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3 years ago

Simplify (6x2 − 3 + 5x3) − (4x3 − 2x2 − 16). (1 point) a 2x3 − x2 + 21 b −2x3 + x2 − 21 c x3 + 8x2 + 13 d −x3 − 8x2 + 13

Mathematics

2 answers:

tatiyna3 years ago

4 0

Answer:

the answer is C.

Step-by-step explanation:

sattari [20]3 years ago

3 0

$(6x^2-3+5x^3)-(4x^3-2x^2-16)\\\\=6x^2-3+5x^3-4x^3+2x^2+16\qquad\text{combine like terms}\\\\=(5x^3-4x^3)+(6x^2+2x^2)+(-3+16)\\\\=x^3+8x^2+13\to\boxed{c.}$

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Veseljchak [2.6K]

For $x$ between $-\pi$ and $\pi$ , we have

$\cos x=\frac{\sqrt2}2=\frac1{\sqrt2}$ when $x=\pm\frac\pi4$ ;
$\cos x=1$ for $x=0$ ; and
$\cos x=0$ for $x=\pm\frac\pi2$

$\cos x$ is continuous over its domain, so the intermediate value theorem tells us that

$\cos x\ge\frac{\sqrt2}2$

is true for $-\frac\pi4\le x\le\frac\pi4$ .

For all $x$ , we take into account that $\cos x$ is $2\pi$ -periodic, so the above inequality can be expanded to

$-\dfrac\pi4\le x+2n\pi\le\dfrac\pi4$

where $n$ is any integer. Equivalently,

$-\dfrac\pi4-2n\pi\le x\le\dfrac\pi4-2n\pi$

To get the corresponding solution set for

$\cos\left(x+\dfrac\pi3\right)\ge\dfrac{\sqrt2}2$

simply replace $x$ with $x+\frac\pi3$ :

$-\dfrac\pi4-2n\pi\le x+\dfrac\pi3\le\dfrac\pi4-2n\pi$

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2 years ago

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 20%

zhuklara [117]

Answer:

a. 5% of the employees will experience lost-time accidents in both years

b. 24% of the employees will suffer at least one lost-time accident over the two-year period

Step-by-step explanation:

a. What percentage of the employees will experience lost-time accidents in both years?

20% last year, of those who suffered last year, 25% during this year. So

$p = 0.2*0.25 = 0.05$

5% of the employees will experience lost-time accidents in both years.

b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?

5% during the two years.

10% during the current year. 25% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.

So the 10% is composed of 5% during both years(25% of 20%) and 5% of the 80% who did not suffer during the first year.

First year yes, not on the second.

75% of 20%. So, total:

$0.05 + 0.05*0.8 + 0.75*0.2 = 0.24$

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2 years ago