Answers:
Part A: The value of x must be 0
Part B: The value of x can be any real number
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Explanation:
Part A) We have the equation (7^2)^x = 1 which simplifies to 7^(2x) = 1. The only way to get the left side equal to the right side is to have the exponent of 2x equal zero. If 2x = 0, then x = 0. So that's why x = 0 is the only solution here.
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Part B) Similar to part A above, but the exponent is slightly different now. We have (7^0)^x = 1 which turns into 7^(0*x) = 1. The exponent 0*x is really 0 no matter what x is. We can plug in any real number we want for x and the left side will always be 1. This is why the solution set to this equation is the set of all real numbers.
Answer:
Step-by-step explanation:
Considering the function:
The independent variable is "x" and we are asked to model it in terms of the variable "y":
Then, in order to solve for x (which resides in the exponent), we need to use the logarithm function.
Since the base of the exponent is 1.5, we need to use the logarithm base 1.5, to lower that exponent "x":
Explicit rule:
a(n)=(2/5)(5^(n-1))
For a recursive rule, we need to express a(n) in terms of a(n-1), which we can obtain from the explicit rule
a(n)=(2/5)(5^(n-1))
substitute n-1 for n above
a(n-1)=(2/5)(5^((n-1)-1))
=(2/5)(5^n-2)
Divide:
a(n)/a(n-1)=(2/5)(5^(n-1)) / ((2/5)(5^(n-2)))
=1/5^(-1)
=5
Therefore, multiplying both sides by a(n-1)
a(n)=5 a(n-1)
a(1)=(2/5)(5^(1-1))=2/5
So the recursive rule is
a(1)=2/5, a(n)=5 a(n-1)
Money is written with two places after the decimal. To round to the nearest scent, round to the hundredths place. In 0.1369 the 3 is in the hundredths place. Use the number directly after it, 6, to round. Because six is five or greater, it rounds the 3 up to 4. The answer is $0.14
