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Answer:
1 Cards = 36%
2 Cards = 28%
3 Cards = 24%
4 Cards = 12.5%
Step-by-step explanation:
To model this situation, we are going to use the exponential function:

where

is the initial number of cars

is the growing rate in decimal form

is number of tames the growing rate is increasing per year

is the time in years
To convert the growing rate to decimal form, we are going to divide the rate by 100%


Since the growing rate is increasing quarterly,

. We also know that the initial number of cars is 920, so

. Lets replace all those values in our function:



We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03
With some simplification,
cos⁻¹(x) - 5 cos⁻¹(x) - π/3 = 2π/3
becomes
-4 cos⁻¹(x) = π
or
cos⁻¹(x) = -π/4
However, the inverse cosine function has a range of 0 ≤ cos⁻¹(x) ≤ π, so there are no solutions to this equation.
Step-by-step explanation:
Letthenumberofpensbexand
numberofpencilsbey
then
x+y=16ory=16−x
andtheirvalue
8x+1.5y=50
8x+(
2
3
)(16−x)=50
8x+24−(
2
3
)x=50
8x−(
2
3
)x=50−24
(
2
13x
)=26∴x=4
theny=16−x=16−4=12