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3 years ago

Find the slope and the y-intercept of the line. 7x – 2y = -2 Write your answers in simplest form.

Mathematics

1 answer:

Flauer [41]3 years ago

3 0

Answer:

slope = 7/2 or 3.5 as a decimal.

y-intercept = 1 or (0, 1) in coordinate form.

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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

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

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

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

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

$v = 1.955$

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Find the slope and the y-intercept of the line. 7x – 2y = -2 Write your answers in simplest form.​

Find the slope and the y-intercept of the line. 7x – 2y = -2 Write your answers in simplest form.