Math problems for the first grade of junior high school, math problems for the first to junior high

Solution: Because, the minute hand travels 360 60 = 6° in one minute, the hour hand travels 360 (12*60)= in one minute, and the hour hand travels 360 12 = 30° in one hour.

Let the current time be 1 o'clock x minutes, at which point the hour and minute hands on the clock are at an angle of 0° (together).

i.e. (1*30°+x*, then x=60 11 is 1:60 11 minutes.

Let the current time be 2 o'clock x minutes, at this moment, the angle between the hour and minute hands on the clock is 0°, that is, (2*30°+x* then x=2*60 11 is 1:120 11 minutes.

In the same way, at n o'clock N*60 11 minutes, the angle between the hour hand and the minute hand on the clock is 0°, and for 24 hours, then at > 12 o'clock n, and at N:00 (n-12)*60 11 minutes, the angle between the hour hand and the minute hand on the clock is 0°

Let the current time be 1 o'clock x minutes, at which point the hour and minute hands on the clock are at an angle of 0° (together).

i.e. (1*30°+x*, then x=60 11 is 1:60 11 minutes.

Let the current time be 2 o'clock x minutes, at this moment, the angle between the hour and minute hands on the clock is 0°, that is, (2*30°+x* then x=2*60 11 is 1:120 11 minutes.

Use angular velocity to set the equation.

Angular velocity here we use the number of degrees per revolution per minute.

The minute hand moves 360 = 6° in one minute

The hour hand moves 360 (12*60)=

The minute hand and the hour hand coincide, and the minute hand must have traveled 360° more integer multiples. Hence the results.

The time elapsed at the time of coincidence is x minutes.

6° = 360°* m

m can be solved.

Let n points and x points coincide.

then x=5(n+x 60) is counted as 60 parts per circle.

x=(60/11)*n

1.Let the purchase price of A be $x and the purchase price of B be $y, then.

3600/x+3600/y=750,7200*2/3)/x+(7200*1/3)/y=750-50

x=12, y=8

Therefore, the purchase price of commodity A is 12 yuan, and the purchase price of commodity B is 8 yuan; The selling price of commodity A is 12 * (1 + 20%) = yuan, and the selling price of commodity B is 8 * (1 + 25%) = 10 yuan.

2.Because the profitability of commodity B is 25%, which is higher than the profitability of commodity A (20%), you should buy 600 pieces of commodity B first, and then buy commodity A with the remaining money, so that you can get the maximum profit. The maximum profit is 600*(10-8)+[7200-600*8) 12]*(yuan.

If the daily electricity consumption of the room is constant, then.

Guest A: 11 + 2*20 = 51 half-daysGuest B: 11 half-days.

Tenant A should pay: 104*51 62 = Tenant B should pay: 104*11 62 = If the electricity consumption is the same per person per day. So.

Guest A: 31 days.

Tenant B: 11 days.

Tenant A should pay: 104*31 42 = Tenant B should pay: 104*11 42 = -

Think critically: The respective reasonable expenses should be somewhere between the above two fees. If the electricity consumption is dominated by a single air conditioner and a single refrigerator, which is more suitable for the southern summer, then the first situation is closer.

If the electricity consumption is mainly electric stoves, heating lamps, and table lamps, and gas is used for the second situation, such as winter.

The daily electricity bill is 104 31=, 104-67) 2=, then tenant A should pay 67+, and tenant B should pay: yuan.

Electricity bills are generated on an average basis on a daily basis. In other words, the electricity cost incurred every day is fixed and does not change.

Then, A stayed for 31 days and B for 11 days, for a total of 42 days. 42 accommodation days incurred 104 yuan in electricity bills.

Then A's shared cost = 104 * 31 42 = yuan.

B's shared electricity cost = 104 * 11 42 = yuan.

Suppose that the electricity used by A and B every day is constant and the same. The daily electricity cost is expressed by the letter t (yuan).

Then A should bear 30t (yuan) for electricityB should bear 10t (yuan) for electricitythen 30t+10t 104

40t＝104

t then A bears $30).

B bears $10).