4.2 Equations

$y=x-7$

$3t=6s$

$u=v^5$

$r=\frac{2}{9}s$

$b=\frac{3}{4}a$

$f=0.97k+55$

$w=4z^3-21$

$q^2=9x^8+2y$

$I=m^{2}q{b}^5+3.115p$

Geometry (circumference of a circle)
$\begin{array}{cc}C=2\pi r.& \text{Find}C\text{if}\pi \text{is}\text{approximated}\text{by}3.14\text{and}r=5.\end{array}$

Geometry (area of a rectangle)
$\begin{array}{cc}A=lw.& \text{Find}A\text{if}l=15\text{and}w=9.\end{array}$

Electricity (current in a circuit)
$\begin{array}{cc}I=\frac{E}{R}.& \text{Find}I\text{if}E=21\text{and}R=7.\end{array}$

Electricity (current in a circuit)
$\begin{array}{cc}I=\frac{E}{R}.& \text{Find}I\text{if}E=106\text{and}R=8.\end{array}$

Business (simple interest)
$\begin{array}{cc}I=prt.& \text{Find}I\text{if}p=3000,r=.12\text{and}t=1.\end{array}$

Business (simple interest)
$\begin{array}{cc}I=prt.& \text{Find}I\text{if}p=250,r=0.07\text{and}t=6.\end{array}$

Geometry (area of a parallelogram)
$\begin{array}{cc}A=bh.& \text{Find}A\text{if}b=16\text{and}h=6.\end{array}$

Geometry (area of a triangle)
$\begin{array}{cc}A=\frac{1}{2}bh.& \text{Find}A\text{if}b=25\text{and}h=10.\end{array}$

Geometry (perimeter of a rectangle)
$\begin{array}{cc}P=2l+2w.& \text{Find}P\text{if}l=3\text{and}w=1.\end{array}$

Geometry (perimeter of a rectangle)
$\begin{array}{cc}P=2l+2w.& \text{Find}P\text{if}l=74\text{and}w=16.\end{array}$

Geometry (perimeter of a rectangle)
$\begin{array}{cc}P=2l+2w.& \text{Find}P\text{if}l=8\frac{1}{4}\text{and}w=12\frac{8}{9}.\end{array}$

Physics (force)
$\begin{array}{cc}F=32m.& \text{Find}F\text{if}m=6.\end{array}$

Physics (force)
$\begin{array}{cc}F=32m.& \text{Find}F\text{if}m=14.\end{array}$

Physics (force)
$\begin{array}{cc}F=32m.& \text{Find}F\text{if}m=\frac{1}{16}.\end{array}$

Physics (force)
$\begin{array}{cc}F=32m.& \text{Find}F\text{if}m=\mathrm{6.42.}\end{array}$

Physics (momentum)
$\begin{array}{cc}p=mv.& \text{Find}p\text{if}m=18\text{and}v=5.\end{array}$

Physics (momentum)
$\begin{array}{cc}p=mv.& \text{Find}p\text{if}m=44\text{and}v=9.\end{array}$

Physics (momentum)
$\begin{array}{cc}p=mv.& \text{Find}p\text{if}m=9.18\text{and}v=\mathrm{16.5.}\end{array}$

Physics (energy)
$\begin{array}{cc}E=\frac{1}{2}m{v}^2.& \text{Find}E\text{if}m=12\text{and}v=5.\end{array}$

Physics (energy)
$\begin{array}{cc}E=\frac{1}{2}m{v}^2.& \text{Find}E\text{if}m=8\text{and}v=15.\end{array}$

Physics (energy)
$\begin{array}{cc}E=\frac{1}{2}m{v}^2.& \text{Find}E\text{if}m=24.02\text{and}v=7.\end{array}$

Astronomy (Kepler’s law of planetary motion)
$\begin{array}{cc}{P}^2=k{a}^3.& \text{Find}{P}^2\text{if}k=1\text{and}a=4.\end{array}$

Astronomy (Kepler’s law of planetary motion)
$\begin{array}{cc}{P}^2=k{a}^3.& \text{Find}{P}^2\text{if}k=8\text{and}a=31.\end{array}$

Astronomy (Kepler’s law of planetary motion)
$\begin{array}{cc}{P}^2=k{a}^3.& \text{Find}{P}^2\text{if}k=4\text{and}a=\mathrm{5.1.}\end{array}$
( Hint: On the calculator, Type 5.1, Press $\begin{array}{||}\hline y^x\\ \hline\end{array}$ , Type 3, Press $\begin{array}{||}\hline =\\ \hline\end{array}$ , Press $\begin{array}{||}\hline \times \\ \hline\end{array}$ , Type 4, Press $\begin{array}{||}\hline =\\ \hline\end{array}$ .)

Astronomy (Kepler’s law of planetary motion)
$\begin{array}{cc}{P}^2=k{a}^3.& \text{Find}{P}^2\text{if}k=53.7\text{and}a=\mathrm{0.7.}\end{array}$

Business (profit, revenue, and cost)
$\begin{array}{cc}P=R-C.& \text{Find}P\text{if}R=3100\text{and}C=2500.\end{array}$

Business (profit, revenue, and cost)
$\begin{array}{cc}P=R-C.& \text{Find}P\text{if}R=4240\text{and}C=3590.\end{array}$

Geometry (area of a circle)
$\begin{array}{cc}A=\pi r^2.& \text{Find}A\text{if}\pi \text{is}\text{approximately}3.14\text{and}r=3.\end{array}$

Geometry (area of a circle)
$\begin{array}{cc}A=\pi r^2.& \text{Find}A\text{if}\pi \text{is}\text{approximately}3.14\text{and}r=11.\end{array}$

$\begin{array}{cc}t=21x+6.& \text{Find}t\text{if}x=3.\end{array}$

$\begin{array}{cc}t=21x+6.& \text{Find}t\text{if}x=97.\end{array}$

$\begin{array}{cc}E=m{c}^2.& \text{Find}E\text{if}m=2\text{and}c=186,000.\end{array}$
( Hint: The number 10 that occurs on the display a few spaces away from the other number on the display is the exponent of 10 in the scientific notation form of the number.)

$\begin{array}{cc}E=m{c}^2.& \text{Find}E\text{if}m=5\text{and}c=186,000.\end{array}$

An object travels on a horizontal line. The distance it travels is represented by $d$ and is measured in meters. The equation relating time of travel, $t$ , and distance of travel, $d$ , is
$d=t^2-4t+20$
Determine the distance traveled by the object if it has been in motion for 6 seconds.

In medicine, there are several rules of thumb used by physicians to determine a child’s dose, $D_c$ , of a particular drug. One such rule, Young’s Rule, relates a child’s dose of a drug to an adult’s dose of that drug, $D_a$ . Young’s Rule is
$D_c=\frac{t}{t+12}·D_a$
where $t$ is the child’s age in years. What dose should be given to a child 8 years old if the corresponding adult dosage is 15 units?

A hemispherical water tank of radius 6 feet has water dripping into it. The equation relating the volume, $V$ , of water in the tank at any time is $V=6\pi h^2-\frac{\pi }{3}{h}^3$ ,where $h$ represents the depth of the water. Using $3.14$ to approximate the irrational number $\pi$ , determine the volume of water in the tank when the depth of the water is 3 feet.

The equation $W=3.51L-192$ has been established by the International Whaling Commission to relate the weight, $W$ (in long tons), of a mature blue whale to its length, $L$ (in feet). The equation is only used when $L\ge 70$ . When
$0<L<70$
blue whales are considered immature. At birth, a blue whale is approximately 24 feet long. Determine the weight of a blue whale that measures 83 feet in length.

A relationship exists between the length of a cantilever beam and the amount it is deflected when a weight is attached to its end. If a cantilever beam 20 feet long has a 600 pound weight attached to its end, the equation relating beam length and amount of deflection is
$d=\frac{60x^2-x^3}{16,000}$
where $d$ is the amount of deflection measured in inches and $x$ is the length from the supported part of the beam to some point on the beam at which the amount of deflection is measured. Find the amount of deflection of the beam 17 feet from the supported end.

There is a relationship between the length of a suspension bridge cable that is secured between two vertical supports and the amount of sag of the cable. If we represent the length of the cable by $c$ , the horizontal distance between the vertical supports by $d$ , and the amount of sag by $s$ , the equation is $c=d+\frac{8s^2}{3d}-\frac{32s^4}{5d^3}$ . If the horizontal distance between the two vertical supports is 190 feet and the amount of sag in a cable that is suspended between the two supports is 20 feet, what is the length of the cable?

( [link] ) simplify $(4x^3{y}^8)(3x^{2}y)$ .

( [link] ) simplify $-|-8|$ .

( [link] ) Find the value of $4^{-2}·8^2-3^2$ .

( [link] ) For the expression $5(a+b)+2x^2$ , write the number of terms that appear and then write the terms themselves.

( [link] ) How many $x{y}^3\text{'}s$ are there in $5x^2{y}^5$ ?