Answer:
<em>The train must travel at 50 km/hr to make it on time.</em>
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Step-by-step explanation:
distance to be covered = 55 km
time to cover this distance = 1 hr 20 min
1 hr 20 min = 1.33 hrs (20 min = 20/60 hrs = 0.33 hrs)
The train travels the first 30 km distance at a speed of 36 km/hr
and we know that time taken = distance/speed
therefore the time taken to run this 30 km will be
time = 30/36 = 0.83 hr
The train still has 55 - 30 = 25 km to cover,
and the time left is 1.33 - 0.83 = 0.5 hrs left
to make it on time, the train must travel at
speed = distance/time = 25/0.5 = <em>50 km/hr</em>
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
Answer: -5
Step-by-step explanation:
13-4(2) / 2(2)^2-7(2)+5
5 / -1
Answer:
10 cups of sugar are required in order to make cookies
