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3 years ago

Find x such that x - 4, x, and 3x - 8 are three consecutive terms in a geometric sequence

1 answer:

8 0

In a geometric sequence dividing any term by the term before it yields the common multiplier.
Then x/(x+8) = (3x-8)/x
Solving for x: reduces to x^2-10x +16 factor into (x-2)(x-8)
Then x = 2 or 8
2 produces a sequence of -2, 2, -2 ...
8 produces a sequence of 4, 8, 16 ...

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monitta

Answer:

$A\approx 282.7\ m^2$

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is to use the Pythagorean theorem to find the height of the cone. Then one can substitute the values given and found on the cone into the formula to find the surface area in order to solve for the surface area of the given cone.

2. Height of the cone

Imagine drawing a line from the tip of the cone down to the center of the base. This line will form a right angle with the base, thus, a right triangle is formed between the line, the radius (the distance from the center to the circumference or outer edge on a circle) of the base, and the incline of the cone. The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula is as follows:

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$a^2+25=169$

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3. Find the surface area of the cone.

The following formula can be used to find the surface area of a cone:

$A=\pi r(r+\sqrt{h^2+r^2})$

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$A=\pi r(r+\sqrt{h^2+r^2})$

$A=\pi 5(5+\sqrt{12^2+5^2})$

Simplify,

$A=\pi 5(5+\sqrt{12^2+5^2})$

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$A=\pi 5(18)$

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$A\approx 282.743$

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3 years ago

A segment in the coordinate plane has an endpoint with coordinates (1,2) and midpoint with coordinates (4,3). What are the coord

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Answer:

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midpoint formula (x1+x2)/2 , (y1+y2)/2

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