1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Igoryamba
3 years ago
15

Harmonic mean if a number h such that (h-a)/(b-h)=a/b Prove h is H(a,b) iff satisfies either relation a. (1/a)-(1/h) = (1/h) - (

1/b) b. h = (2ab)/(a+b)
Mathematics
1 answer:
Fudgin [204]3 years ago
7 0
A.

\displaystyle\frac1a-\frac1h=\frac1h-\frac1b
\implies\displaystyle\frac{h-a}{ah}=\frac{b-h}{bh}
\implies\displaystyle\frac{h-a}{b-h}=\frac{ah}{bh}
\implies\displaystyle\frac{h-a}{b-h}=\frac ab

b.

\displaystyle h=\frac{2ab}{a+b}
\displaystyle\implies\frac{h-a}{b-h}=\frac{\frac{2ab}{a+b}-a}{b-\frac{2ab}{a+b}}
\displaystyle\implies\frac{h-a}{b-h}=\frac{2ab-a(a+b)}{b(a+b)-2ab}
\displaystyle\implies\frac{h-a}{b-h}=\frac{ab-a^2}{b^2-ab}
\displaystyle\implies\frac{h-a}{b-h}=\frac{a(b-a)}{b(b-a)}
\displaystyle\implies\frac{h-a}{b-h}=\frac ab

The other direction can be proved by following the manipulations in the reverse order.
You might be interested in
X^2+17x=-42 <br> how do i find the solutions to this problem?
ELEN [110]

photo math duhhhhhhhhhhhhhhhhhhhh

3 0
3 years ago
What is the length of the diagonal of a rectangle that is 12 inches long and 6 inches wide?​
lakkis [162]
To find the diagonal of the rectangle we have to use Pythagorean theorem!

Pythagorean theorem is used to find the length of a missing angle such as the hypotenuse or the sides a and b.

Steps to solve:

1. 12 in is the length or the base of the right triangle, and 6 in is the wide or the side a.
2. Now use the formula: a^2+b^2=c^2, and plug in the numbers!
3. 6^2+12^2=c^2, now just solve the squared numbers.
4. 36+144=c^2
5. 180=c^2
6. Find the square root of 180.

And that is you answer!
If helped mark me the brainiest!!
4 0
3 years ago
martin pidio 1/8 de kg de clavos de 1/2 pulgada si la bascula es digital y pesa en kilogramos ¿cuantos tienes q marcar en este c
love history [14]

Martin will have to mark 0.125 on the

Let the original weight of the scale be 1kg. Hence we can say the original mark for 1kg weight is 1 that is:

1kg = 1 ................ 1

Since we are to calculate where to mark for a 1/8 kg weight, we can write;

1/8 kg = x  ..................2

Divide both expressions

\frac{1}{1/8}= \frac{1}{x}\\\\Cross \ multiply\\8= \frac{1}{x} \\x =  \frac{1}{8}

This means Martin will have to mark 0.125 on the scale.

Learn more here: https://brainly.lat/tarea/13002863

3 0
3 years ago
What is the value of (gof)(4)?
Alinara [238K]
I hope this helps you

7 0
3 years ago
Read 2 more answers
Alma wants to buy socks. She has $11.00 and the socks cost $3.00 per pair. How many pairs of socks can Alma buy? How much money
Llana [10]

Answer:

She can buy 3 pairs for $9.00 with $2.00 extra.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • each cub inside the rectangular prism has an edge length of 3/4 inch. what is the volume of the rectangular
    15·1 answer
  • PLEASE HELP<br> Simplify the expression<br><br> x^2 + 3x - 28/ x^2 - 7x + 12<br><br> Show your work.
    9·1 answer
  • I need help with how to find 2 equations for thy problem
    5·1 answer
  • State whether the equation represents exponential growth, exponential decay, or neither. y=2*0.68^x
    8·2 answers
  • If two angles are right angles, then they are supplementary angles.
    11·2 answers
  • 4÷5 = 12 divided by how much
    8·2 answers
  • Mrs. Miller sells a house for $179,000. If she earns a commission of 6%, how much money does she earn? Write a proportion and sh
    10·2 answers
  • Clare estimates that her brother is 4 feet tall. When they get measured at the doctor’s office, her brother’s height is 4 feet,
    10·1 answer
  • PLEASE HELP ME I NEED THIS IN LIKE 10 MINUTES!!!!!
    7·2 answers
  • Pleas I really need help with this all I need is the answer
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!