Step-by-step explanation:
Angle C must = [180 - 73 - 57 ] = [180 - 130] = 50°
And using rhw Law if Sines, we have.....
AB/sin C = AC/sin B → 24/sin(50) = AC/sin(73) → AC = 24*sin(73)/sin(50) = about 29.96 in
Whats 4 less than the product of 6 and a number
1 answer:
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The volume of the region R bounded by the x-axis is:
If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:
here:
- (x₁, y₁) and (x₂, y₂) are two points on the straight line
Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:
y = 4x
Now, our region bounded by the three lines are:
- y = 0
- x = 2
- y = 4x
Similarly, the change in polar coordinates is:
- x = rcosθ,
- y = rsinθ
where;
- x² + y² = r² and dA = rdrdθ
Therefore;
- rsinθ = 0 i.e. r = 0 or θ = 0
- rcosθ = 2 i.e. r = 2/cosθ
- rsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)
- ⇒ r = 0 to r = 2/cosθ
- θ = 0 to θ = tan⁻¹ (4)
Then:
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The sum of the first four terms of the sequence is 22.
In this question,
The formula of sum of linear sequence is
The sum of the first ten terms of a linear sequence is 145
⇒
⇒ 145 = 5 (2a+9d)
⇒
⇒ 29 = 2a + 9d ------- (1)
The sum of the next ten term is 445, so the sum of first twenty terms is
⇒ 145 + 445
⇒
⇒ 590 = 10 (2a + 19d)
⇒
⇒ 59 = 2a + 19d -------- (2)
Now subtract (2) from (1),
⇒ 30 = 10d
⇒ d =
⇒ d = 3
Substitute d in (1), we get
⇒ 29 = 2a + 9(3)
⇒ 29 = 2a + 27
⇒ 29 - 27 = 2a
⇒ 2 = 2a
⇒ a =
⇒ a = 1
Thus, sum of first four terms is
⇒
⇒
⇒ S₄ = 2(2+9)
⇒ S₄ = 2(11)
⇒ S₄ = 22.
Hence we can conclude that the sum of the first four terms of the sequence is 22.
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