The original number to the nearest tenth is 23.8
A conversion factor is used to change the units of a measured quantity without changing its value. Because of the identity property of multiplication, the value of a number will not change as long as it is multiplied by one.
Step-by-step explanation:
a2 = a1×r
a3 = a1×r²
a1×r + a1×r² = 6×a4 = 6×a1×r³
1.
r + r² = 6r³
6r³ - r² - r = 0
r×(6r² - r - 1) = 0
the first solution is obvious : r = 0.
but this is no useful ratio for a geometric sequence.
the other 2 solutions are in
6r² - r - 1 = 0
the general solutions for a quadratic equation are
(-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 6
b = -1
c = -1
so,
(1 ± sqrt(1 - 4×6×-1))/12
r = (1 ± sqrt(25))/12
r = (1 ± 5)/12
r1 = (1+5)/12 = 6/12 = 1/2
r2 = (1-5)/12 = -4/12 = -1/3
2.
we can ignore r2 (negative) and just focus on r1 (1/2).
the second term is 8. that means
a2 = 8 = a1×r = a1×1/2
a1 = 2×a2 = 16
so, we have
a1 = 16
a2 = 8
a3 = a2×1/2 = 8×1/2 = 4
a4 = a3×1/2 = 4×1/2 = 2
a5 = a4×1/2 = 2×1/2 = 1
a6 = a5×1/2 = 1×1/2 = 1/2
a7 = a6×1/2 = 1/2 × 1/2 = 1/4
Answer:
Step-by-step explanation:
First, find the volume of the half sphere:
Volume of a regular sphere:
Divide 20 by 2, and plug in.
4/3 (3.14) (10)^3 = 4188.79
Then divide by 2, to get the half.
4188.79 / 2 = 2094.39 = 2094
Second, find the volume of the cone:
Volume of a cone:
(Use 10 for the radius as you do above)
(3.14) (10)^2 (24/3) = (3.14) x 100 x 8 = 2513.27
Round: 2513.27 = 2513
Last, add the two volumes:
2094 + 2513 = 4607
Answer:
The group of points that satisfies the equation 3x - 4y < - 4 is {(-4,4), (0,3)}.
Step-by-step explanation:
The first point is (-4,4) and putting those values in the left hand side of the inequality equation, we get,
3(-4) - 4(4) = - 12 - 16 = - 28 < - 4
Now, the second point is (0,3) and putting those values in the left hand side of the inequality equation, we get,
3(0) - 4(3) = - 12 < - 4.
Therefore, the group of points that satisfies the equation 3x - 4y < - 4 is {(-4,4), (0,3)}. (Answer)