Answer:
Step-by-step explanation:
To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how.
Let's try it with the fractions
2
3
and
3
12
12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also.
Now you have the following:
8
12
and
3
12
These fractions now have common denominators! Now they're all set for adding or subtracting fractions.
Try another:
2
6
and
3
5
: The least common multiple of 6 and 5 is 30. (the product of the denominators)
Transform each fraction by multiplying by "1":
2
6
⋅
5
5
=
10
30
and
3
5
⋅
6
6
=
18
30
One last problem:
4
9
and
7
6
What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the LEAST number that you could use. How about 18? YES!
4
9
⋅
2
2
=
8
18
and
7
6
⋅
3
3
=
21
18
Ready to go...
Hope this helped!
Answer:
52°
Step-by-step explanation:
y= 180°-67°= 113°
x=180°-15°-113°=52°
<span> You have :
----------------
v0 = 35 m/s
B = angle of elevation = 30 deg
a suby = - g
v suby0 = ( v0 ) ( sin B )
v suby0 = ( 35 m/s ) ( sin 30 ) = 17.5 m/s
At maximum height :
------------------------------
v suby = vy* = 0.0
t = t*
y = ymax = y*
Basic kinematics gives :
-------------------------------------
a suby = dv suby / dt = -g ------> dt = dv suby /a suby
v suby = dy/dt ------> dt = dy / vsuby
dt = dv suby / a suby = dy / v suby
( v suby ) ( d v suby) = ( a suby ) dy = ( -g ) dy
Now integrate and get :
-----------------------------------
( v suby* )^2 - ( v suby0)^2 ( 1/2 ) = ( -g ) ( ymax )
ymax = [ ( v suby0 )^2 - ( v suby* )^2 ] / [ ( 2 ) ( g ) ]
ymax = ( 17.5 m/s )^2 - ( 0.0 m/s )^2 ] / [ ( 2 ) ( 9.807 m/s^2 ) ]
ymax = 15.6 m <------------------
Check the result:
--------------------------
t* = v suby0 / g = ( 17.5 m/s ) / ( 9.807 m/s^2 ) = 1.784 s
y* - y0 = ( v suby0 ) ( t* ) - ( g/2 ) ( t* )^2
y* = ( 17.5 m/s ) ( 1.784 s ) - ( 9.807 m/s^2 / 2 ) ( 1.784 s )^2
y* = ymax = 31.23 m - 15.61 m = 15.6 m
The ymax values agree.</span>
Answer:
P = 2(l + w)
Step-by-step explanation:
If we sum the lengths of four sides of any quadrilateral then we will get its perimeter.
Now, in the case of a rectangle, the opposite sides are equally long.
Hence, in the perimeter of a rectangle, the length will be twice and the width is also twice.
If l represents the length and w represents the width of the rectangle then the perimeter will be equal to
P = 2l + 2w = 2(l + w). (Answer)
