The sum of 2 number is 8 .the sum of its resiprocal is 1/4 find the numbers

5 and 20

Step-by-step explanation:

Let one of the numbers be x, and let the other number be y.

Since the sum of the two numbers is 25, we can write the following equation:  

x + y = 25

Since the sum of their multiplicative inverses (reciprocals) is 1/4, we can also write this equation:  

1/x + 1/y = 1/4

Since we have two equations in two unknowns, we can solve for x and y. We will use the substitution method to solve these two simultaneous equations.

Using the first equation, we’ll solve for y in terms of x:

y = 25 ‒ x.  

Now, substituting this result into the second equation, we get:

1/x + 1/(25 ‒ x) = 1/4. For this fractional equation, we can see by inspection that the lowest or least common denominator (LCD) is the product of all the different, individual denominators, i.e., 4(x)(25 ‒ x). Now, multiplying both sides of the fractional equation by the LCD in order to clear the equation of fractions, we get:

4(x)(25 ‒ x)[1/x + 1/(25 ‒ x)] = (1/4)[4(x)(25 ‒ x)]

4(x)(25 ‒ x)(1/x) + 4(x)(25 ‒ x)[1/(25 ‒ x)] = (1/4)[4(x)(25 ‒ x)]

4(x)(1/x)(25‒x) +4(x){(25 ‒ x)[1/(25 ‒ x)]}= x[(1/4)(4)](25‒x)]

4(1)(25‒x) + 4(x){1} = x[(1)](25‒x)]

4(25‒x) + 4x = x(25‒x)

100 ‒ 4x + 4x = 25x ‒ x²

100 + (4 ‒ 4)x = 25x ‒ x²

100 + (0)x = 25x ‒ x²

100 = 25x ‒ x²

Transposing everything to the left side of the equation, we get:

x² ‒ 25x + 100 = 0

Now, we conveniently have a quadratic equation in standard form, i.e., ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.

By inspection, we see that we can easily solve this quadratic equation by factoring:

(x ‒ 5)(x ‒ 20) = 0

We know from a property of equality that the product ab = 0 if and only if a = 0 or b = 0; therefore, we can continue with our search for the solution to this problem by writing the following two equations and then solving for x for each:

x ‒ 5 = 0 or x ‒ 20 = 0

x ‒ 5 + 5 = 0 + 5 or x ‒ 20 + 20 = 0 + 20

x = 5 or x = 20

Now, solving for the other number y by substituting these two values for x as follows:

For x = 5:  

y = 25 ‒ x  

= 25 ‒ 5  

y = 20

For x = 20:

y = 25 ‒ x

= 25 ‒ 20

= 5

We see that y equals the same two numbers as x, but in reverse order from x! So, in terms of x and y, we have two solutions: x = 5, y = 20 and x = 20, y = 5.

CHECK:

For x = 5 and y = 20:

x + y = 25  

5 + 20 = 25  

25 = 25  

1/x + 1/y = 1/4

1/5 + 1/20 = 1/4

4/20 + 1/20 = 1/4

5/20 = 1/4

1/4 = 1/4

CHECK:

For x = 20 and y = 5:

x + y = 25  

20 + 5 = 25  

25 = 25  

1/x + 1/y = 1/4

1/20 + 1/5 = ¼

1/20 + 4/20 = 1/4

5/20 = 1/4

1/4 = 1/4

CONCLUSION: In reality, as we can see, there is really just one pair of numbers, regardless of with which variable, x or y, that each number in the pair is associated with, that satisfies the original conditions set forth by this problem; Those two numbers are, to answer the original question: “What are the two numbers?” : 5 and 20.

answer: 4 meters

step-by-step explanation: to you understand 2/3 better you can do 1 divided by 3 = . then multiply that by the 2 which is .66666666666666667 then you would do 6 x .66666666666666667 which is 4.      

hope this .

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !