Radii and chord form an equilateral triangle. The angle of the larger segment is
.
The length of the larger segment is
3000 = p( 1 + .06/2)^(4 * 2)
<span>3000 = p(1.03)⁸ </span>
<span>p = 3000/ 1.03⁸ </span>
<span>p = 2368.2277029 </span>
<span>$2368.23 <-----</span>
Answer:
Step-by-step explanation:
Distance between origin (0, 0) and point (x, y) is given as:
Answer: 
<u>Step-by-step explanation:</u>
The explicit rule for a geometric sequence is: 
The information provided is: a₁ = 
and r = 5
Answer:
yes
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem, so the triangle is a right triangle.
7.5² +10² = 12.5²
56.25 +100 = 156.25
_____
You may recognize that the ratios of side lengths are ...
7.5 : 10 : 12.5 = 3 : 4 : 5
A 3-4-5 triangle is a well-known right triangle, as this is the smallest set of integers that satisfy the Pythagorean theorem. They also happen to be consecutive integers, so form an arithmetic sequence. Any arithmetic sequence that satisfies the Pythagorean theorem will have these ratios.
_____
If you're familiar with trigonometry, you know the law of cosines tells you ...
c² = a² + b² - 2ab·cos(θ) . . . . where θ is the angle between sides a and b. This reduces to the Pythagorean theorem when θ=90°, which makes cos(θ)=0. If the sides do not satisfy the Pythagorean theorem, cos(θ)≠0 and the triangle is not a right triangle.
