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3 years ago

Solve for x..................

Mathematics

1 answer:

vampirchik [111]3 years ago

6 0

 so the answer is 15.

Hope this will help u....

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A factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where t is the number of years tha

alexandr402 [8]

Answer:

The total amount of pollution discharged during the first 7 years of operation is 1.955 tons

Step-by-step explanation:

Given

$r(t) = \frac{t}{t^2 + 1}$

Required

The total amount in the first 7 years

This implies that:

$r(t) = \frac{t}{t^2 + 1}; [0,7]$

The total amount is calculated by integrating r(t) i.e.

$v = \int\limits^a_b {r(t)} \, dt$

So:

$v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt$

--------------------------------------------------------------

We have:

$t^2 + 1$

Differentiate

$d(t^2 + 1) = 2t$

Rewrite as:

$2t = d(t^2 + 1)$

Solve for t

$t = \frac{1}{2}d(t^2 + 1)$

---------------------------------------------------------------------------

So:

Make t the subject

$v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt$

$v = \int\limits^7_0\frac{1}{2}* {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt$

$v = \frac{1}{2}\int\limits^7_0 {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt$

Integrate

$v = \frac{1}{2}\ln(t^2 +1)|\limits^7_0$

Expand

$v = \frac{1}{2}[\ln(7^2 +1) - \ln(0^2 +1)]$

$v = \frac{1}{2}[\ln(50) - \ln(1)]$

$v = \frac{1}{2}[3.91 - 0]$

$v = \frac{1}{2}[3.91]$

$v = 1.955$

7 0

3 years ago

Find the area of the shaded polygons: Area of shaded polygon is __square units

nevsk [136]

Answer:

9 sq units

Step-by-step explanation:

1.5+1.5+4.5+1.5 = 9

8 0

3 years ago

Which digit is in the thousandths place? 1,356.209

Butoxors [25]

Answer: 9

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Divide using any method 2x^2+5x+1 ÷ X+3

Natali [406]

Question:

Solve the equation 2x2−5x+3=0 by the method of completing square.

Answer:

We have,

2x2−5x+3=0

⇒x2−25x+23=0 (Dividing throughough by 2)

⇒x2−25x=−23 (Shifting the constant term on RHS)

⇒x2−2(45)x+(45)2=(45)2−23 (Adding (21Coeff.ofx)2 onboth sides)

⇒(x−45)2=1625−23⇒(x−45)2=16

3 0

3 years ago

Please show work 26 lbs of onion cost $127.40. How much would 18 lbs cost\

Irina18 [472]

127.40/26 = $4.90 per pound
18 * 4.9 = $88.20
It would cost $88.20

5 0

3 years ago