You've established that
so all you need to do is compute the integral. Rewrite the integrand as
and replace
, so that
. Then
By the fundamental theorem of calculus, this evaluates to
and so the series converges.
You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.
Answer:
t ≤ 4x + 10
Step-by-step explanation:
The amount of money that Josh spends on rides is the variable T, found in the problem. Josh wants to spend AT MOST t. That means he can spend as little as he wants, but he can't ride too many times so that the cost goes over T. Therefore, it has to be less than. But, it can also be equal to, as he can ride exactly many rides up to T, it just can't go over it.
Next, the cost to get into the fair is ten dollars, meaning if he goes on only one ride, that will cost him 4 dollars, but actually will have cost him 14 dollars because of the entrance fee. So, no matter how many rides he goes on, there is always the entrance fee added on.
Finally, the cost for each ride is 4 dollars per ride or 4 times x with x being the number of rides he goes on.
So, for our answer, we have t ≤ 4x + 10!
Answer:
34
Step-by-step explanation:
if it's to the power of 2 it's timed by itself 3 x 3 is 9 and 5 x 5 is 25 just add those and it's 34
You would subtract 52-7 and your answer would be 45
9514 1404 393
Answer:
y = 3.02x^3 -5.36x^2 +5.68x +8.66
Step-by-step explanation:
Your graphing calculator (or other regression tool) can solve this about as quickly as you can enter the numbers. If you have a number of regression formulas to work out, it is a good idea to become familiar with at least one tool for doing so.
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If you're trying to do this by hand, the x- and y-values give you 4 equations in the 4 unknown coefficients.
a·1^3 +b·1^2 +c·1 +d = 12
a·3^3 +b·3^2 +c·3 +d = 59
a·6^3 +b·6^2 +c·6 +d = 502
a·8^3 +b·8^2 +c·8 +d = 1257
Solving this by elimination, substitution, or matrix methods is tedious, but not impossible. Calculators and web sites can help. The solutions are a = 317/105, b = -75/14, c = 1193/210, d = 303/35. Approximations to these values are shown above.
