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baherus [9]
3 years ago
15

Find an equation of the vertical line through (3 comma negative 1 )in the form axplusbyequals​c, where​ a, b, and c are integers

with no factor common to all​ three, and agreater than or equals0.
Mathematics
1 answer:
Sati [7]3 years ago
8 0

The equation of the vertical line is 1x+0y=3

Explanation:

It is given that the vertical line passes through the points (3,-1)

For vertical line, the slope is undefined.

Hence, b=0

Let us substitute the coordinate (3,-1) in the equation ax+by=c, we have,

3a+0y=c

Simplifying, we have,

3a=c

3=\frac{c}{a}

where a=1 and c=3

Substituting the values of a, b and c in the equation ax+by=c, we have,

1x+0y=3

Thus, the equation of the vertical line is 1x+0y=3

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For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of
kotykmax [81]

Answer:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = 3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}

Number of term N = 3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}

here;

m = 5

n = 9

r = 0.5

Then:

\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}

\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}

\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}

\sum \limits ^n_{k=m}ar^k =0.186

6 0
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