an = 7/n(n+3), when n ≥ 2.
To solve this problem, we need to use the formula for the nth partial sum of a series:
Sn = a1 + a2 + ... + an
where a1, a2, ..., an are the terms of the series up to the nth term. We are given that
Sn = 3n + 2/n + 3
so we can write
a1 = 3(1) + 2/1 + 3 = 5/4
a2 = 3(2) + 2/2 + 3 = 8/5
a3 = 3(3) + 2/3 + 3 = 11/6
and so on.
We can use partial fractions to rewrite Sn in terms of the individual terms an:
Sn = a1 + a2 + ... + an
= (7/12) - (7/(n+2)) + (7/(n+3)) - (7/(n+4))
= 7/n(n+3)
where we have used the fact that the partial sums are equal to the sum of the first n terms minus the sum of the first (n-1) terms.
Therefore, we have an = 7/n(n+3), when n ≥ 2.
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The figure is made up of a rectangle, 2 right triangles and a 3rd triangle.
What is the area of the figure?
Responses
34 in2
52 in2
46 in2
136 in2
Answer:
52in^2
Step-by-step explanation:
The area of a triangle is A= 1/2bh
The area of a rectangle is A=lw
The top triangleThe base of the top triangle would be the length of the base of the two right triangles plus the length of the width of the the rectangle.
A=1/2bh
A=1/2(2+2+4)(4)
A=1/2(8)(4)
A=1/2(32)
A=16in^2
2. The two right triangles
A=1/2bh
A=1/2(2)(6)
A=1/2(12)
A=6in^2
(Because the two triangle are the same we just multiply the area by 2 to get the value of both)
A=12in^2
3. The rectangle
A=lw
A=6(4)
A=24in^2
-
Now just add the value of the areas for the different shapes.
16in^2 + 12in^2 + 24in^2 = 52in^2
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From the picture, the rate of the increase can be obtained as 10 m/s^2.
What is the acceleration?Acceleration is the rate of change of velocity over time. It is a vector quantity, which means that it has both magnitude and direction. Acceleration can be positive, negative, or zero, depending on whether an object is speeding up, slowing down, or maintaining a constant velocity. The standard unit of acceleration is meters per second squared (m/s²) in the SI system, but other units like feet per second squared (ft/s²) or kilometers per hour squared (km/h²) may also be used.
Given that
F = ma
a = F/m
a = 50 N/5 Kg
a = 10 m/s^2
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