9514 1404 393
Answer:
a(n) = 1/2(-8)^(n-1)
Step-by-step explanation:
The general term of a geometric sequence is ...
a(n) = a(1)×r^(n-1)
where a(1) is the first term, and r is the common ratio.
Here, the first term is a(1) = 1/2. The common ratio is the ratio of any two sequential terms: r = 32/-4 = -8. Then the explicit formula is ...
a(n) = 1/2(-8)^(n-1)
Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
Let's first establish that the origin is always ( 0, 0 ).
Next, as shown in the diagram attached, we can establish that there is a right-angle triangle formed when we connect the different points given from the problem. We can use this to solve the problem.
As the shape is a right-angle triangle, we can use Pythagoras' Theorem which is as follows:
a^2 + b^2 = c^2
Where c = hypotenuse of the right-angle triangle
Where a and b = other two sides of the right-angle triangle which aren't the hypotenuse
From this, we will substitute the values from the problem into Pythagoras' Theorem.
a^2 + b^2 = c^2
a = 12
b = 5
c = distance from the origin = d
THEREFORE:
( 12 )^2 + ( 5 )^2 = d^2
d^2 = 12^2 + 5^2
d^2 = 144 + 25
d^2 = 169
d = square root of ( 169 )
d = 13
FINAL ANSWER:
Therefore, the point ( 12, 5 ) is 13 units from the origin.
Hope this helps! :)
Have a lovely day! <3
The correct answer is the Last choice b=3-2a
Answer: 22 millimeters
Step-by-step explanation:
The radius is the line that connects any part of the circle to its center, while a diameter is the line that cut into two equal halves the circle while passing through the centre.
Thus, Diameter is twice a radius
So, if radius of the circle is 11 millimeters.
Diameter = 2 x radius
= 2 x 11 millimeters
= 22 millimeters