Suppose the point (2,4) is on the graph of f(x). Find a point of the function y=3f(x)

The sum of the geometric progression up to the 6th term is 512/7

To find the sum of a geometric series, you can use the formula for the sum of a finite geometric series:

Where:

- Sₙ is the sum of the first n terms of the series.

- a is the first term of the series.

- r is the common ratio.

- n is the number of terms in the series.

In your case, you have the geometric series: 16, 2, 1/4, ...

1. Identify the values for the formula:

  - The first term (a) is 16.

  - The common ratio (r) is found by dividing the second term by the first term: 2/16 = 1/8.

  - You want to find the sum of the first 6 terms (n = 6).

2. Plug these values into the formula and calculate S₆:

S₆ = (16(1 - (1/8)⁶))/(1 - 1/8)

Now, calculate the individual terms in the formula:

S₆ = (16(1 - 1/262144))/(7/8)

S₆ = (16(262143/262144))/(7/8)

S₆ = ((4194288/262144)/(7/8)

Now, perform the division:

S₆ = (4194288/262144) \* (8)/(7)

S₆ = 64 * 8/7

Now, multiply:

S₆ = 512/7

So, the sum of the geometric progression up to the 6th term is 512/7

Learn more about geometric series here

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Answer:

1450

Step-by-step explanation:

Step-by-step explanation:

The vertices and foci are on the x-axis. Thus, the equation for the hyperbola will have the form x2a2−y2b2=1 x 2 a 2 − y 2 b 2 = 1 . The vertices are (±6,0) ( ± 6 , 0 ) , so a=6 a = 6 and a2=36 a 2 = 36 . The foci are (±2√10,0) ( ± 2 10 , 0 ) , so c=2√10 c = 2 10 and c2=40 c 2 = 40 .

Answer:

Polygon: A polygon is a simple closed curve entirely made up of line segments.

1. As starting from triangle

Three kind of triangles: Isosceles, Scalene , and equilateral triangle

In none of these  measure of an exterior angle at the vertex of the triangle equals the measure of the adjacent interior angle.

2. Quadrilateral = Parallelogram, Rhombus, Rectangle, Square, Kite, Trpzm

Apart from Rectangle and Square none other quadrilateral have The measure of an exterior angle at the vertex of the quadrilateral equals the measure of the adjacent interior angle.

we can also consider other polygons also like pentagon,hexagon,heptagon.

Decagon and found that it is not always possible that measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.

So, the correct option is Sometimes.