Answer:
use logarithms
Step-by-step explanation:
Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.
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You will note that this approach works well enough for ...
a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents
(x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs
but doesn't do anything to help you solve ...
x +3 = b^(x -6)
There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.
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Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.
In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.
Answer:
4
Step-by-step explanation:
Machine A:
60 / 10 = 6 - 10 minute segments per hour
7 x 6 = 42 - parts per hour
42 x 12 = 504 - parts made on Monday
Machine B:
60 / 15 = 4 - 15 minute segments per hour
16 x 4 = 64 - parts per hour
64 x 10 = 640 - parts made on Monday
504 + 640 = 1144 - parts made by the two machines on Monday
Hope this helps!! :)
Answer:
a. x
b. 35
c. 45
d. y
Explanation:
a. The independent variable is not dictated by any other variable. x is the only variable here that fits that description is x.
b. A coefficient is a constant that multiplies any variable. 35 multiplies x, so it is a coefficient.
c. A constant is a number that cannot change and isn't a coefficient. 45 cannot be changed.
d. The dependent variable is dictated by other variables. y is dictated by x, so it is the dependent variable.
Tan T = UV/VT
UV = VT tan T = 40 tan 54
UV = 55.055 ft —> 55.1ft
