The LCM is 2³ · 3 = 24 (Answer C)
The LCM of 8 and 12 is what? Factor 8 and factor 12 and look for common factors:
2³ and 2² · 3. Note that 2² is a factor of 2³ so may now be neglected.
Then the LCM is 2³ · 3 = 24 (Answer C)
I',m 100% sure
We know that the magnitude of the induced emf, ε = -ΔΦ/Δt where Φ = magnetic flux and t = time. Now ΔΦ = Δ(AB) = AΔB where A = area of coil and change in magnetic flux = Now ΔB = 0 - 0.750 T = -0.750 T, since the magnetic field changes from 0.750 T to 0 T.
The are , A of the circular loop is πD²/4 where D = diameter of circular loop = 16.7 cm = 16.7 × 10⁻²m
So, ε = -ΔΦ/Δt = -AΔB/Δt= -πD²/4 × -0.750 T/Δt = 0.750πD²/4Δt.
Also, the induced emf ε = iR where i = current in the coil and R = resistance of wire = ρl/A where ρ = resistivity of copper wire =1.68 × 10⁻⁸ Ωm, l = length of wire = πD and A = cross-sectional area of wire = πd²/4 where d = diameter of wire = 2.25 mm = 2.25 × 10⁻³ m.
So, ε = iR = iρl/A = iρπD/πd²/4 = 4iρD/d²
So, 4iρD/d² = 0.750πD²/4Δt.
iΔt = 0.750πD²/4 ÷ 4iρD/d²
iΔt = 0.750πD²d²/16ρ.
So the charge Q = iΔt
= 0.750π(16.7 × 10⁻²m 2.25 × 10⁻³ m)²/16(1.68 × 10⁻⁸ Ωm)
= 123.76 × 10⁻² C
= 1.2376 C
≅ 1.24 C
1) Parallel line:
3) Perpendicular line:
4) x-coordinate: 2.7
7) Perimeter: 12.4 units
8) Area: 8 square units
9) Two slopes of triangle ABC are opposite reciprocals
10) Perpendicular line:
The equation of a line is in the form
where m is the slope and q is the y-intercept.
Two lines are parallel to each other if they have same slope m.
The line given in this problem is
So its slope is . Therefore, the only line parallel to this one is the line which have the same slope, which is:
Since it also has
We can verify that this is a rectangle by checking that the two diagonals are congruent. We have:
- First diagonal:
- Second diagonal:
The diagonals are congruent, so this is a rectangle.
Given points A (0,1) and B (-2,5), the slope of the line is:
The slope of a line perpendicular to AB is equal to the inverse reciprocal of the slope of AB, so:
And using the slope-intercept for,
Using the point we find:
The endpoints of the segment are X(1,2) and Y(6,7).
We have to divide the sgment into 1/3 and 2/3 parts from X to Y, so for the x-coordinate we get:
The distance between two points and is given by
In this problem, the two points are
So the distance is given by
Point C divides the segment into two parts with 3:5 ratio.
The distance between the x-coordinates of A and B is 8 units: this means that the x-coordinate of C falls 3 units to the right of the x-coordinate of A and 5 units to the left of the x-coordinate of B, so overall, the x-coordinate of C falls at
of the distance between A and B.
To find the perimeter, we have to calculate the length of each side:
So the perimeter is
p = 3.6 + 3.2 + 2 + 3.6 = 12.4
The area of a triangle is
For this triangle,
Base = XW
Height = YZ
We calculate the length of the base and of the height:
So the area is
A triangle is a right triangle when there is one right angle. This means that two sides of the triangle are perpendicular to each other: however, two lines are perpendicular when their slopes are opposite reciprocals. Therefore, this means that the true statement is
"Two slopes of triangle ABC are opposite reciprocals"
The initial line is
A line perpendicular to this one must have a slope which is the opposite reciprocal, so
Using the slope-intercept form,
And using the point
Learn more about parallel and perpendicular lines:
C is the answer
the answer is 2
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