Answer:
Let 3x and 2x are divided into 250.
Step-by-step explanation:
3x + 2x = 250
⇒ 5x = 250
⇒ x = = 50
∴ 3x = 3 × 50 = 150 and
2x = 2 × 50 = 100
Thus, the required numbers are 150 and 100.
Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
Answer: Line segment.
Step-by-step explanation:
In geometry, a line is an undefined term in which an infinite number of points extending in opposite directions.
It has only one dimension.
When it has endpoints on both the sides, it is known that a line segment (which is an defined term).
Hence, If points A and B are connected by a series of points that extend infinitely in opposite directions, then AB is a line.
So, the term best describes the geometric figure: 'Line segment"
Answer:
or approximately (0.544, 4.179)
Step-by-step explanation:
A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):
Set equal to 8/7 and solve for x:
Therefore, will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into to get the y-coordinate:
⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)
Answer:
c 364
Step-by-step explanation:
this is the correct answer because the rest are lower answers