Answer:
The possible pairs of sides are 90 and 120, 30 and 45, and 80 and 40.
Step-by-step explanation:
We know that 60 is a multiple of 15, 20, and 30, so we multiply by each factor to find all possible pairs: 10x6=60, 20x6=120, and 15x6=90, that gives your first pair, <u>90 and 120</u>.
We have now multiplied our first factor, 6. Now we need to multiply our second factor, 3: 20x3=60, 15x3=45, and 10x3=30. That gives your second pair, <u>30 and 45</u>.
Finally, we need to multiply by our 3rd factor, 4: 15x4=60, 20x4=80, and 10x4=40. That gives you your final possible pair, <u>80 and 40</u>.
I hope this helps :-)
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>
Answer:
(-2,11) (0,3) (2,-5) (4,-13)
Step-by-step explanation:
used desmos calculator
Answer:
The answer would be (7,9).
Step-by-step explanation:
If you partition that line by 6 you'd get (3,5), (4,6), (5,7), (6,8), and (7,9) in the middle of the two points. And the ratio of 5:1 would be seen at point (7,9).
Y = 5x + 4
Gradient = slope = 5
(0,4) = y - intercept
