Solve Equation in Terms of Other Variables
Read this topicExplanations 3
- (Video) Solving Literal Equations by YourMathGal This video YourMathGirl explains what literal equations. We can use this video to help us solve literal equations in terms of on…
By Alex Federspiel, Zora Gilbert, Amy Feraco, Jonathan Heller, Anusha Rahman
- Most literal equations have more than one variable, so you'll be asked to solve the equation in terms of one of the variables. For instance, if the literal equation contains var…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Jonathan Heller, Anusha Rahman
- Solve Formulas for a Given Variable Solving equations in terms of other variables is very similar to solving any other equation. You need to manipulate the equation to isolate t…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 66
- The equation for the escape velocity from a planet or star is given by Vesc=2GMR.V_{\text{esc}}=\sqrt{\frac{2GM}{R}}.Vesc=R2GM. Solve the equation for RRR.
- Solve the equation for the variable www, assuming lll and hhh are positive. V=lwhV=lwhV=lwh
- Solve the equation for rrr, assuming hhh is positive. V=13 πr2hV=\frac{1}{3}\ \pi r^2hV=31 πr2h (Note: π=3.14…\pi=3.14\dotsπ=3.14… is a constant. In a cylinder, VVV stands for …
- If h≠0h\neq0h=0, solve the following equation for uuu. y=h(u+v)y=h(u+v)y=h(u+v)
- Solve for lll if AAA and rrr are nonzero. A=r2lA=\frac{r}{2l}A=2lr
- Solve for yyy, assuming z≠0z\neq0z=0. x=yz3x=\frac{yz}{3}x=3yz
- Solve for nnn, assuming ddd is nonzero. L=a+d(n−1)L=a+d(n-1)L=a+d(n−1)
- Solve for LLL. T=2πLgT=2\pi\sqrt{\frac{L}{g}}T=2πgL
- The area of a circle is 16π16\pi16π. Use this to find the radius of the circle.
- Solve for the radius of a sphere, rrr, in terms of the volume, VVV. V=43 πr3V=\frac{4}{3}\ \pi r^3V=34 πr3
- Find a formula for the base bbb of a triangle, in terms of the height hhh and area AAA of the triangle.
- The equation for a line is y=mx+by=mx+by=mx+b. Solve for mmm when xxx is nonzero.
- The Pythagorean theorem is given by: a2+b2=c2a^2+b^2=c^2a2+b2=c2. Solve for aaa.
- The surface area of a cone can be found using the following equation. SA=πrr2+h2S_A=\pi r\sqrt{r^2+h^2}SA=πrr2+h2 Solve for hhh.
- The equation for compound interest is A=P(1+rm)tmA=P(1+\frac{r}{m})^{tm}A=P(1+mr)tm. Solve for rrr.
- The diameter of the moon is 215921592159 miles. The volume of Earth is about 49.349.349.3 times larger than that of the moon. What is the Earth's diameter, approximately?
- Electrical engineers use the equation V=PRV=\sqrt{PR}V=PR to calculate voltage, where PPP is the power measured in watts and RRR is the resistance measured in ohms. Solve for RRR.
- You know that c=a2+b2c=\sqrt{a^2+b^2}c=a2+b2. You also know that b=d+fb=\sqrt{d+f}b=d+f. Solve for aaa.
- If 5z−3x+4y=4z+x−7y5z-3x+4y=4z+x-7y5z−3x+4y=4z+x−7y, solve for zzz in terms of xxx and yyy.
- 100x+50y+25z+10a=15x+25y+11z+9a100x+50y+25z+10a=15x+25y+11z+9a100x+50y+25z+10a=15x+25y+11z+9a Find aaa in terms of x,y,zx,y,zx,y,z in the equation above.
- Solve for qqq in terms of y,zy,zy,z: 25.5q−5z−4.5y=24.5q+5.5z−4y.25.5q-5z-4.5y=24.5q+5.5z-4y.25.5q−5z−4.5y=24.5q+5.5z−4y.
- What is the slope and intercept for the equation 2y−3x+1=02y - 3x + 1 = 02y−3x+1=0? (Hint: It may help to first solve for yyy in terms of xxx.)
- What is the slope and intercept for the line 2y=6x+82y = 6x + 82y=6x+8? (Hint: Solve for yyy in terms of xxx.)
- The volume of a circular cone is V=13(π)r2hV=\frac{1}{3}(\pi)r^2hV=31(π)r2h. Solve for hhh.
- Given the formula for a triangle's height in terms of its area and base, solve for AAA in terms of bbb and hhh: 2Ab=h\frac{2A}{b}=hb2A=h
- The diameter, ddd, is twice the radius, rrr. If possible, express ddd as a function of CCC.
- Ignoring drag, the height of a paper airplane in the air could be calculated by: h=h0+12t2(12ρV2⋅S⋅Clm−g)h=h_0+\frac12t^2\bigg(\frac{\frac12\rho V^2\cdot S\cdot C_l}{m}-g\bigg)h…
- Solve for xxx, writing it in terms of aaa and bbb. Suppose a≠0a\neq0a=0. ax=bax=bax=b
- Find xxx in terms of aaa and bbb: xa=b\frac{x}{a}=bax=b
- If p≠0p\neq0p=0, find xxx in terms of p,n,tp, n, tp,n,t. xp=nt\frac{x}{p}=\frac{n}{t}px=tn
- Find xxx in terms of nnn and ppp. xn=p\frac{x}{n}=pnx=p
- ax=b\frac{a}{x}=bxa=b If aaa and bbb are nonzero, isolate xxx in the equation above.
- Find xxx in terms of mmm and nnn, if mmm and nnn are nonzero. m=nxm=\frac{n}{x}m=xn
- When y=4y=4y=4, solve the literal equation x+y=6x+y=6x+y=6 for xxx.
- Solve the literal equation x+y=9x+y=9x+y=9 for xxx, when y=5y=5y=5.
- Solve the literal equation x−y=2x-y=2x−y=2 for xxx, when y=6y=6y=6.
- Solve the following literal equation for xxx. 2x+3y=72x+3y=72x+3y=7
- Solve the following literal equation for xxx. 4x+y=34x+y=34x+y=3
- Solve the following literal equation for xxx. 2x−5y=62x-5y=62x−5y=6
- Solve the following literal equation for xxx. 4x−y=34x-y=34x−y=3
- In physics we have the equation v=vi+at.v=v_i+at.v=vi+at. Solve for time, ttt.
- Here is the formula for gravitational attraction: F=Mmgr2F = \frac{Mmg}{r^2}F=r2Mmg Solve for the gravitational constant ggg, assuming the masses MMM and mmm are positive.
- What is the term for the technique of getting a variable "by itself" in an equation?
- When isolating, how do we undo multiplication by a nonzero expression?
- When isolating, how do we undo division by a nonzero expression?
- What operation would you use to isolate aaa below? a+b=ca+b=ca+b=c
- What operation would you use to isolate aaa below? a−b=ca-b=ca−b=c
- If b≠0b\neq0b=0, what operation would you use to isolate aaa below? a×b=ca\times b=ca×b=c
- What operation would you use to isolate aaa below? a÷b=ca\div b=ca÷b=c
- Isolate aaa in the equation a+b=ca+b=ca+b=c.
- Isolate aaa below. a−b=ca-b=ca−b=c
- Isolate aaa below, assuming b≠0b\neq0b=0. a×b=ca\times b=ca×b=c
- Given a÷b=c,a\div b=c,a÷b=c, solve for aaa in terms of bbb and ccc.
- Isolate π\piπ in the following equation. C=dπC=d\piC=dπ
- Isolate hhh, the height of a cylinder, in the formula for its volume: V=hπr2V=h\pi r^2V=hπr2
- Isolate the radius rrr of a circle from its diameter ddd: d=2rd=2rd=2r
- Solve for xxx in terms of bbb and ccc, if b≠0b\neq0b=0. 2x⋅bc=52x\cdot\frac{b}{c}=52x⋅cb=5
- What is bbb in the slope-intercept form equivalent to?
- The slope of a line is 333 and the line passes through (−4,−13)(-4, -13)(−4,−13). Find the equation in slope-intercept form and simplify it.
- What is the yyy-intercept?
- Using this information, what is the acceleration due to gravity, ggg, of Middle Earth?
- If we know that z=x−y+2xz=x-y+2xz=x−y+2x, can you write zzz in terms of only yyy? \\ Hint: Can you first write xxx in terms of yyy?
- Solve for rrr in terms of xxx. rx=6\frac{r}{x}=6xr=6
- You need to get ppp pizzas for your party to distribute among nnn friends. Each pizza has sss slices. If everyone gets the same amount of pizza, write an equation for how many s…
- Solve for xxx in terms of aaa and yyy, if aaa is nonzero. ax+6y3=2y\frac{ax+6y}{3}=2y3ax+6y=2y
- Solve for xxx in terms of aaa. ax+(a+1)=(a+1)x+aax+(a+1)=(a+1)x+aax+(a+1)=(a+1)x+a