Answer:
$150
Step-by-step explanation:
Let n = the number of students and
Let x = the contribution per student.
We have two conditions:
(1) 12 900 = nx
(2) 12 900 = (n+14)(x - 21)
Set (1) = (2) nx = (n+14)(x - 21)
Remove parentheses: nx = nx - 21n + 14 x - 294
Subtract nx from each side 0 = -21n + 14x - 294
Divide each side by -7 (3) 0 = 3n - 2x + 42
Divide each side of (1) by x (4) n = 12 900/x
Substitute (4) into (3) 0 = (3 × 12 900)/x - 2x + 42
0 = 38 700/x - 2x + 42
Multiply each side by x 0 = 38 700 - 2x² + 42x
Multiply each side by -1 0 = 2x² - 42x - 38 700
Solve the quadratic equation
x = [-b±√(b² - 4ac)]/(2a)
x = {42 ± √[(42² - 4×2(-38700)]}/(2 × 2)
= [42 ± √(1764 +309 600]/4
= [42 ± √(311 364)]/4
= (42 ± 558)/4
= 600/4
= 150
Each student contributes $150.
Answer:
The volume of the bucket is 122.52 cm³.
Step-by-step explanation:
Given : A frustum is a cone with the end chop off a bucket in the shape of a frustum has diameters of 10 cm and 4 cm at its ends and a depth of 3 cm.
To find : Calculate the volume of this bucket ?
Solution :
The diameters of frustum is
D=10 cm ⇒ R= 5 cm
d=4 cm ⇒ r= 2 cm
The height is h=3 cm
The volume of the frustum is given by,
Substitute the value in the formula,
Therefore, the volume of the bucket is 122.52 cm³.
Answer:
(x, y) = ( 1, 10/3)
Step-by-step explanation:
2x + 3y + 12
6 - 4x + 3y = 12
Simplify the equation:
2x + 3y = 12
-4x + 3y = 6
Multiply both sides by -1:
2x + 3y = 12
4x - 3y = -6
Eliminate one variable by adding the equations:
6x = 6
Divide both sides by 6:
x = 1
Substitute the value of x into the equation:
-4 x 1 + 3y = 6
Solve the equation:
y = 10/3
A possible solution:
(x, y) = ( 1, 10/3 )
Check the solution:
2 x 1 + 3 x 10/3 = 6 -4 x 1 + 3 X 10/3 = 12
Simplify the expression:
12 = 12 = 12
Answer:
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Step-by-step explanation:
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