Select the equation of the line that passes through the point (5, 7) and is perpendicular to the line x = 4.
1 answer:
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All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Answer:
Measures are SV=9 units., SY=14 units, YW= , YW=
Step-by-step explanation:
Given Y is the circumcenter of ΔSTU. we have to find the measures SV, SY, YW and YX.
As Circumcenter is equidistant from the vertices of triangle and also The circumcenter is the point at which the three perpendicular bisectors of the sides of the triangle meet.
Hence, VY, YW and YX are the perpendicular bisectors on the sides ST, TU and SU.
Given ST=18 units.
As VY is perpendicular bisector implies SV=9 units.
Also in triangle VTY
⇒
⇒ VY^{2}=115
As vertices of triangle are equidistant from the circumcenter
⇒ SY=YT=UY=14 units
Hence, SY is 14 units
In ΔUWY,
⇒
⇒ ⇒ YW=
In ΔYXU,
⇒
⇒ ⇒ YW=
Hence, measures are SV=9 units., SY=14 units, YW= , YW=
To solve system of equations by substitution, we are going to use the first equation to substitute into the second equation wherever you see y.
_______________
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(rounded)
Next, substitute x = 3.29 into the first equation, or to any equation you'd like, to find y.
So, your final answer would be (3.29, 4.87).