Simplify the expression.
1 answer:
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Answer:
The sum of the first 6 terms of the series is 504.
Step-by-step explanation:
Given that,
Common ratio in a geometric series is, r = 0.5
First term of the series, a = 256
We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:
The sum of n terms of a GP is given by :
Here, n = 6
So, the sum of the first 6 terms of the series is 504.
Answer:
The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
Step-by-step explanation:
Here is the complete question
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.
y=35x; y=-0.05(x-400)²+9,492
what does the solution of the system represent in this context?
Solution
The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .
So, 35x = -0.05(x-400)² + 9,492.
Expanding the right side, we have
35x = -0.05(x² - 800x + 160000) + 9492
35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492
35x = -0.05x² +40x - 8000 + 9492
35x = -0.05x² +40x + 1492
Collecting all the terms to the left side, we have
0.05x² - 40x - 1492 + 35x = 0
0.05x² - 5x -1492 = 0
Using the quadratic formula,
We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.
The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
We confirm that by plugging in x = 229.83 in both equations.
y = 35x = 35(229.83) = 8044.05 ≅ 8044.1
y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1
Answer:
D. 1
Step-by-step explanation:
We have the expression,
We get, eliminating the cosecant function,
As, sinx is reciprocal of cosecx and cosx is reciprocal of secx,
i.e.
i.e.
Since, we know that,
Thus,
So, after simplifying, we get that the result is 1.
Hence, option D is correct.