Midterm 3: Version C
For problems 1–4, perform the indicated operations and simplify.
- [latex]\dfrac{15m^3}{4n^2}\div \dfrac{30m^3}{17n^3}\cdot \dfrac{3m^4}{34n^2}[/latex]
- [latex]\dfrac{5v^2-25v}{5v+25}\div \dfrac{v^2-11v+30}{10v}[/latex]
- [latex]\dfrac{8}{2x}=\dfrac{2}{x}+1[/latex]
- [latex]\dfrac{\dfrac{x^2}{y^2}-16}{\dfrac{x+4y}{y^3}}[/latex]
Reduce the expressions in questions 5–7.
- [latex]\sqrt{25y^2}+2\sqrt{81y^2}+\sqrt{36y^3}[/latex]
- [latex]\dfrac{28}{7-3\sqrt{5}}[/latex]
- [latex]\left(\dfrac{27a^{-\frac{1}{8}}}{a^{\frac{1}{4}}}\right)^{\frac{1}{3}}[/latex]
Find the solution set.
- [latex]\sqrt{3x-2}=\sqrt{5x+4}[/latex]
For problems 9–12, find the solution set by any convenient method.
- [latex]\phantom{1}[/latex]
- [latex]2x^2=72[/latex]
- [latex]2x^2=8x[/latex]
- [latex]\phantom{1}[/latex]
- [latex]x^2+6x+5=0[/latex]
- [latex]x^2=10x-4[/latex]
- [latex]\dfrac{8}{4x}=\dfrac{2}{x}+3[/latex]
- [latex]x^4-17x^2+16=0[/latex]
- The width of a rectangle is 6 m less than its length, and its area is 12 units more than its perimeter. What are the dimensions of the rectangle?
- Find three consecutive odd integers such that the product of the first and the third is 31 more than the second.
- It took a tugboat 5 hours to travel against an ocean current to get to an isolated outpost 60 km from its home port and 3 hours to return back to port going with the ocean current. What is the speed of the ocean current and what speed can the tug travel on still water?