Answer:
1) Rizza's average speed is 27 km/h.
2) The distance between Barretto and Pampanga is 294 km.
3) Aaron's journey was 3.5 hours long.
Step-by-step explanation:
1) Time taken to cove the distance = 20 minutes
60 minutes = 1 hour
So that, 20 minutes = 
hours
= 
hours
Distance covered = 9 km
But,
speed = 
Rizza's average speed = 9 ÷
= 9 x 3
= 27 km/h
Rizza's average speed is 27 km/h.
2) Time taken = 3.5 h
the car's average speed = 84 km/h
Distance between Barretto and Pampanga = average speed x time taken
= 84 km/h x 3.5 h
= 294 km
The distance between Baretto and Pampanga is 294 km.
3) The uniform speed implies that Aaron did not accelerate during his journey.
Distance covered = 210 km
uniform speed = 60 km/h
time taken = 
= 
= 3.5 hours
Aaron's journey was 3.5 hours long.
Step-by-step explanation:
its y-(-6)= 3 over 2(x-(-1))
If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.
We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.
Therefore the box has length and breadth as 4 ft each and a height of 2 ft.
Answer:
0.355
Step-by-step explanation:
I used units that are familiar to me.
perhaps you know a quart is about a liter?
a quart is 32 oz
so 12 ox = 12/32 = 3/8 of a quart or liter
= .325 quart
which is not greatly different from .355 liter
Answer:
There will be 22.5 grams left after 32 hours.
Step-by-step explanation:
A half-life is how long it takes for half of the amount to go away. In this case, we see that we have two half-life periods worth, which you can determine by dividing the total time by the half-life time.
32hrs/8hrs = 4 half lives.
Now we can raise 1/2 to the power of how many half lives we have (2). Then we multiply that by the amount in the sample.
(1/2)^4 * 360
1/16 * 360
22.5 grams
And this is an exponential function.
