The system of equations does not have one solution because the lines will never intersect (last one)
The answer is simply 290 pennies divided by 10 pennies per dime. The answer is 29 dimes.
The diameter of a circle that has an area of 325 is 20.34
Answer:
The answer to your question is there were 88 children
Step-by-step explanation:
Data
Total number of people = 188
total cost = $5040
12 more adults than seniors
number of children = ?
adults = a
children = c
Process
1.- Write equations that help to solve this problem
a + c = 188 Equation l
a = c + 12 Equation ll
2.- Solve by substitution. Substitute equation equation ll in equation l
(c + 12) + c = 188
-Solve for c
c + 12 + c = 188
2c + 12 = 188
2c = 188 - 12
2c = 176
c = 176 / 2
c = 88
3.- Conclusion
There were 88 children
The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.
<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>
<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>
<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>
<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>
<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>
<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>
<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>
<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>
<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
