See harmonics

It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.

Result

Yes

No

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Roots
   Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
2. Seats
   Seats in the sport hall are organized so that each subsequent row has five more seats. First has 10 seats. How many seats are: a) in the eighth row b) in the eighteenth row
3. Median and modus
   Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
4. Sequence
   Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
5. Harmonic and arithmetic means
   The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calculat
6. Carpenters
   Carpenters 1 and 2 spend 10 days and 5 days respectively to make one table. If 50 tables were made by the first carpenter and 30 tables were made by the second carpenter, What is the average time spent on the products?
7. Roof
   Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
8. Trapezoid IV
   In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
9. Theorem prove
   We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
10. Calculation of CN
    Calculate: ?
11. Trinity
    How many different triads can be selected from the group 43 students?
12. 75th percentile (quartille Q3)
    Find 75th percentile for 30,42,42,46,46,46,50,50,54
13. Geometric progression 2
    There is geometric sequence with a₁=5.7 and quotient q=-2.5. Calculate a₁₇.
14. Median
    The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.
15. Quadratic equation
    Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
16. Discriminant
    Determine the discriminant of the equation: ?
17. Fish tank
    A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?