Find the sum of the first 10 terms of the following series, to the nearest integer.

Mathematics

1 answer:

Alona [7]2 years ago

4 0

Answer:

Step-by-step explanation:

you can see this is a geometric progression which a ratio of ${2\over{5}}$ . the sum of the firs n term is:

$S=a_1\frac{(1-r^n)}{(1-r)}=175\frac{1-(\frac{2}{5})^{10}}{1-\frac{2}{5}}=291.6360832$

the nearest integer would be:

292

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Answer:

B = (-1, 0)

C = (1, 0)

Step-by-step explanation:

Properties of an Equilateral Triangle

Three sides of equal length
All interior angles are 60°

Given:

ΔABC is an equilateral triangle
Vertex A is at (0, √3)

Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.

A 30-60-90 triangle is special right-angled triangle where:

Angles are in the ratio 1 : 2 : 3
Sides are in the ratio 1 : √3 : 2

Therefore, the formula for the sides is: b : b√3 : 2b, where:

b = shortest side opposite the 30° angle
b√3 = side opposite the 60° angle
2b = longest side (hypotenuse) is opposite the right angle

As Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.

Using the ratios to find b (shortest side length):

b√3 = √3 ⇒ b = 1

As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are: