100 points for knowing and 100 points for math problems

1.If a car travels 40 kilometers per hour and arrives in 7 hours from A to B, it actually travels 25 percent more per hour than planned, how many hours can it get to B?

Solution: Actual arrival time = (40x7) [40x(1+25%)] = hours.

2.If a cylindrical piece of wood is 60 decimeters long and has a cross-sectional diameter of 4 decimeters, what is the shortest volume if this timber is sawn into three sections at 3:4:5?

Solution: Area of cross-section = square decimeter.

The shortest segment is long = 60x3 (3+4+5) = 15 dm.

Volume = cubic decimeter.

3.A wine bottle is 30 cm deep, the bottom diameter is 10 cm, the wine in the bottle is 15 cm deep, the bottle mouth is plugged tightly and the bottle mouth is turned downward, this is the depth of the wine 25 cm, ask how many cubic centimeters of the wine bottle volume?

Solution: Bottom radius = 10 2 = 5 cm.

Base area = square centimeters.

Volume of wine = cubic centimeters.

Bottle volume = cubic centimeters.

2.Volume v = base area multiplied by height.

2π r²×60×3/(3+4+5)

3.Let the volume be v

The base area is *5 =25

then v=25 *15+25 *5=500

1.Hours: 40*70=2800, i.e. the total distance.

40*(1+i.e. the current speed.)

60*(3 (3+4+5))=15 is the minimum length of the truncated segment.

15* base area multiplied by length equals volume in cubic decimeters.

30-25 = 5 remaining length of empty wine bottles.

5* Remaining volume.

15*5*5*Occupied volume.

Units cubic centimeters.

280 50 = 15 vultures 4 = 600 vultures 25 = 375 vultures 25 vultures 25 = 625 vultures 625 vultures - 375 vultures = 250 vulture 30 vultures 25 = 750 vultures 750 vultures - 250 vultures = 500

Solution: Profit y=px-r

y=(24200-1/5x^2)x-(50000+200x)y=-1/5x^3+24000x-50000y'=-3/5x^2+24000

Lingy'=03/5x^2+24000=0

x^2=24000x5/3

x^2=40000

x=200x<200,y'>0,y increases monotonically; x>200，y'<0,y decreases monotonicallySo, x = 200 tons, and y reaches the maximum.

Maximum profit = -1 5x200 3 + 24000x200-50000 = 3150000 (yuan).

Cost px = (24200-1 5x 2) x = 24200x-1 5x 3 Production cost = 50000 + 200x

Then solve this cubic function.

The production of 200 tons is the most profitable, and the maximum profit is 10,000 yuan.