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3 years ago

The sum of a number and its reciprocal is 41/20. Find the number. smaller value larger value

Mathematics

1 answer:

Natali [406]3 years ago

6 0

Step-by-step explanation:

Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :

$x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0$

It is a quadratic equation. The values of x are :

$20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}$

The smaller number is 4/5 and the larger number is 5/4.

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Answer: Last Option

$H (m) = 25 + 3m\\H (m) = 10 + 8m$

Step-by-step explanation:

The initial height of the plant of species A is 25 cm and grows 3 centimeters per month.

If m represents the number of months elapsed then the equation for the height of the plant of species A is:

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Finally, the system of equations is:

$H (m) = 25 + 3m\\H (m) = 10 + 8m$

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Apopulation grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.a) Write a function to model the

solong [7]

Answer:

a) $P(t) = 22000(1.071)^{t}$

b) The population increases 7.1% each year.

Step-by-step explanation:

The continuous population growth model is given by:

$P(t) = P_{0}(1+r)^{t}$

In which $P(t)$ is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

In this problem, we have that:

A population grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.

This means that $P_{0} = 22000, r = 0.071$

a) Write a function to model the population increase.

$P(t) = 22000(1 + 0.071)~{t}$

$P(t) = 22000(1.071)^{t}$

b) By what percent does the populaiion increase each year?

$r = 0.071$

So the population increases 7.1% each year.

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3 years ago

Select all of the roots of x3 + 2x2 – 16x– 32.

Luba_88 [7]

Answer:

-2, -4, 4

Step-by-step explanation:

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