I’d say the second one, the fourth one and the fifth one.
Hope it works :)
Answer:
Here, we will use the formula from trigonometry which defines a radian
we know that an angle is a radian when the length of the radius of the circle is equal to the length of the arc formed
hence, if the radius is r and the arc is r, the angle (in radians) will be 1
if the radius is r and the arc is 2r, the angle in radians will be equal to:
length of arc / radius = 2r/r = 2 radians
I believe this will explain what is actually happening in these type of questions
So, the equation:
Θ(in radians) = s / r (where the length of arc is s and the radius is r)
π/4 = s / 12
s = 3π or 9.42 inches
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
Given:
1 m : 25 cm
8 in : 1 ft
12 in : 1 ft
First, we convert each
variable given on the right:
1 m : 0.25 m (this means that
1 meter is made to represent 25 cm)
8 in : 12 feet (this means
that 8 in is made to represent 1 feet)
12 in : 12 in (this means
that 12 in is made to represent 1 feet)
<span>After converting the
variables, we can now know if the ratios are enlargement, reduction or
preservation. Therefore:
1 m : 25 cm = Enlarge</span>
<span>8 in : 12 feet = Reduce
12 in = 1 ft = Preserve</span>
2m = 25/2
m= 25/2 divided by 2
m= 25/4
3m= 25/4 x 3
3m= 75/4
so she does 3 miles in 18 3/4 hours
