Alan

You probably mean G(s) = s - 0.5/(s + 1) and you want G(jω), in which case you just replace s by jω.

 G(jω) = jω - 0.5/(jω + 1)

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The calculator is in degree mode by default, so you can just type in 90.

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cost = 4*14*23.11 dollars

You can use the calculator to crunch the numbers!

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If you mean f(x) = -4x² - x and you want to know f(3) then DarkBlaze347 has supplied the right answer.

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28% = 28/100 = 0.28;  14% = 14/100 = 0.14;  8% = 8/100 = 0.08 so:

money = 0.28*250*3.65 + 0.14*250*1.2 + 0.08*250*7.5

$${\mathtt{money}} = \left({\mathtt{0.28}}{\mathtt{\,\times\,}}{\mathtt{3.65}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.14}}{\mathtt{\,\times\,}}{\mathtt{1.2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.08}}{\mathtt{\,\times\,}}{\mathtt{7.5}}\right){\mathtt{\,\times\,}}{\mathtt{250}} \Rightarrow {\mathtt{money}} = {\mathtt{447.5}}$$

money = $447.50

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3*(x-4.5)⁵ = 80

Divide both sides by 3

(x - 4.5)⁵ = 80/3

Take the fifth root of both sides

x - 4.5 = (80/3)^1/5

Add 4.5 to both sides

$${\mathtt{x}} = {\left({\frac{{\mathtt{80}}}{{\mathtt{3}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{5}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{4.5}} \Rightarrow {\mathtt{x}} = {\mathtt{6.428\: \!385\: \!008\: \!005\: \!254\: \!5}}$$

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sin(angle) = opposite/hypotenuse

so opposite = hypotenuse*sin(angle)

$${\mathtt{X}} = {\mathtt{74}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{32}}^\circ\right)} \Rightarrow {\mathtt{X}} = {\mathtt{39.214\: \!025\: \!553\: \!242}}$$

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Use them on lots of practice problems.

Keep the following saying in mind:

I hear and I forget.

I see and I remember.

I do and I understand.

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Or just:

f(1) = -4

f(2) = f(1) + 3   so f(2) = -4 + 3  or f(2) = -1

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Add 7 to both sides:

41 + 7 = 12*d

48 = 12*d

Divide both sides by 12

48/12 = d

or

d = 4

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