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2 years ago

Plz help me with this

Mathematics

1 answer:

Genrish500 [490]2 years ago

7 0

Answer: D) 10 sin (πx) - 5

<u>Step-by-step explanation:</u>

The range (maximum - minimum) is 5 - (-15) = 20

The amplitude (A) is range (20) ÷ 2 = 10

The vertical shift (D) is maximum (5) - amplitude (10) = -5

Of the given options, only A & D are candidates. Now we need to decide if it is a cos graph (A) or a sin graph (D). If we shift the graph up 5 units (to eliminate the vertical shift) , the graph would pass through the origin. Thus it is a sin graph and the answer must be option D.

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Which of the following points are solutions to the system of inequalities shown below?

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Answer:

b. (3,0)

e. (5,-6)

f. (2,1)

Are solutions to the system of inequalities

Step-by-step explanation:

b. (3,0)

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3 years ago

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If $S$ denotes the sum of the first $n$ terms of a geometric series with first term $a$ and common ratio $r$ , then

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$rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n$
$\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n$
$\implies (1-r)S=a(1-r^n)$
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Using summation notation, you have

$S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}$

In this case, you have $a=2$ , $r=\dfrac12$ , and $n=16$ . So the value of the sum is

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