iL(6s-4)/((s-2)^(2) +16)

2022-03-24

iL(6s-4)/((s-2)^(2) +16)

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asked 2022-04-02

Equation of the line tangent to $\left\{\begin{array}{l}y={x}^{2}\\ {z}^{2}=16-y\end{array}\right.$, at the point (4,16,0) ?

a) $\left\{\begin{array}{l}4x=y\\ z=0\end{array}\right.$

b)$\left\{\begin{array}{l}x=4\\ y=16\end{array}\right.$

c)$\left\{\begin{array}{l}y-x=12\\ z=0\end{array}\right.$

d)$\left\{\begin{array}{l}x+y=20\\ z=0\end{array}\right.$

asked 2022-03-24

asked 2022-03-27

Definition of polynomial ring

Given a ring R, the polynomial ring is defined as

$R\left[x\right]\phantom{\rule{0.222em}{0ex}}=\{\sum _{k=0}^{n}{a}_{k}{x}^{k}:n\ge 0,\text{}{a}_{k}\in R\text{}\text{for}\text{}k\in \{0,1,\cdots ,n\}\}.$

However, it is not usually specified what x is. In order for multiplication to make sense, I guess it has to be an element in R at least. But is R[x] the set of all functions $P:R\to R,\text{given by}\text{}x\mapsto \sum _{k=0}^{n}{a}_{k}{x}^{k}$, or the set of those functions evaluated at x?

Sometimes R is required to be commutative. Does that make any difference for R[x]?

asked 2022-05-14

A partly filled barrel 300 lb water and 100 lb of ice at 32ºF. How many pounds of steam at 212ºF must be run into the barrel to bring its contents up to 80ºF?

asked 2022-04-09

A population of values has a normal distribution with μ=121.3$\mu =121.3$ and σ=5.8$\sigma =5.8$. You intend to draw a random sample of size n=149$n=149$.

Find the probability that a single randomly selected value is between 119.8 and 121.2.*P*(119.8 < *X* < 121.2)

Find the probability that a sample of size n=149$n=149$ is randomly selected with a mean between 119.8 and 121.2.*P*(119.8 < *M* < 121.2)

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact *z*-scores or *z*-scores rounded to 3 decimal places are accepted.

asked 2022-03-23

Let L : P2 $\to $ P3 be a linear transformation for which we

know that L(1) = 1, L(t) = t 2, L(t 2) = t 3 + t.

(a) Find L(2t 2 - 5t + 3). (b) Find L(at 2 + bt + c).

asked 2022-04-09

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 121.1-cm and a standard deviation of 2.2-cm. For shipment, 26 steel rods are bundled together.

Find *P*91, which is the average length separating the smallest 91% bundles from the largest 9% bundles.*P*91 = -cm

Enter your answer as a number accurate to 2 decimal place. Answers obtained using exact *z*-scores or *z*-scores rounded to 3 decimal places are accepted.