Answer:
Step-by-step explanation:
Identities : -
cot = cos / sin
tan = sin / cos
( cot + tan ) sin = sec
LHS
= ( cot + tan ) sin
= ( ( cos / sin ) + ( sin / cos ) ) sin
= ( ( cos sin ) / sin ) + ( sin² / cos )
= cos + ( sin² / cos )
LCM = cos
= ( cos² / cos ) + ( sin² / cos )
= ( cos² + sin² ) / cos
Identity : -
cos² + sin² = 1
= 1 / cos
= sec
= RHS
Hence proved.
Recall to always convert the mixed fractions to "improper" fractions first,
Answer:
Exponential
Step-by-step explanation:
<em>Starter:</em>
According to the title:
"Every day, half a bacteria population dies."
Exponential: y = ab^x ( b > 0 , b ≠ 1)
So the answer is C.
<em>Calculations:</em>
An exponential model is of the form y = a • b^t.
If you start with population of 500 million bacteria
t = 0
so 500 million = a • b^0 = a
Since every day half the population dies then in 1 day population will be 250 million
so a = 500 million, y = 250 million and t = 1
250 million = 500 million • b^1
b = 0.5
Therefore your equation would be
y = 500 million (or whatever the pop) • 0.5^t
Where t = number of days
This could also be written in exponential form ( e = 2.73)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
The price p, in dollars, of a specific car that is x year old is modeled by the function p(x)=22,255(0.91)^x
a) to determine the cost of a 2 year old car, we will substitute 2 for x in the given function. Therefore
p(2)=22,255(0.91)^2
p(2)=22,255 × 0.8281 = $18673.655
Approximately $18674
b) to determine the cost of a 7 year old car, we will substitute 7 for x in the given function. Therefore
p(7)=22,255(0.91)^7
p(2)=22,255 × 0.51676101936 = 11500.51648579693
Approximately $11501
c) 0.91 indicates exponential decay rate. It is a fixed percentage by which the value of the car decreases every year. It is determined by (1 - rate of decay)
