Answer:
Step-by-step explanation:
Given that,
...(1)
We need to find the value of x.
We know that,
sin30 = 1/2
Use it in equation (1).
So, the value of x is equal to 
.
Answer:
It has to be less than 20 kids per team.
Step-by-step explanation:
Because 1107/56 is 19.767857142.
Answer:
7/5
Step-by-step explanation:
Answer:
43 feet
Step-by-step explanation:
How far is referring to the distance between the two numbers given.
In general, the distance between two numbers, a and b,
is given by |b-a| .
You have that you are finding the distance between -45.5 ft and -88.5 ft.
So the distance between those numbers is given by:
|-45.5-(-88.5)|
|-45.5+88.5|
|88.5-45.5|
|43.0|
|43|
43 (Since the number inside the | | has a distance of 43 from 0)
The distance between -45.5 ft and -88.5 ft is 43 ft.
Answer:
The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Step-by-step explanation:
Given
Rectangle Pyramid
Base Length = 3x + 1
Base Width = x
Height = 12
Volume = 96
Required
Dimension of the base of the pyramid
Given that the volume of the pyramid is ⅓ of the base area * the height.
This is represented mathematical as
Volume = ⅓ * base area * height.
Where
Base area = width * length
Base area = (3x + 1) * x
Base area = 3x² + x.
So,
Volume becomes
Volume = ⅓ * (3x² + x) * 12.
Volume = (3x² + x) * 4
Substitute 96 for volume
96 = (3x² + x) * 4
Divide both sides by 4
96/4 = (3x² + x) * 4/4
24 = 3x² + x
Subtract 24 fr both sides
24 - 24 = 3x² + x - 24
0 = 3x² + x - 24
3x² + x - 24 = 0
Expand
3x² + 9x - 8x - 24 = 0
Factorize
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
3x - 8 = 0 or x + 3 = 0
3x = 8 or x = -3
x = 8/3 or x = -3
Recall that
Length = 3x + 1
Width = x
For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.
Substitute x = 8/3
Length = 3x + 1
Length = 3(8/3) + 1
Length = 8 + 1
Length = 9
Width = x
Width = 8/3
Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
