asinus

What is an equation of the line that passes through the points (-3, 3) (3,−7) Put your answer in fully reduced form.

Hello Guest!

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-3}{3-(-3)}\)

\(m=\frac{5}{3}\)

\(y=m(x-x_1)+y_1\)

\(y=\frac{5}{3}\cdot(x+3)+3\\ y=\frac{5}{3}x+5+3\)

\(y=\frac{5}{3}x+8\)

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Find b!

Hello Guest!

 \(b^2=a^2+c^2-2ac\cdot cos 115^{\circ}\)

\(b^2=(28^2+18^2-2\cdot 28\cdot 18\cdot cos \ 115^{\circ})m^2\\ b^2=1534m^2\)

\(b=39.166m\)

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Richard cuts a 4 1/2 x 7 1/2 ft x 11 1/4 ft rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?

Hello Guest!

\(2\ rectangular\ prism\ 4.5\times 4.5 \times 4.5\ will\ he\ produce.\)

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Matt wants to make a 25% alcohol solution. He has already poured 1.5 qt. of pure water into a beaker. How many qt. of a 30% alcohol solution must he add to this to create the desired mixture?

Hello Guest!

\(x\cdot 30\%=(1.5qt.+x)\cdot 25\%\\ x\cdot 30\%=1.5qt.\cdot 25\%+x\cdot 25\%\\ 0.3x-0.25x=0.25\cdot 1.5qt.\\ 0.05x=0.375qt. \)

\(x=7.5qt.\)

 \(7.5qt.\) of a 30% alcohol solution must he add to this to create the desired mixture.

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The difference between a number and its reciprocal is 3. What are the possible values of the number?

Hello Guest!

\(a-\frac{1}{a}=3\\ \frac{a^2-1}{a}=3\\ a^2-1=3a\\ a^2-3a-1=0\)

\(a=1.5\pm\sqrt{1.5^2+1}\)

\({\color{blue}a_1}=1.5+1.803=\color{blue}3.303\\ {\color{blue}\frac{1}{a_1}}=\color{blue}0.303 \)

\({\color{blue}a_2}=1.5-1.803=\color{blue}-0.303\\ {\color{blue}\frac{1}{a_2}}=\color{blue}-3.303\)

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Write an equation of a line that is parallel to 2x-3y=0 that passes through the point (-3,-1)

Hello Guest!

\(2x-3y=0\)

is identical

\(y=\frac{2}{3}x\)

\(m=\frac{2}{3}\)

\(f(x)=m(x-x_1)+y_1\)

\(f(x)=\frac{2}{3}(x-(-3))+(-1)=\frac{2}{3}x+2-1\)

\(y=\frac{2}{3}x+1\)

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wie kann man die brüche rechnen?

Hallo Gast!

Du musst eine Aufgabe ins Forum stellen. Nur so kann ich dir helfen.

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Find the equation of the parabola that goes through the three points (0, 9), (1, 7) and (2, 7).

Hello Guest!

\(y=ax^2+bx+c\)

Put the coordinates of the three points in
the equation \(y=ax^2+bx+c\), and solve for a, b, and c.

I.    \(9=c\)

II.   \(7=a+b+9\)

III.  \(7=4a+2b+9\)

4 * II  .     \(28=4a+4b+36\)

  - III.         \(\underline{7=4a+2b+9}\)

                21  =           2b  + 27 

\(2b=21-27=-6\)

\(b=-3\)

\(7=a+b+9\)

\(7=a-3+9\)

\(a=1\)

The general equation  \(y=ax^2+bx+c\)

becomes the real equation \(y=x^2-3x+9\).

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Solve for p: 2(p + 1) + 8(p - 1) = 5p

Hello Guest!

\(2(p + 1) + 8(p - 1) = 5p \\ 2p+2+8p-8-5p=0\\ 5p=6\)

\(p=1.2\)

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Hello ElectricPavlov, hello Alan!

Thanks for the correction.

I'm trying differential calculus. Is that OK?

\(\color{blue}h(v)=vt-\frac{v^2}{2g}\\ \frac{dh(v)}{dv}=t-\frac{v_0}{g}=0\\ v_0=gt=\frac{9.81m\cdot4.5s}{s^2}\)

\(v_0=44.145m/s\)

\(h_{max}=v_0\cdot t-\frac{v_0^2}{2g}\\ h_{max}=44.145m/s\cdot4.5s-\frac{44.145^2}{2\cdot 9.81}m\)

\(h_{max}=99.33m\)

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