In the context of science, the rate is defined as a <span>metric that is evaluated in relation to another measured metric. To determine the rate for each set of data, we calculate the slope. The calculations proceed as follows:
Megan's growth rate = (12 - 4.5) / (4 - 1) = 2.5 inches weekly
Suzanne's growth rate = (11 - 5) / (4 - 1) = 0.5 inches weekly
Thus, it's clear that Megan’s plant grew more rapidly at a rate of </span><span>2.5 inches each week.</span>
The paraboloid intersects the x-y plane when x²+y²=9, defining a circle with a radius of 3, centered at the origin.
<span>Utilizing cylindrical coordinates (r,θ,z), the paraboloid transforms into z = 9−r² and f = 5r²z. </span>
<span>If F represents the average of f over the area 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>Thus, F = 10935π/8 ÷ 81π/2 = 135/4</span>
Answer:r=1.104
Step-by-step explanation:
Starting value a_1=256
Also
can be expressed as
where r=common ratio
r=1.104
The conditional probabilities for X equaling 1, 2, and 3 are 0.7333 (73.33%), 0.25 (25%), and 0.0167 (1.67%) respectively.
Answer:
24
Step-by-step explanation:
Based on the logarithmic expressions given 
, we need to identify the value of 
By substituting x = a³, y = a⁷, and z = a⁻² into the logarithmic function , we will derive;
Therefore, the result of the logarithmic expression is 24
