Answer:
a) the radius of the balloon increases at a rate of 5.42 in/s
b) the surface area of the balloon increases at a rate of 3 in²/s
Step-by-step explanation:
a) since the volume of a sphere V is
V= 4/3*π*R³
where R= radius , then the rate of change of the volume is
V' = dV/dR= 4*π*R²
using the chain rule
dV/dt = dV/dR*dR/dt
thus
k = 4*π*R² * dR/dt
dR/dt = k/(4*π*R²)
replacing values
dR/dt = k/(4*π*R²) = (33 in³/s) /(4*π*(22 in)²] = 5.42 in/s
then the radius of the balloon increases at a rate of 5.42 in/s
b) since the surface area is
S=4*π*R²
then
S' = dS/dR= 8*π*R
and
dS/dt = dS/dR*dR/dt = 8*π*R * k/(4*π*R²) = 2*k/R
replacing values
dS/dt = 2*k/R = 2*(33 in³/s)/( 22 in) = 3 in²/s
then the surface area of the balloon increases at a rate of 3 in²/s
You have $284 in your credit card balance. 186-174= 12. 99+35= 134 and then 12-134= -122. So 406-122= 284.
Espero que te sea de ayuda.
Answer:
-11
Step-by-step explanation:
g(-5)=-5^2+8(-5) +4
=25+-40+4
=-11
Answer:
Data Set B
Step-by-step explanation:
Mean Absolute Deviation(MAD) can be defined as the distance between one data point (value) to the Mean in a give Data set
It can also be defined as the deviation of the mean from the data points or values given in a data set.
From the above question, we are told that:
The mean of data set A ls 43.5 and the MAD is 3.7.
The mean of data set B is 12.8 and the MAD is 4.1.
Comparing the two Data set, the Mean Absolute Deviation of Data set A is smaller than that of Data set B.
Hence, Data set B shows a greater degree of variability because the distance between a data point(value) and the mean is 4.1. This also means that the data points in Set B are more spread out compared to the data points in Set A.