A passenger car and a freight car leave each other from a and B. when the passenger car runs 2 / 5 of the whole journey and the freight car runs 1 / 3 of the whole journey, the distance between the two cars is 60 km How many kilometers are the two places apart

A passenger car and a freight car leave each other from a and B. when the passenger car runs 2 / 5 of the whole journey and the freight car runs 1 / 3 of the whole journey, the distance between the two cars is 60 km How many kilometers are the two places apart

Party A and Party B have walked 1 / 3 + 2 / 5 = 11 / 15
The remaining 1-11 / 15 = 4 / 15
The distance between a and B is 60 / (4 / 15) = 225 km

Given four points a (1,1,1), B (- 4,0,2) C (- 3, - 1,0) d (- 1,0,4) in space, then the angle between the line AD and the plane ABC is

Because AB = (- 5, - 1,1), AC = (- 4, - 2, - 1),
Therefore, the normal vector of plane ABC is n = ab × AC = (3, - 9,6), | n | = √ (9 + 81 + 36) = 3 √ 14,
And ad = (- 2, - 1,3), | ad | = √ (4 + 1 + 9) = √ 14,
So cos = ad * n / (|n | * |ad |) = (- 6 + 9 + 18) / (3 * 14) = 1 / 2,
So, = π / 3,
Then the angle between AD and plane ABC is π / 2 - π / 3 = π / 6

(2012 · Bazhou city simulation) the two engineering teams a and B built a total of 360 meters of roads. The length ratio of the two teams was 5:4. How many meters did team a repair more than team B?

A: team a repaired 40 meters more than team B

For a class of natural numbers, the sum of their digits is 200. Then, what is the smallest one of these natural numbers?
It's the sum of the numbers in the children's palace
Need process!

Because the quotient of 200 / 9 is more than 2, if you want to minimize this number, you need to use 9 as far as possible, that is 22 9s, and there are only 2 left in front. The result is 299 9 (22 9s in total)

The bus and the minibus start from city a to city B at the same time. The bus runs 90 kilometers per hour. The car runs 60 kilometers in the first hour, and then increases 5 kilometers per hour. Does it take () hours for the car to catch up with the bus?
We need formula and explanation

(30 / 5) * 2 + 1 = 13 hours
Explain that in the first hour, the bus is 30 kilometers faster than the car. Because the car increases by 5 kilometers per hour, when the speed of the two cars is equal at (30 / 5) + 1 = 7 hours, the speed of the bus is 30 kilometers faster than the bus after another 30 / 5 = 6 hours, so the car needs (13) hours to catch up with the bus

In △ ABC, ab = 3, AC = 4, ∠ a = 90 ° rotate RT △ ABC around the straight line AC to get a cone with a total area of_____

In RT △ ABC, from Pythagorean theorem: BC = 5;
The base radius of the cone is ab = 3, the perimeter is 3 × 2 × π = 6 π, and the base area is 3 × 3 × π = 9 π;
The radius of the expanded side view of the cone is BC = 5, the arc length is 6 π of the bottom circumference, and the center angle is 6 π △ 5 = (6 / 5) π = 216 °;
The side area of the cone is 5 × 5 × π × (216 / 360) = 15 π;
The total area of the cone is 9 π + 15 π = 24 π

Trucks travel 45 kilometers per hour, and cars travel 1.4 times as fast as trucks. They start from two places 162 kilometers apart at the same time and face each other. If they start at 8:15, when do they meet?

162 △ (45 + 45 × 1.4), = 162 ^ (45 + 63), = 162 ^ 108, = 1.5, 1.5 = 1:30, 8:15 + 1:30 = 9:45, a: it's 9:45 when we meet

Calculation: (4a ^ 2-9b ^ 2) divided by (2a + 3b)

When a batch of goods is to be transported to a certain place, the owner of the goods is going to rent two kinds of trucks from the automobile transportation company. The situation of renting these two kinds of trucks in the past is shown in the table below: the number of trucks of the first time and the second time 2 5 the number of trucks of the second time 3 6 the accumulated tonnage of goods transported 20.546 (1) how many tons of goods are transported by the trucks of the first time and the second time? (2) Now we hire three A-type trucks and five B-type trucks from the company. We have just finished the goods at one time. If the freight is 30 yuan per ton, how much is the freight payable by the owner?

(1) Suppose that each load of a truck is x tons, and each load of B truck is y tons, then 2x + 3Y = 20.55x + 6y = 46, and the solution is x = 5Y = 3.5. Answer: each load of a truck is 5 tons, and each load of B truck is 3.5 tons. (2) 5 × 3 + 3.5 × 5 = 32.5 (tons), 32.5 × 30 = 975 (yuan). Answer: the freight owner should pay 975 yuan

Given that the circle passes through two points a (3,1) B (- 1,3), and its center is on the straight line 3x-y-2 = 0, the equation of the circle is obtained

Let the center of the circle be (x, y),
The distance from the center of a circle to two points is equal
(x-3)^2+（y-1）^2=(x+1)^2+(y-3)^2
The center of the circle is 3x-y-2 = 0, y = 3x-2,
Substituting into the equation, x = 2, y = 4, R ^ 2 = (2-3) ^ 2 + (4-1) ^ 2 = 10
So the circular equation is (X-2) ^ 2 + (y-4) ^ 2 = 10