Answer:
90°
Step-by-step explanation:
Circle C has radius √36 = 6
Circle D has radius √18 = 3√2
As the D radius intersecting either point of tangency, does so at a right angle.
The half angle θ between the tangents is
sinθ = 3√2 / 6 = ½√2
θ = 45°
so the angle between the tangents is 2(45) = 90°
The total weight of candies is unknown. Let x = the total weight of candies.
"One student ate 3/20 of all candies and another 1.2 lb":
The first student ate (3/20)x plus 1.2 lb which is 0.15x + 1.2.
"The second student ate 3/5 of the candies and the remaining 0.3 lb."
The second student ate (3/5)x and 0.3 lb which is 0.6x + 0.3.
Altogether the 2 students ate 0.15x + 1.2 + 0.6x + 0.3.
That was all the amount of candies, so that sum equals x.
0.15x + 1.2 + 0.6x + 0.3 = x
Now we solve the equation for x to find what the total amount of candies was.
0.75x + 1.5 = x
-0.25x = -1.5
x = 6
The total amount of candies was 6 lb.
The first student ate 0.15x + 1.2 = 0.15(6) + 1.2 = 0.9 + 1.2 = 2.1, or 2.1 lb of candies.
The second student ate 0.6x + 0.3 = 0.6(6) + 0.3 = 3.6 + 0.3 = 3.9, or 3.9 lb of candies.
Answer: The first student ate 2.1 lb of candies, and the second student ate 3.9 lb of candies.
42 - 19 = 23
the difference between 42 and 19 is 23
Answer:
To determine the explicit rule for the arithmetic sequence of 20.5, 16, 11.5, 7, 2.5, ..., the following logical reasoning must be performed:
20.5 - 16 = 4.5
16 - 11.5 = 4.5
11.5 - 7 = 4.5
7 - 2.5 = 4.5
Thus, the explicit rule of the arithmetic sequence is that the numbers are gradually subtracted by 4.5, with which the next number of said sequence would be -2.
