A 360 degrees counter-clockwise rotation will bring the triangle at the same place.
So, divide 1980 by 360 and find the remainder.
On dividing, we can find that
1980 = 5(360) + 180
A 1800 degrees rotation will rotate the triangle 5 times and will bring it in the same place.
A further 180 degrees rotation will rotate the triangle to two quadrants back and will bring it in the first quadrant.
Answer:
c=12
Step-by-step explanation:
12c - 53= 91
12c=144
c=12
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>
If so, start by factoring the numerator. Then cancel any common term in the numerator and denominator. If you end up with no denominator, then use the original denominator. Set it equal to zero and solve for x. That value of x will be the restriction.
The square root of 125 is in between 11 and 12. It is 11.1803.
