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2 years ago

Can I plz get some help on this I haven't had time to do this and im confused on this

Mathematics

1 answer:

kolezko [41]2 years ago

5 0

Answer:

What are you confused about?

Step-by-step explanation:

You might be interested in

rosa quilts a square rug that has an area of 400 square inches. what is the length of each side of the rug?

OLga [1]

A = L * L

400 = L²

√L² = √400

L = 20

The lenght of each side is 20

3 0

3 years ago

Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet

frosja888 [35]

There seems to be one character missing. But I gather that f(x) needs to satisfy

• $x^3$ divides $f(x)$

• $(x-1)^3$ divides $f(x)^2$

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

$f(x) = x^5 + \cdots$

Since $x^3$ divides $f(x)$ , and

$f(x) = x^3 p(x)$

where $p(x)$ is degree-2, and we can write it as

$f(x)=x^3 (x^2+ax+b)$

Now, we have

$f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2$

so if $(x - 1)^3$ divides $f(x)^2$ , then $p(x)$ is degree-2, so $p(x)^2$ is degree-4, and we can write

$p(x)^2 = (x-1)^3 q(x)$

where $q(x)$ is degree-1.

Expanding the left side gives

$p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2$

and dividing by $(x-1)^3$ leaves no remainder. If we actually compute the quotient, we wind up with

$\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}$

If the remainder is supposed to be zero, then

$\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}$

Adding these equations together and grouping terms, we get

$(a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1$

Then $b=-1-a$ , and you can solve for a and b by substituting this into any of the three equations above. For instance,

$2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1$

So, we end up with

$p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}$

6 0

2 years ago

Convert0.9285714 into a fraction

jenyasd209 [6]

0.9285714 has 7 digits after the decimal sign. So it is equivalent to the fraction with a numerator 9285714 and a denominator 10000000

$\bf{0.9285714=\dfrac{9285714}{10000000},reduced \ by \ 2 \ : \dfrac{4642857 }{5000000} }$

Result:

The decimal number 0.9285714 is equivalent to the fraction

4642857 / 5000000

$\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}$

8 0

1 year ago

PLEASE HELP NEED THIS DONE.

Mandarinka [93]

A.40,48 is the right answer

7 0

3 years ago

Read 2 more answers

74% of freshmen entering public high schools in 2006 graduated with their class in 2010. A random sample of 81 freshmen is selec

Assoli18 [71]

Answer: Probability that the proportion of students who graduated is greater than 0.743 is P = 0.4755

Step-by-step explanation:

Given that,

Probability of freshmen entering public high schools in 2006 graduated with their class in 2010, p = 0.74

Random sample of freshman, n = 81

Utilizing central limit theorem,

$P(\hat{p}$

So,

$(P(\hat{p}>0.743) = P(Z>0.743 - \frac{0.74}{\sqrt{\frac{0.74(1-0.74)}{81} } } )$

= P( Z > 0.0616)

= 0.4755 ⇒ probability that the proportion of students who graduated is greater than 0.743.

7 0

3 years ago