The volume of the region R bounded by the x-axis is: 
<h3>What is the volume of the solid revolution on the X-axis?</h3>
The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border 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.
In the graph, the given straight line passes through two points (0,0) and (2,8).
Therefore, the equation of the straight line becomes:
where:
- (x₁, y₁) and (x₂, y₂) are two points on the straight line
Thus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:
y = 4x
Now, our region bounded by the three lines are:
Similarly, the change in polar coordinates is:
where;
- x² + y² = r² and dA = rdrdθ
Now
- 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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Answer:
45
Step-by-step explanation:2025....use the smallest prime number to divide the number 2025 till you get to a point were it can't be divided again . Group each prime number with a partner of its value like this :
5×5×3×3×3×3........ then use bracket to separate them like this (5×5)(3×3)(3×3)........ then take a number from each 5×3×3 then multiply to get 45
The distance formula is the square root of (x1-x2)^2+ (y1-y2)^2
So it would be square root [ (-2-3)^2 + (6-(-2))^2]
So it would be square root(25+64)
Square root(89)= 9.433
2 (3x - 7) = -4x - 6 + 9x - 8 Simplify 2 (3x - 7)
6x - 14 = -4x - 6 +9x - 8 Combine like terms (-4x and 9x) (-6 and -8)
6x - 14 = 5x - 14 Subtract 5x from both sides
x - 14 = -14 Add 14 to both sides
x = 0
Check your answer.
2 (3x - 7) = -4x - 6 + 9x - 8 Substitute x for 0
2 (3(0) - 7) = -4(0) - 6 + 9(0) - 8 Multiply 3(0)
2 (0 - 7) = -4(0) - 6 + 9(0) - 8 Multiply -4(0)
2 (0 - 7) = 0 - 6 + 9(0) - 8 Multiply 9(0)
2 (0 - 7) = 0 - 6 + 0 - 8 Subtract (0 - 7)
2(-7) = 0 - 6 + 0 - 8 Multiply 2(-7)
-14 = 0 - 6 + 0 - 8 Get rid of the unneccesary 0s
-14 = -6 - 8 Subtract (-6 - 8)
-14 = -14
So, x = 0 .
Answer:
The equivalent trigonometric ratio in Quadrant I is 
Step-by-step explanation:
The terminal side of 
is in the 3rd quadrant.
The principal angle is 
In other words, the terminal side of makes an acute angle of radian with the positive x-axis. Acute angles are in the first quadrant.
Since the cosine ratio is negative in the 3rd quadrant,
