MATHEMATICS HIGH SCHOOL

The first term of an infinite geometric sequence is 18, while the third term is 8. There are two possible sequences. Find the sum of each sequence.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

The sequence is geometric with

a = 18

Third term = 8.

Let the second term be x.

The infinite geometric sequence will be in the form

18,x,8,......

For geometric sequence, the ratio of two consecutive terms are equal. Hence, we have

$(x)/(18)=(8)/(x)\n\nx^2=144\nx=\pm12$

So, there are two possible sequences

18,-12,8,......

and

18,12,8,......

Thus, the common ratios are

$r=(-12)/(18),(12)/(18)\n\nr=(-2)/(3),(2)/(3)$

The sum of the infinite geometric for $r=(-2)/(3)$

$S=(a)/(1-r)\n\n(18)/(1-(-2)/(3))\n\nS=(18)/((5)/(3))\n\nS=(54)/(5)$

The sum of the infinite geometric for $r=(2)/(3)$

$S=(a)/(1-r)\n\n(18)/(1-(2)/(3))\n\nS=(18)/((1)/(3))\n\nS=54$

Answer 2

Answer: Hello,
Let'q the ratio
$u_(1) =18\n u_(2) =18*q\n u_(3) =18*q^2=8\ ==\ \textgreater \ q^2= (4)/(9) ==\ \textgreater \ q=\pm\ (2)/(3) \n1) if \ q= (2)/(3) \ then \ \sum_(i=0)^(\infty)\ 18* ((2)/(3) )^i= 18*(1)/(1+ (2)/(3) ) = (18*3)/(5)= 10.8\n\n2) if \ q= -(2)/(3) \ then \ \sum_(i=0)^(\infty)\ 18* (-(2)/(3) )^i= 18*(1)/(1- (2)/(3) ) = (18*3)/(1)= 54\n\n$

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A student wants to construct the inscribed circle of a triangle. What is the first step he/she should take?a) Construct a circle using one of the vertices of the triangle
b) Construct the perpendicular bisector of each side of the triangle
c) Construct a line parallel to the vertex of the triangle
d) Construct the angle bisector of each angle in the triangle

Answers

The correct answer is:

d) Construct the angle bisector of each angle in the triangle

Explanation:

The incenter, or center of an inscribed circle, is the point where the angle bisectors of a triangle intersect. This means the first thing we will need to construct is the bisector of each angle of the triangle.

Answer:

construct the perpendicular bisector of each side of the triangle

Step-by-step explanation:

The graph shows two lines, A and B:A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 3, 0 and the ordered pair 0, 6. Another straight line labeled B joins the ordered pair 0, 0 and the ordered pair 5, 5.

Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?

A (0, 6) is the solution to both lines A and B.
B(0, 6) is the solution to line B but not to line
C(2, 2) is the solution to both lines A and B.
D (2, 2) is the solution to line A but not to line

Answers

The correct answer for the question that is being presented above is this one: "A (0, 6) is the solution to both lines A and B." The statement that is correct about the solution to the system of equations for lines A and B is that (0, 6) is the solution to both lines A and B.

Answer:

C(2, 2) is the solution to both lines A and B.

Step-by-step explanation:

Line A is given as:

A straight line labeled A joins the ordered pair 3, 0 and the ordered pair 0, 6.

We know that the equation of a line passing through (a,b) and (c,d) is calculated as:

$y-b=(d-b)/(c-a)* (x-a)$

Hence, the equation of line is:

$y-0=(6-0)/(0-3)* (x-3)\n\ny=(6)/(-3)* (x-3)\n\ny=-2* (x-3)\n\ny=-2x+6$

Hence, equation of line A is:

$y=-2x+6$

Similarly B is a line passing through (0,0) and (5,5).

Hence, the equation of line B is:

$y=x$

So, from the graph we observe that, the point of intersection of the two lines is (2,2).

Thus, option C is correct.

5-2 cos (3x + pie divide 2) + 2

Answers

This should be the answer. I haven't Cos, Sine, and Tangent involving x in a while.
5-2cos(3x+3.14/2)+2=7.299838055
7.3

1/4 of a liter is equal to how many mL

Answers

$1 \ liter = 1000 \ mL \n \n(1)/(4) * 1000 = 250 \ mL$

250mL 1/4 x 1000 = 1000/4 OR 250

The net of a triangular prism and its dimensions are shown in the diagram. what is the lateral surface area of the triangular prism in square centimeters A-264 cm
B-240cm
C-225cm
D “Not here”

Answers

Answer: 120 sq in.

Step-by-step explanation:

The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?

Answers

This one is a bit confusing but I'll try to answer. Since the sum is given and one of the addend is given, we need to perform subtraction to get the other addend.

8d⁵ - 3c³d² + 5c²d³ - 4cd⁴ + 9 ⇒ SUM
- 2d⁵ - c³d² + 8cd⁴ + 1 ⇒ 1ST ADDEND
6d⁵ - 2c³d² + 5c²d³ -12cd⁴ - 8 ⇒ 2ND ADDEND

Answer:

A which is 6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8

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