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3 years ago

Help with this please

Mathematics

1 answer:

Scilla [17]3 years ago

8 0

Answer:

(7,4)

Step-by-step explanation:

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative. (7,8)

Afterwards, four units down means changing the y coordinate we have, thus making our (8) into (4.)

Hope this helps!

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The mass, m grams, of a radioactive substance, present at time t days after first being observed, is given by the formula m=24e^

Reika [66]

Answer:

(i) The value of m when t = 30 is 13.2

(ii) The value of t when the mass is half of its value at t=0 is 34.7

(iii) The rate of the mass when t=50 is -0.18

Step-by-step explanation:

(i) The m value when t = 30 is:

$m = 24e^{-0.02t} = 24e^{-0.02*30} = 13.2$

Then, the value of m when t = 30 is 13.2

(ii) The value of the mass when t=0 is:

$m_{0} = 24e^{-0.02t} = 24e^{-0.02*0} = 24$

Now, the value of t is:

$ln(\frac{m_{0}/2}{24}) = -0.02t$

$t = -\frac{ln(\frac{24}{2*24})}{0.02} = 34.7$

Hence, the value of t when the mass is half of its value at t=0 is 34.7

(iii) Finally, the rate at which the mass is decreasing when t=50 is:

$\frac{dm}{dt} = \frac{d}{dt}(24e^{-0.02t}) = 24(e^{-0.02t})*(-0.02) = -0.48* (e^{-0.02*50}) = -0.18$

Therefore, the rate of the mass when t=50 is -0.18.

I hope it helps you!

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Arada [10]

Answer:

Is there a question here?

Step-by-step explanation:

t - 4t² + 2t³ = t(1 - 4t + 2t²)

= t(2t² - 4t +1)

≠≠≠≠ t(2t - 1)(t -1)

used a graphing calculator to find the roots

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