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defon
3 years ago
7

After filling a gas tank the odometer read 82,803.6 After the next filling it read 83,034.6 it took 16.5 gallons to fill the tan

k. How many miles per gallon did the driver get?
Mathematics
1 answer:
ELEN [110]3 years ago
8 0
83,034.6 - 82,803.6 = 231 miles

231/16.5 = 14 miles per gallon
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I found the interval of convergence, but I am not sure how to do the second part, finding the sum of the series as a function of
antiseptic1488 [7]

The given series is geometric with common ratio 6^x - 9, which converges if |6^x - 9| (i.e. the interval of convergence). We have the well-known result

\displaystyle |r| < 1 \implies \sum_{n=0}^\infty ar^n = \frac{a}{1-r}

If you're not familiar with that result, it's easy to reproduce.

Let S_N be the N-th partial sum of the infinite series,

\displaystyle S_N = \sum_{n=0}^N \left(6^x - 9\right)^n = 1 + \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \cdots + \left(6^x - 9\right)^N

Multiply both sides by the ratio.

\left(6^x - 9\right) S_N = \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \left(6^x - 9\right)^3 + \cdots + \left(6^x - 9\right)^{N+1}

Subtract this from S_N to eliminate all the powers of the ratio between 0 and N+1.

\left(1 - \left(6^x - 9\right)\right) S_N = 1 - \left(6^x - 9\right)^{N+1}

Solve for S_N.

S_N = \dfrac{1 - \left(6^x - 9\right)^{N+1}}{10-6^x}

Now as N\to\infty, the exponential term converges to 0 and we're left with

\displaystyle \sum_{n=0}^\infty \left(6^x-9\right)^n = \lim_{N\to\infty} S_N = \boxed{\frac1{10-6^x}}

7 0
2 years ago
A company has been forced to reduce its number of employees. Today the company has 34% fewer employees than it did a year ago. I
jenyasd209 [6]
Since there are 34% fewer, you multiply 297 x 0.34 = 100.98
Then you add 100.98 to 297 = 397.98
They had 397 employees.
6 0
2 years ago
I need help with this question
Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

f(x) = 6x³-x²+4x+5

g(x) = 9x³-1

(f+g)(x) = {6x³-x²+4x+5} + {9x³-1}

open brackets

6x³-x²+4x+5 + 9x³-1

choose like terms

6x³+ 9x³-x²+4x+5 -1

15x³-x²+4x+4= x²(15x-1)+4(x+1)= (x²+4)(x+1)(15x-1)

(f+g)(x)= 15x³-x²+4x+4 =  (x²+4)(x+1)(15x-1)

(f+g)(2) = 15(2)³-(2)²+4(2)+4 = 15(8)-4+8+4 = 120+8 = 128

(f-g)(x) = {6x³-x²+4x+5} - {9x³-1}

open brackets

6x³-x²+4x+5 - 9x³+1

choose like terms

6x³- 9x³-x²+4x+5 +1

-3x³-x²+4x+6= -x²(3x+1)+2(2x+3)= (-x²+2)(3x+1)(2x+3) =  (2-x²)(3x+1)(2x+3)

(f-g)(x) = -3x³-x²+4x+6 = (2-x²)(3x+1)(2x+3)

(f-g)(-3) = -3(-3)³-(-3)²+4(-3)+6 = -3(-3x-3x-3)-(-3x-3)-12+6=-3(-27)-3(9)-12+6= 81-27-12+6 = 54-6= 48

(f-g)(-3) = 48

4 0
3 years ago
Which of the following is an integer?<br> 95.2<br> 73<br> 54<br> 41<br> -26
HACTEHA [7]

Answer:

95.2 is not an integer

and other are integers

7 0
3 years ago
Based on the markings in the diagram, which conclusion must be true?
Yakvenalex [24]
The correct answer is B) AC = BC
We know this because the two triangles are equal due to SAS
6 0
3 years ago
Read 2 more answers
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