Step-by-step explanation:
let the speed of diesel train = x
the equation would be:
(2+6)x = 6(x+15)
8x = 6x+90
8x-6x = 90
2x = 90
x = 90/2
x = 45
Therefore, the speed of diesel train =
45 mph
Answer:
60 °
Step-by-step explanation:
Applying the law of sine we have the following:
160 / Sin B = 80 / Sin 30 °
We solve for B and we have:
160 / Sin B = 80 / 0.5
160 / Sin B = 160
Without B = 160/160
B = Arc Sin (1)
B = 90 °
Now to calculate the other angle (true
course) would be:
A = 180 ° - (B + C)
A = 180 ° - (90 ° + 30 °)
A = 60 °
That is to say that true course is 60 °
Notice that
That is, the <em>n</em>-th term (where <em>n</em> = -1, 0, 1, …, 9) in the sum on the left side has a partial fraction decomposition of
and in the sum, some adjacent terms will cancel and leave you with
Now solve for <em>x</em>, bearing in mind that we cannot have <em>x</em> = 0, -1, -2, …, -10 :
Combine the fractions on the left side:
Then we must have
so that either <em>x</em> = 2 or <em>x</em> = -11.
Answer:
A) [First try is correct for all U1 to U4]
Step-by-step explanation:
1. Trying each option
(let x = 1,2,3,4) since it goes from U1 to U4 (Geometric sequence)
A.) 10(-4/5)^x
10(-4/5)^1 = -8
10(-4/5)^2 = 6.4
10(-4/5)^3 = -5.12
10(-4/5)^4 = 4.096
Let the initial width, depth and height of the prism be w, d, and h respectively.
surface area of a rectangular prism is 2(w * d + w * h + d * h).
After quadrupling the dimentions, new dimentions is 4w, 4d and 4h.
New surface area is 2(4w * 4d + 4w * 4h + 4d * 4h) = 2(16 * w * d + 16 * w * h + 16 * d * h) = 16 * 2(w * d + w * h + d * h)
Ratio of old surface area to new surface area is 2(w * d + w * h + d * h) : 16 * 2(w * d + w * h + d * h) = 1 : 16
