Answer:
v=26.41 m/s
Step-by-step explanation:
From the Newtons laws of motions, we sew that x= (2v₁²sin∅os∅)/g where x is the horizontal distance v is the initial speed and ∅ is the launch angle.
From trigonometry we see that 2 sin∅cos∅=sin 2∅
Therefore, x=(v²sin2∅)/g
x=22m
∅=9°
g=9.8m/s²
22m=v²×sin(2×9)/(9.8m/s²)
v²=(22×9.8)/(sin 18)
v²=697.696
v=√697.696
v=26.41 m/s
An integer may be a multiple of 3.
An integer may be 1 greater than a multiple of 3.
An integer may be 2 greater than a multiple of 3.
It is redundant to say an integer is 3 greater than a multiple of 3 (that's just a multiple of 3, we've got it covered). Same for 4, 5, 6, 7...
Let's consider a number which is a multiple of 3. Clearly, we can write 3+3+3+3+... until we reach the number. It can be written as only 3's.
Let's consider a number which is 2 greater than a multiple of 3. If we subtract 5 from that number, it'll be a multiple of 3. That means we can write the number as 5+3+3+3+3+... Of course, the number must be at least 8.
Let's consider a number which is 1 greater than a multiple of 3. If we subtract 5 from that number, it'll be 2 greater than a multiple of 3. If we subtract another 5, it'll be a multiple of 3. That means we can write the number as 5+5+3+3+3+3+... Of course, the number must be at least 13.
That's it. We considered all the numbers. We forgot 9, 10, 11, and 12, but these are easy peasy.
Beautiful question.
The equation of a straight line is given by:
y = mx + c
where m is the slope and c is the y-intercept.
From the given graph, the y-intercept is 1.
The slope of a straight line is given by:
Where
and
are two points on the line.
From the graph, (0, 1) and (14, 8) are two points on the line, thus:
Therefore, the equation representing the graph is
Answer:
The width of the building is 50 lamps and 60 lamps will be needed.
Step-by-step explanation:
The perimeter is computed by the sum of the sides of the building, since the length and width are equal on the oposite sides of the building, the perimeter is given by:
perimeter = 2*length + 2*width
900 = 2*(400) + 2*width
2*width + 800 = 900
2*width = 900 - 800
2*width = 100
width = 100/2 = 50 feets
To know how many lights bulbs will be needed we need to take the perimeter of the building and divide it by the space between the lamps. We have:
number o lamps = 900/15 = 60 lamps
21.25% because 85/400 = .2125 which is 21.25%
