Mathematics, 24.11.2019 22:31 kobiemajak

Yis inversely proportional to the square of x.
a table of values for x and y is shown.

a) express y in terms of x.
b) work out the positive value of x when y = 25

Yis inversely proportional to the square of x. a table of values for x and y is shown.

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Answer from: chasadyyy

To find the value of and we have to find the proportionality constant. The y in terms of x is $y=\frac{2}{\sqrt{x}}$ and positive value of $x=\frac{2}{5}$ .

Given:

From the given problem y is inversely proportional to the square of x.

A table of values for x and y is shown.

From the table:

(a) As we know that, y is inversely proportional to the square of x,

Here k is proportionality constant.

$y\propto\frac{1}{\sqrt{x}}$

Then, $1\times \sqrt4 =2\times \sqrt{1}=2=k$

Therefore, y in terms of x is $y=\frac{2}{\sqrt{x}}$ .

(b) we have an expression of $y=\frac{2}{\sqrt{x}}$

Putting the value of y=25 , we get:

$25=\frac{4}{{x^2}}\\x^2=\frac{4}{25}\\\\x=\sqrt{\frac{4}{25}}\\x=\frac{2}{5}$

Therefore, the positive value of $x=\frac{2}{5}$ .

Learn more about Proportion and ratio here:

link

Answer from: babas97

a) $y=\frac{K}{x^{2} }$ b) $x=\frac{2}{5}$

Step-by-step explanation:

If is inversely propotional to the square of , then the relation would be like

$y=\frac{K}{x^{2} }$

Where is the constant of propotionality.

Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use (1,4)

$y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4$

Replacing this constant, the expression between variables is

$y=\frac{4}{x^{2} }$

Which is the answer to a).

Now, if y=25 the value of would be

$y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}$

Therefore, the answer to b) is $x=\frac{2}{5}$

Answer from: Quest

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

$3x-6$

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

$3x-6=0$

$3x=6$

$x=\frac{6}{3}=2$

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

Answer from: Quest

answer: i could not see part the question so ill explain how to get the answer

step-by-step explanation: for instance the distance she travele d is 10 and she traveled the same amout each mile so do 10 divided by how many miles she drove each time and you ge your answer.

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Yis inversely proportional to the square of x.
a table of values for x and y is shown.

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