Alan

Let w be the number of white hydrangeas in the first bed and p be the number of pink ones.

Then

w + p = 45           1st bed       so  p = 45 - w

2w + 3p = 120      2nd bed     or  2w +3(45 - w) = 120   so  -w + 135 = 120  or w = 15

Since p = 45 - w  then p = 30

Total number of whites = 3w = 45

Total number of pinks = 4p = 120

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There is no value of x which equals arcsec(0) as arcsec(0) doesn't exist:

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Take logs of both sides:

log(0.85^x) = log(1/2)

From a properrty of logarithms we can write:

x*log(0.85) = log(1/2)

so x = log(1/2)/log(0.85)

$${\mathtt{x}} = {\frac{{log}_{10}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{{log}_{10}\left({\mathtt{0.85}}\right)}} \Rightarrow {\mathtt{x}} = {\mathtt{4.265\: \!024\: \!281\: \!798\: \!725\: \!7}}$$

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32 is 2⁵ and 4 is 2², so you have (2⁵)^x = 2²

or 2^5x = 2²

so 5x = 2

or x = 2/5

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One way is to notice that $$27=3^3$$ so you have

 $$27^x=(3^3)^x=3^{3x}$$

Your equation then becomes

$$3^{3x}=3^1$$

so 3x = 1

so x = 1/3

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Just answered it

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Yes you do!  The work done by F₂ is the component parallel to the incline's surface (F₂cos(30°)) multiplied by the distance moved.

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