Answer:
Basically it has to be divisible by 8, 9, and 10 because any number that is divisible by 2, 3, 4, 5, 6 must also be divisible by 8, 9 and 10. We know that the number has to end in 0, the sum of its digits must be divisible by 9 and the last three digits must be divisible by 8. Therefore, the smallest number is 10080 and the largest is 999360.
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:
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Answer:
New length is 3 3/20 ft.
Step-by-step explanation:
The total board is 2 5/8 feet long. And since 5/6 of a foot is trimmed off, that means each piece of wood is 5/6 feet.
We can now set up an equation like this ---> 5/6 ⋅ x = 2 5/8
Now we're going to simplify ---> 5/6 ⋅ x = 2 5/8
5/6 ⋅ x = 21/8
(multiply both sides by 6)
5x = 63/4
(divide both sides by 5)
x = 63/20
x= 3.15
So, the new length is 3.15 feet long, or 3 3/20 in mixed fraction.
The equation (1) is divided by 2 to create new equivalent system of equations.
Step-by-step explanation:
The given systems of equations are:
Considering 8y instead of 8 in eq(1)
We need to identify what action was completed to create this new equivalent system of equations?
Comparing given equations we came to know that equation(1) is divided by 2 to get the new equation i.e
While second equation is same as given.
So, The equation (1) is divided by 2 to create new equivalent system of equations.
Keywords:System of Equation
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