intersection = 12 meters
Therefore, we have
Distance between both cars at intant = √(12² + 5²) = 13 m
Rate of cahnge of distance is given by;
2ddd/dt = d(x² + y²)/dt = 2xdx/dt + 2ydy/dt
= 26dd/dt = 2×5×7 + 2×12×3 = 142
dd/dt = 142/26 = 5.46 m/s.
That is the rate of change of the distance between the cars at that instant = 5.46 meters per second.
