Answer:
Step-by-step explanation:
Solution
-=−
5
Answer:
<h2>
Tₙ = -3(2)ⁿ</h2>
Step-by-step explanation:
The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;
a is the first term of the geometric sequence
r is the common ratio
n is the number of terms
If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;
T₁₂ = ar¹²⁻¹
T₁₂ = ar¹¹
Given T₁₂ = -12,288 and r = 2, we can calculate the first term a
-12,288 = a2¹¹
a = -12,288/2¹¹
a = -12,288/2048
a = -6
Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;
Tₙ = -6(2)ⁿ⁻¹
Tₙ = -6 * 2ⁿ * 2⁻¹
Tₙ = -6 * 2ⁿ * 1/2
Tₙ = -3(2)ⁿ
Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ
the polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor (= a factor) of f(x), if and only if f(r)=0.
first we are dividing by x - 2.
so, r = 2.
as this is a factor, the remainder must be 0.
so,
0 = f(2) = 2³ + a2² - 15×2 + b = -22 + 4a + b
22 = 4a + b
then we divide by x + 3.
so, r = -3.
and the remainder is 75.
so,
75 = f(-3) = (-3)³ + a×(-3)² - 15×-3 + b = 18 + 9a + b
57 = 9a + b
now we have 2 equations with 2 variables to solve.
and since one term (+b) is the same in both equations, we use a little trick to subtract the first from the second equation.
57 = 9a + b
- 22 = 4a + b
---------------------
35 = 5a + 0
a = 7
22 = 4×7 + b = 28 + b
-6 = b
a = 7
b = -6
Answer:
28.26
Step-by-step explanation:
To find the area of a circle you take pi times the radius squared (
)
And to find the radius you divide the diameter by two.
