Mathematics: Hewwo! In a circle of radius 5 cm , AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords , if they are :i. on the same side of the centreii. on the opposite side of the centre *Show your workings!

Hewwo! In a circle of radius 5 cm , AB and CD are

Tips101

17.04.2021

AB=8cm⇒AE=4cmCD=6m⇒CF=3cmIn△AEDAE=4cm,AO=5cmOE=(AO)2−(AE)2=52−42=3cmIn△OFCCF=3cm,CO=5cmOF=OC2−CF2=52−32=4cm

∴ Distance between the chords=4cm−3cm=1cm

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tumadreeve7852

27.04.2021

$x^{\frac{20}{3}}$ .

Step-by-step explanation:

We are asked to describe how we can transform the given radical expression into an expression with a rational exponent.

Given expression: $(\sqrt[3]{x^4})^5$ .

We will use radical rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$ to solve our given problem.

We can see that for our given expression n=3 , m=4 and a=x .

Now, we can write our given expression as:

$(\sqrt[3]{x^4})^5=(x^{\frac{4}{3}})^5$

Using power rule of exponents $(a^m)^n=a^{m\cdot n}$ , we can write our expression as:

$(x^{\frac{4}{3}})^5=x^{\frac{4}{3}\cdot 5}$

$(x^{\frac{4}{3}})^5=x^{\frac{4\cdot 5}{3}}$

$(x^{\frac{4}{3}})^5=x^{\frac{20}{3}}$

Therefore, the given expression with a rational exponent would be $x^{\frac{20}{3}}$ .

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