asinus

Find the length of the zip line. (Round your answer to the nearest ft.)

Hello Guest!

You calculated correctly. The height of the tower is 300 ft.

Now follows Pythagoras:

\(z^2=200^2ft^2+300^2ft^2\\ z=\sqrt{(200^2+300^2)ft^2}\\ z=\sqrt{(130\ 000)ft^2}\\ \color{blue}z=360.555ft\)

The length of the zip line is 361ft.

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How many real numbers are not in the domain of the function f(x)?

Hello Guest!

There are no whole numbers (integer) in the domain of the function f(x).

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Hallo Gast!

\(\sqrt[ 5]{\dfrac{bx^{-2}}{a^{-4}y^6}}\cdot \sqrt[ 5]{\dfrac{bx^4}{a^{-2}y^6}}:\sqrt[ -5]{\dfrac{bx^4}{a^{-2}y^6}}\\ = \sqrt[5]{\dfrac{b\cdot a^4}{x^2\cdot y^6}\cdot \dfrac{a^2\cdot b\cdot x^4}{y^6}\cdot \dfrac{a^2\cdot b\cdot x^4}{y^6}}\)

\(=\sqrt[5]{\dfrac{a^8\cdot b^3\cdot x^6}{y^{18}} }\\ =\color{blue}\dfrac{a\cdot x}{y^3}\cdot \sqrt[5]{\dfrac{a^3\cdot b^3\cdot x}{y^{3}}}\)

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wieso fällt bei der Stückvariablen-Kostenfunktion: kv(x)=0,4x2 −5x+80 die (321/x) weg?

Hallo Gast!

Woher stammen die Daten in deiner Gleichung? Ohne das zu wissen, kann deine Frage wohl kaum beantwortet werden. Beschreibe zuerst den Vorgang.

Hab's mal nachgerechnet:

\(\frac{25 \cdot 0,84 + 24 \cdot 0,65}{25+24} = 0,7469 \)

\(\dfrac{49 \cdot 0,7469 + 0 \cdot x}{49+x} = 0,61 \ \ | \cdot (49+x) \\ 36,6 = 0,61 \cdot (49+x) \\ 36,6 = 29,89 + 0,61x \ \|-29,89 \\ 6,71 = 0,61x \ \ |:0,61 \\ 11 = x \)

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Wieviel Liter Wasser muss man hinzufügen, damit 61prozentiger Alkohol entsteht?

Hallo Gast!

\(\color{blue}25l \cdot 0,84+24l\cdot 0,65=(25l+24l+x)\cdot 0,61\\ 21l+15,6l=15,25l+14,64l+0,61x\\ 21l+15,6l-15,25l-14,64l=0,61x\\ 0,61x=6,71l\\ x=\dfrac{6,71l}{0,61}\)

\(x=11l\)

Man muss 11 Liter Wasser  hinzufügen, damit 61prozentiger Alkohol entsteht.

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a) Write an equation of the function

b) Discuss its domain and range

Hello Guest!

a)
\(\color{blue}f(x)=\frac{3}{4}\cdot (\frac{1}{2})^x+t\\ f(0)=\frac{3}{4}+t \)

reflected in y

\(\color{blue}g(x)=\frac{3}{4}\cdot (\frac{1}{2})^{-x}+t\\ f(0)=\frac{3}{4}+t \)

b)

domain f(x) and g(x):  - \(\infty\) < x < \(\infty\) 

range f(x):   t < f(x) < \(\infty\) 

range g(x):   t < g(x) < \(\infty\) 

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a) Write an equation of the function.

b) Discuss its domain and range

Hello Guest!

a)

\(f(x)=\frac{3}{4}\cdot (\frac{1}{2})^x-4\\ f(0)=-\frac{13}{4}\)

reflected

\(g(x)=\frac{3}{4}\cdot (\frac{1}{2})^{-x}-4\\ g(0)=-\frac{13}{4}\)

b)

domain f(x) and g(x) : \(-\infty\) < x < \(\infty\)

range f(x) : - 4 < f(x) < \(\infty\)

range g(x) : - 4 < g(x) < \(\infty\)

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A carpenter chisels a square hole of side 2 in. through a round post of radius 2 in. The axis of the hole
intersecting that of the post at right angles. Find the volume of the wood cut out.

Hello Guest!

The face of the side of the body is made up of two segments of a circle and four right triangles.

\(A_{ segment}=\frac{\pi r^2}{6}=\frac{\pi \cdot2^2in^2}{6}=\color{blue}\frac{2}{3}\pi\ in^2\)

\(A_{triangle }=\frac{2\cdot sin(30°)\cdot 1 }{2}=\color{blue}\frac{1}{2}in^2\)

\(A_{body}=2\cdot A_{ segment}+4\cdot A_{triangle }=2\cdot \frac{2}{3}\pi\ in^2+4\cdot \frac{1}{2}in^2=\color{blue}6.189\ in^2\)

\(V_{body}=A_{body}\cdot 2\ in\\ V_{body}=6.189\ in^2\cdot 2\ in\\ \color{blue}V _{body}=12.378\ in^3\)

The carpenter cut 12.378 cubic inches of wood from the log.

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Each solution to x^2 + 5x + 18 = 0 can be written in the form a + bi where a and b are real numbers. What is a^2 + b^2?

Hello Guest!

\(x^2 + 5x + 18 = 0\\ x=-2.5\pm \sqrt{6.25-18}\\ a+bi=-2.5\pm \sqrt{11.75}\cdot i\)

\(a^2+b^2=6,25-11.75\)

\(a^2+b^2=-5.5\)

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