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lisabon 2012 [21]

2 years ago

5

What is the constant proportionality of $0.59 per pound

1 answer:

Tanya [424]2 years ago

6 0

Answer:

The constant of proportionality is just 0.59

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Zina [86]

For the integral

$I=\displaystyle\int_1^3\frac{\mathrm dx}{x\sqrt{1-(\log x)^2}}$

(assuming $\log x$ is the natural logarithm with base $e$ ) substitute $u=\log x$ and $\mathrm du=\frac{\mathrm dx}x$ . Then the integral is equivalent to

$I=\displaystyle\int_{\log1}^{\log e}\frac{\mathrm du}{\sqrt{1-u^2}}=\int_0^1\frac{\mathrm du}{\sqrt{1-u^2}}$

Next, substitute $u=\sin t$ and $\mathrm du=\cos t\,\mathrm dt$ :

$I=\displaystyle\int_{\sin^{-1}0}^{\sin^{-1}1}\frac{\cos t}{\sqrt{1-\sin^2t}}\,\mathrm dt=\int_0^{\frac\pi2}\frac{\cos t}{\sqrt{\cos^2t}}\,\mathrm dt$

We have $\sqrt{x^2}=|x|$ for all $x$ , but in the given integration interval, $\cos t\ge0$ , so

$I=\displaystyle\int_0^{\frac\pi2}\frac{\cos t}{\cos t}\,\mathrm dt=\int_0^{\frac\pi2}\mathrm dt=\boxed{\dfrac\pi2}$

(Of course, with a little foresight, you could have immediately combined the two substitutions and started off with letting $\sin u=\log x$ .)

5 0

3 years ago

of the 30 students in the six period Math class, eight or also in the same fourth period Science class. which can be used to det

Dmitry_Shevchenko [17]

Answer:

the answer to your question is bbbbb

Step-by-step explanation:

4 0

3 years ago

9(x + 8) + 11(3x + 4)

Sav [38]

Simplify the expression : 42x + 116

Hope this helps!
Have a great day!

5 0

3 years ago

Find the equivalent expressions for (x + 7)(x + 1).

Natali5045456 [20]

Answer:

The answers should be

x^2 + 8x + 7

x(x + 8) +7

Step-by-step explanation:

(x + 7)(x + 1)

x(x) + x(1) + 7(x) + 7(1)

x^2 + x + 7x + 7

x^2 + 8x + 7

5 0

3 years ago

Read 2 more answers

Please help!! i don’t understand how to do this

Arisa [49]

Answer: A is the right angle

Step-by-step explanation:

a. 20^2 + 15^2 = 25^2

400 + 225 = 625

625 = 625

hope this helps :)

8 0

2 years ago