asinus

\( x +x +\frac{1}{5}\cdot x+\frac{2}{15}=\color{blue}2\frac{1}{5}x+\frac{2}{15}\)

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 ... for two quadratic functions to intersect in an infinite number of locations?

Hello Melody!

Do quadratic functions have to be parabolas?

There are no parabolas that intersect other parabolas at an infinite number of points.

If they touch at an infinite number of points, they don't intersect.

The function values of f(x) and g(x) are squares between zero and one.

f(x) = sin^2(x) may not fit in the standard expression "quadratic function".

But he fulfills the conditions of the question asked.

If the "quadratic function" is found, please let me know.

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Hello Julia!

My proposition: answer c).

\(f(x)=sin^2(x)\\ g(x)=cos^2(x)\\ axis\ of\ reflection: y=0.5\)

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Thanks proyaop, you are right! I will correct.

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 What is angle DAC in degrees?

Hello Guest!

\(AEF+BAC+BAD=180^o\\ 12BAC=180^o\\2BAC=\color{red}DAC=30^o\ error \\ \)

\(10BAC-22^o+DAC=180^o\\ 5DAC-22^o+DAC=180^o\\ 6DAC=202^o\\ \color{blue}DAC=33\frac{2}{3}^o\)

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the smallest possible value for k must be ____ degrees.

Hello Julia!

\(cos(k)=-\frac{\sqrt{3}}{2}\\ arccos(-\frac{\sqrt{3}}{2})=k\in\{(150+n\cdot 360)deg,(210+n\cdot 360)deg\}\)

\(\{510deg,570deg\} \) \(\subset \{k\) | 450deg < k < 630deg\(\}\)

The smallest possible value for k must be: k = 510 degrees.

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Five sevenths of what amount is equal to 20?

Hello Guest!

\(\frac{5}{7}\cdot x=20\ |\ \cdot \frac{7}{5}\\ x=20\cdot \frac{7}{5}\\ \color{blue}x=28\)

Five sevenths of 28 amount is equal to 20.

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She is the mother of science.

Which of the following ordered pairs must be part of the original function f(x) ?

Hello Julia,

the ordered pair a) (-5,0) is part of the original function f(x) = x+5.

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 By what percent does the length of the arc increase?

Hello proyaop!

If the angle of the arc increases by 20% and the radius of the circle increases by 25%, the arc will increase by 1.20 * 1.25 = 1.50. So the arc will be 50% larger.

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