I need help on how to find a dog's average weight.

If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

castortr0y [4]

$6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\\\\=(3x+2)(2x-1)\\\\3x+2=0\to x=-\frac{2}{3}\\\\2x-1=0\to x=\frac{1}{2}\\\\\alpha=-\frac{2}{3};\ \beta=\frac{1}{2}\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{-\frac{2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{-\frac{2}{3}}=-\frac{2}{3}\cdot\frac{2}{1}-\frac{1}{2}\cdot\frac{3}{2}=-\frac{4}{3}-\frac{3}{4}\\\\=-\frac{16}{12}-\frac{9}{12}=-\frac{25}{12}=-2\frac{1}{12}$

$use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2$

$6x^2+x-2\\\\a=6;\ b=1;\ c=-2\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{1^2}{6\cdot(-2)}-2=\frac{1}{-12}-2=-2\frac{1}{12}$

7 0

3 years ago

You have $55,000 in your savings account that pays 2.5% annual interest and the inflation rate is 3.4%. how much buying power in

lianna [129]

Your interest formula is given to you.

Interest in a year = principal (the amount invested) * rate (the interest rate) * period (the time you're measuring) 

Interest = 55,000 * 2% * 1 year = 55,000 * 0.02 * 1 = $1,100 

How much would you need to have made for your spending power to keep with inflation? Your interest rate would have needed to match the inflation rate, otherwise, prices are going up faster than you're saving. 

Required interest = 55,000 * 3.24% * 1 year = 55,000 * 0.0324 * 1 = $1,782 

How much buying power did you lose? The difference between your required interest and your actual interest. 
Buying power lost = 1,782 - 1,100 = $682. You lost this much in buying power.

6 0

3 years ago

Read 2 more answers

Help me with this problem please

gavmur [86]

Answer:

7 yards

Step-by-step explanation:

the absolute value of -2 and 2/3- 51/3 is 7

6 0

3 years ago

What is the answer explained to 6+(-9)-(-5)-(5×0)

Zarrin [17]

Answer:

the answer is 2

Step-by-step explanation:

7 0

3 years ago

(GIVING BRAINLIST) Which form of precipitation would most likely be predicted based on the following information?

Luda [366]

Answer:

Sleet because the temperature in the cloud is below freezing but the temperature beneath the cloud is above freezing

Step-by-step explanation:

8 0

2 years ago