USE DISTANECE= RATE * TIME
2 answers:
Answer:
1). Anjali's speed on the outbound trip was 5.1 miles per hour.
2). Speed of the boat was 8.2 km per hour.
Step-by-step explanation:
1). Anjali traveled to teh recycling plant in 5.8 hrs and trip back took 5.1 hrs.
Her speed was 7 mph faster on the return trip.
Let her outbound trip speed was = s mph
Then her speed for the return trip will be = (s + 7) mph
Distance traveled to plant = Speed × time
= s×5.8 miles
Distance traveled in the back trip = (s + 7)×5.1 miles
Since distances covered to outbound trip and return trip are same
So, 5.8s = (s + 7)×5.1
5.8 s = 5.1 s + 7×5.1
5.8 s - 5.1 s = 35.7
0.7 s = 35.7
s =
= 5.1 miles per hour
Therefore, Anjali's speed on the outbound trip was 5.1 miles per hour.
2). Let the speed of the ship is s km per hour
Ship traveled for 11 hours so distance covered by the ship = Speed × time = s×11
Since speed of the ship was 12.5 km per hour faster than the boat then
Speed of the boat will be = s - 12.5
Since boat started traveling 0.5 hrs before the ship then total time the boat traveled = 11 + 0.5 = 11.5 hours
Now the distance covered by the boat = (s - 12.5)×11.5
Since distance between the ship and the boat is 322 km so the equation will be
11s + (s - 12.5)11.5 = 322
11s + 11.5s - 12.5×11.5 = 322
22.5s - 143.75 = 322
22.5s = 322 + 143.75
22.5s = 465.75
s =
= 20.7 km per hour
Now the speed of the boat will be = (s - 12.5)
= (20.7 - 12.5)
= 8.2 km per hour
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Answer:
f(x) is increasing in the intervals (-∞,-4) and (9,∞)
f(x) is decreasing in the ingercal (-4,9)
The local extrema is:
local max at (-4,496)
and local min at (9,-1701)
Step-by-step explanation:
In order to solve this problem we must start by finding the derivative of the provided function, which we can find by using the power rule.
if then
so we get:
in order to find the critical points we mus set the derivative equal to zero, since the local max an min will happen when the slope of the tangent line to the given point is zero, so we get:
we can solve this by factoring, so let's factor that equation:
6(x+4)(x-9)=0
we can now set each of the factors equal to zero so we get:
x+4=0 and x-9=0
when solving each for x we get that:
x=-4 and x=9
These are our critical points, now we can build the possible intervals we are going to use to determine where the function will be increasing and where it will be decreasing:
(-∞,-4), (-4,9) and (9,∞)
so now we need to test these intervals in the derivative to see if the graph will be increasing or decreasing in the given intervals. So let's pick x=-5 for the first one, x=0 for the second one and x=10 for the third one.
When evaluating them into the first derivative we get that:
f'(-5)=84, this is a positive answer so it means that the function is increasing in the interval (-∞,--4)
f'(0)=-216, this is a negative anser so it means that the function is decreasing in the interval (-4,9)
f'(10)=84, this is a positive answer so it means that the function is increasing in the interval (9,∞)
Now, for the local extrema, we can see that at x=-4, the function it's increasing on the left of this point while it's decreasing to the right, which means that there will be a local maximum at x=-4, so the local max is the point (-4,496)
We can see that at x=9, the function it's decreasing on the left of this point while it's increasing to the right, which means that there will be a local minimum at x=-9, so the local min is the point (9,-1701)