All categories

2 years ago

For which function is it true that y →- ∞ as x →∞

Mathematics

2 answers:

nlexa [21]2 years ago

5 0

Answer:

y = -√(x - 6)

Step-by-step explanation:

The first choice on the left

y = -√(x - 6)

The larger x gets

the more negative y becomes

Alecsey [184]2 years ago

4 0

This is not a function because we have an A with many B. It is like saying f (x) = 2 or 4 It fails the "Vertical Line Test" and so is not a function. But is still a valid relationship, so don't get angry with it. It CAN (possibly) have a B with many A. For example sine, cosine, etc are like that. Perfectly valid functions.

You might be interested in

A music buff wants to estimate the percentage of students at a midwestern university who believe that elvis is still alive. how

gulaghasi [49]

Since we are not given any information about the proportion, we will assume the sample proportion to be 0.50

so,
p = 0.50
The Error is 10% percentage point. This means that on either side of the population proportion the error is 5% so E = 0.05
z = 1.645 (Z value for 90% confidence interval)

The margin of error for population proportion is calculated as:

$E=z* \sqrt{ \frac{p(1-p)}{n} } \\ \\ 
 \frac{E}{z} = \sqrt{ \frac{p(1-p)}{n} } \\ \\ 
( \frac{E}{z} )^{2}= \frac{p(1-p)}{n} \\ \\ 
n= p(1-p)* (\frac{z}{E})^{2} \\ \\ 
n=271$

This means 271 students should be included in the sample

5 0

2 years ago

Sally has completed 1/3 of her shift; Jerry has completed 5/6 of his shift; David has finished 1/2 of his shift; Mona has 7/8 of

Step2247 [10]

Sally = 1/3
Jerry = 5/6
David = 1/2
Mona = 1 - 7/8 = 1/8

So, the biggest fraction among them is 5/6.

Jerry has completed the most work time.

3 0

2 years ago

Solve the recurrence relation: hn = 5hn−1 − 6hn−2 − 4hn−3 + 8hn−4 with initial values h0 = 0, h1 = 1, h2 = 1, and h3 = 2 using (

musickatia [10]

(a) Suppose $h_n=r^n$ is a solution for this recurrence, with $r\neq0$ . Then

$r^n=5r^{n-1}-6r^{n-2}-4r^{n-3}+8r^{n-4}$
$\implies1=\dfrac5r-\dfrac6{r^2}-\dfrac4{r^3}+\dfrac8{r^4}$
$\implies r^4-5r^3+6r^2+4r-8=0$
$\implies (r-2)^3(r+1)=0\implies r=2,r=-1$

So we expect a general solution of the form

$h_n=c_1(-1)^n+(c_2+c_3n+c_4n^2)2^n$

With $h_0=0,h_1=1,h_2=1,h_3=2$ , we get four equations in four unknowns:

$\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}$

So the particular solution to the recurrence is

$h_n=-\dfrac8{27}(-1)^n+\left(\dfrac8{27}+\dfrac{7n}{72}-\dfrac{n^2}{24}\right)2^n$

(b) Let $G(x)=\displaystyle\sum_{n\ge0}h_nx^n$ be the generating function for $h_n$ . Multiply both sides of the recurrence by $x^n$ and sum over all $n\ge4$ .

$\displaystyle\sum_{n\ge4}h_nx^n=5\sum_{n\ge4}h_{n-1}x^n-6\sum_{n\ge4}h_{n-2}x^n-4\sum_{n\ge4}h_{n-3}x^n+8\sum_{n\ge4}h_{n-4}x^n$
$\displaystyle\sum_{n\ge4}h_nx^n=5x\sum_{n\ge3}h_nx^n-6x^2\sum_{n\ge2}h_nx^n-4x^3\sum_{n\ge1}h_nx^n+8x^4\sum_{n\ge0}h_nx^n$
$G(x)-h_0-h_1x-h_2x^2-h_3x^3=5x(G(x)-h_0-h_1x-h_2x^2)-6x^2(G(x)-h_0-h_1x)-4x^3(G(x)-h_0)+8x^4G(x)$
$G(x)-x-x^2-2x^3=5x(G(x)-x-x^2)-6x^2(G(x)-x)-4x^3G(x)+8x^4G(x)$
$(1-5x+6x^2+4x^3-8x^4)G(x)=x-4x^2+3x^3$
$G(x)=\dfrac{x-4x^2+3x^3}{1-5x+6x^2+4x^3-8x^4}$
$G(x)=\dfrac{17}{108}\dfrac1{1-2x}+\dfrac29\dfrac1{(1-2x)^2}-\dfrac1{12}\dfrac1{(1-2x)^3}-\dfrac8{27}\dfrac1{1+x}$

From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of $x^n$ , ideally matching the solution found in part (a).

3 0

2 years ago

Can I please get help with this?

mariarad [96]

m<TSU=85°

please see the attached picture for full solution

hope it helps..

Good luck on your assignment...

3 0

2 years ago

At a railway yard, locomotives are used to haul containers carrying oil. A locomotive is chosen according to the volume of oil i

artcher [175]

Volume of cylinder A = π(12^2/4) x (40/2) = 2,262 cubic feet which will be hauled by locomotive BR73.
Volume of cylinder B = π(8^2/4) x 24 = 1,206 cubic feet which will be hauled by locomotive CG35.
Volume of cylinder C = π(16^2/4) x 16 = 3,217 cubic feet which will be hauled by locomotive YH61.
Volume of cylinder D = π(6^2/4) x 12 = 339 cubic feet which will be hauled by locomotive A450.

8 0

2 years ago