Ask question

Ask question

All categories

Makovka662 [10]

2 years ago

8

The soot produced by a garbage incinerator spreads out in a circular pattern. The depth, H(r), in millimeters, of the soot depos

ited each month at a distance r kilometers from the incinerator is given by H(r)=0.113e−2.1r.

1 answer:

Anon25 [30]2 years ago

4 0

Answer:

Step-by-step explanation:

Check attachment for solution

You might be interested in

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

Which Expression can be used to solve 3/5÷7/10A. 5/3*7/10B. 5/3*10/7C. 3/5*10/7D. 3/5*7/10

Harrizon [31]

Which Expression can be used to solve 3/5÷7/10

A. 5/3*7/10

B. 5/3*10/7

C. 3/5*10/7

D. 3/5*7/10

This expression 3/5÷7/10 means

An option to solve the expression is inverting the fraction that is dividing and going to multiply

3/5 x 10/7 C.

________________-

Verification

A and D are the same

6 0

6 months ago

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would c

lara [203]

<span>$408.04 is the answers'
hope it helped!</span>

4 0

3 years ago

Read 2 more answers

What is 7/10 + 7/10 =

Nonamiya [84]

The correct answer is 1.4 or 1 4/10

I did this by turning 7/10 into a decimal which is 0.7.

Now I just add 0.7 + 0.7.

For that equation i got 1.4

This would equal 1 4/10

3 0

2 years ago

Read 2 more answers

Combine like terms in the expression below:<br> 9x + 4.05xy + 15y + 30y - 11x + 9.46

aev [14]

Answer: 4.05 x y − 2 x + 45 y + 9.46

Step-by-step explanation:

9x + 4.05xy + 15y + 30y - 11x + 9.46

4.05xy + 9x - 11x + 15y+ 30y+ 9.46

4.05 x y − 2 x + 45 y + 9.46

6 0

2 years ago