Answer:
Let the train's speed be denoted as x km/h.
Scenario 1:
Distance = 288 km
Speed = x km/h
Time = Distance divided by Speed
= 288/x hours
Scenario 2:
Distance = 288 km
Speed = (x + 4) km/h
Time = 288/(x + 4) hours
As 288/x is greater than 288/(x + 4)
288/x - 288/(x + 4) = 1
288[1/x - 1/(x + 4)] = 1
[x + 4 - x] / [x(x + 4)] = 1/288
[4 / (x^2 + 4x)] = 1/288
x² + 4x = 1152
x² + 4x - 1152 = 0
x² + 36x - 32x - 1152 = 0
x(x + 36) - 32(x + 36) = 0
(x + 36)(x - 32) = 0
x + 36 = 0, x - 32 = 0
x = -36, x = 32
x = -36 is not valid as speed cannot be negative.
Conclusively, the train's speed = 32 km/h
Answer:
24 minutes
Step-by-step explanation:
Let y represent the rate of 120 envelopes per minute.
40/8 = 120/y
40y = 8 * 120
40y = 960
y = 960/40
= 24 minutes
To find the value of z in triangle XYZ, we can utilize the law of sines. We know the following:
1. The measure of angle XYZ is 51 degrees.
2. The measure of angle YZX is 76 degrees.
3. The length of side XZ is 2.6 units.
From these angles, angle XZY can be calculated, and then we can apply the law of sines to determine z.
Thus, we proceed to solve for z using the sine relationship in the triangle.
We will round the result to one decimal place.
In this scenario, we have a function of the following form: A: initial amount, b: rate of decrease, x: time in years. Plugging in the values results in an exponential decay function suitable for this situation: y = 1300 * (0.97) ^ x. The estimated fish population in 2010 is then calculated to be approximately 1083.
