Solve the equation

banganX
2021-02-11
Answered

Solve the equation

You can still ask an expert for help

Clelioo

Answered 2021-02-12
Author has **88** answers

To simplify a rational expression with a root in the denominator, we need to multiply the numerator and denominator by the root.

To simplify

Using the property

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Adding Decimals with Different signs. In January, the weight of a lion at a zoo changed by 1.8 pounds. In February, its weight changed by -2.3 pounds. What was the overall increase or decrease in the lion's weight?

asked 2022-06-01

Let $A=\{(x,y):x\in \mathbb{Q},y\in \mathbb{R}\}$. Show that $m(A)=0$.

We notice that $A=\mathbb{Q}\times \mathbb{R}$. Now since $\mathbb{Q}$ is countable we can denote it as $\{{x}_{1},{x}_{2},\dots \}$. Now consider the intervals $\{({x}_{n}-\frac{\epsilon}{{2}^{k}},{x}_{n}+\frac{\epsilon}{{2}^{k}})\times (k-1,k+1)\}.$

I can show that the sum of the lengths of these intervals is zero as

$\ell ({I}_{k})=\frac{4\epsilon}{{2}^{k}}$

so

$\sum _{k=1}^{\mathrm{\infty}}\ell ({I}_{k})=4\epsilon $

but I don't know how can I show that the intervals cover $\mathbb{Q}\times \mathbb{R}?$?

We notice that $A=\mathbb{Q}\times \mathbb{R}$. Now since $\mathbb{Q}$ is countable we can denote it as $\{{x}_{1},{x}_{2},\dots \}$. Now consider the intervals $\{({x}_{n}-\frac{\epsilon}{{2}^{k}},{x}_{n}+\frac{\epsilon}{{2}^{k}})\times (k-1,k+1)\}.$

I can show that the sum of the lengths of these intervals is zero as

$\ell ({I}_{k})=\frac{4\epsilon}{{2}^{k}}$

so

$\sum _{k=1}^{\mathrm{\infty}}\ell ({I}_{k})=4\epsilon $

but I don't know how can I show that the intervals cover $\mathbb{Q}\times \mathbb{R}?$?

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In a poker hand consisting of 5 cards, find the probability of holding 4 hearts and 1 club.

asked 2022-07-07

Tricky inequality no avail to AM-GM

Let $a,b,c$ be 3 distinct positive real numbers such that abc = 1. Prove that

$\frac{{a}^{3}}{(a-b)(a-c)}\text{}+\frac{{b}^{3}}{(b-c)(b-a)}\text{}+\text{}\frac{{c}^{3}}{(c-a)(c-b)}\text{}\ge 3$

I tried AM-GM in many different ways, but it doesn't work since one of the terms on the LHS inevitably becomes negative. Any help is greatly appreciated.

Let $a,b,c$ be 3 distinct positive real numbers such that abc = 1. Prove that

$\frac{{a}^{3}}{(a-b)(a-c)}\text{}+\frac{{b}^{3}}{(b-c)(b-a)}\text{}+\text{}\frac{{c}^{3}}{(c-a)(c-b)}\text{}\ge 3$

I tried AM-GM in many different ways, but it doesn't work since one of the terms on the LHS inevitably becomes negative. Any help is greatly appreciated.

asked 2021-10-15

Find

asked 2021-11-18

In the following exercises, solve the equation by clearing the fractions.

$\frac{13}{30}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\frac{25}{42}$

asked 2022-02-10

If x and y are in the ratio 3 to 4, and y and z are in the ratio 3 to 4 then what is the ratio of x to z?