asinus

Find all y which does NOT satisfy

\(1 \le 4-3y < 10.\)

Express your answer in interval notation.

Hello imdumb!

4 - 3y = 1

3y = 4 - 1

y = 1

4 - 3y < 10

3y > 4 - 10

y > - 2

\(y=\{\mathbb R\ | except\ \{-2 < y \le 1\}\}\)

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There are two solutions, R and r. Evaluate R - r.

Hello Guest!

The distance \(\overline{AB}\)  intersected by the tangent is divided into a and b.

\(a:(6-a)=r_A:r_B\\ a:(6-a)=1:2\\ 2a=6-a\\ a=2\\ b=4\)

\(r_A:(r_A+R)=a:\overline{AB}\\ 1:(1+R)=2:6\\ 6=2+2R \)

\(R=2\)

The radius of the third circle is 2.

There are not two solutions R. 

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A lattice point is a point whose coordinates are integers. How many lattice points are strictly inside the triangle formed by the points (0,0), (0,7), and (8,0)?

Hello Guest!

\(f(x)=-\frac{7}{8}x+7\)

lattice points: 8+7+6+5+4+3+2+1+1

There are 37 lattice points in the triangle.

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A boat is 130 m from the base of a cliff. The cliff is 80 m high. Determine, to the nearest degree, the angle of depression of the boat from the top of the cliff.

Hello Guest!

\(tan(\delta )=\frac{130m}{80m}=1.625\\ \delta =arctan (1.625)\)

\(\delta \approx 58^0\)

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A spherical orange is cut about the vertical axis into 8 equal slices as shown above.

What is the ratio of the total surface area of the 8 slices to that of the original orange?

Hello Guest!

\(S_{slices}=4\pi r^2+4\times \pi r^2\\ S_{orange}=4\pi r^2\\ \color{blue}S_{orange}:S_{slices}=1:2\)

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Find the vertex of the graph of the equation y = -2x^2 + 9x - 18.

Hello Guest!

\( y = -2x^2 + 9x - 18\\ y'=-4x+9=0\\ \color{blue}x_P= \frac{9}{4}\)

\( y = -2x^2 + 9x - 18\\ y=-2\cdot (2.25)^2 + 9\cdot 2.25) - 18\\ y=-10.125+20.25-18\\ \color{blue}y_P=-7.875\)

\(P_{vertex}(2.25,-7.875)\)

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What is (n/n-1) for any positive integer n? (Answer in terms of n.)

Hello Guest!

\(\frac{n}{n-1}\) for any positive integer n is \(\frac{(2)}{(2)-1}=2\)

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Was ist 1+1.  11 oder?

Hallo Gast!

Ergebnis 11 ist in jedem Zahlensystem falsch.

Im Dezimalsystem (und jedem anderen Zahlensystem, außer dem Binärsystem)

ist 1 + 1 = 2.

Im Binärsystem ist 1 + 1 = 10.

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German

Wozu braucht man diese Addition?   >>>  Why do you need this addition?

Danke für dein Danke. It doesn't happen that often here.

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158 : 7 = ?

\(158:7=22,\overline{571428}=22\ \frac{4}{7}\)

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