Answer:
is the nth term of the given sequence.
Step-by-step explanation:
The sequence given is
We can clearly see that 1st term is and 2nd term is
2nd term is obtained by multiplying the 1st term by 2.
2nd term is and 3rd term is 1.
3rd term is obtained by multiplying the 2nd term by 2.
3rd term is 1 and 4th term is 2.
4th term is obtained by multiplying the 3rd term by 2.
Clearly, the given series is a <em>Geometric Progression(GP)</em> with
First term,
Common Ratio,
We know that term for a GP is:
Putting values of <em>a</em> and <em>r</em>
Hence, is the nth term of the given sequence.
Answer:
a) The number of ants in week three is shown through the following geometric progression: 500*1.1*1.1*1.1
b) 1.21
Step-by-step explanation:
We know that 500 ants are increasing at a rate of 10% every week which means that we can calculate the week one ants like this
500*1.1
Week two
500*1.1*1.1
and so on.
We write the following equation
500(1.1)^n where n is the number of weeks
We plug in 8 and then 6 for n in the equation above and get
500(1.1)^8=1071.79
500(1.1)^6=885.78
Divide and get that p=1.21
Step-by-step explanation:
When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.
Answer:
a = 105 in²
Step-by-step explanation:
Front and back, triangles
a = 2 * (1/2)(5 * 6)
a = 30
Sides, squares
a = 3 * (5 * 5)
a = 75
Total
a = 30 + 75
a = 105 in²
9514 1404 393
Answer:
(3, 2)
Step-by-step explanation:
Reflection across y=x swaps the coordinates:
(x, y) ⇒ (y, x)
Dilation by a factor of 1/2 multiplies each coordinate by 1/2.
(x, y) ⇒ (x/2, y/2)
The combination of these transformations gives you ...
(x, y) ⇒ (y/2, x/2)
(4, 6) ⇒ (3, 2)