6.3 Models and applications  (Page 6/9)

Write the model equation for the cost of renting a truck with plan B.

Find the number of miles that would generate the same cost for both plans.

If Tim knows he has to travel 300 mi, which plan should he choose?

$A=P(1+rt)$ is used to find the principal amount P deposited, earning r % interest, for t years. Use this to find what principal amount P David invested at a 3% rate for 20 yr if $A=\text{\$}\mathrm{8,000.}$

The formula $F=\frac{m{v}^2}{R}$ relates force ( F ), velocity ( v ), mass ( m ), and resistance ( R ). Find $R$ when $m=45,$ $v=7,$ and $F=245.$

$F=ma$ indicates that force ( F ) equals mass ( m ) times acceleration ( a ). Find the acceleration of a mass of 50 kg if a force of 12 N is exerted on it.

$Sum=\frac{1}{1-r}$ is the formula for an infinite series sum. If the sum is 5, find $r.$

Solve for W : $P=2L+2W$

Use the formula from the previous question to find the width, $W,$ of a rectangle whose length is 15 and whose perimeter is 58.

Solve for $f:\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$

Use the formula from the previous question to find $f$ when $p=8\text{and }q=13.$

Solve for $m$ in the slope-intercept formula: $y=mx+b$

Use the formula from the previous question to find $m$ when the coordinates of the point are $\left(4,7\right)$ and $b=12.$

The area of a trapezoid is given by $A=\frac{1}{2}h\left(b_1+b_2\right).$ Use the formula to find the area of a trapezoid with $h=6,b_1=14,\text{ and }{b}_2=8.$

Solve for h: $A=\frac{1}{2}h\left(b_1+b_2\right)$

Use the formula from the previous question to find the height of a trapezoid with $A=150,b_1=19,\text{ and }{b}_2=11.$

Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find the length and width. Use the perimeter formula $P=2L+2W.$

Distance equals rate times time, $d=rt.$ Find the distance Tom travels if he is moving at a rate of 55 mi/h for 3.5 h.

Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of 60 mi/h for 6.75 h.

What is the total distance that two people travel in 3 h if one of them is riding a bike at 15 mi/h and the other is walking at 3 mi/h?

If the area model for a triangle is $A=\frac{1}{2}bh,$ find the area of a triangle with a height of 16 in. and a base of 11 in.

Solve for h: $A=\frac{1}{2}bh$

Use the formula from the previous question to find the height to the nearest tenth of a triangle with a base of 15 and an area of 215.

The volume formula for a cylinder is $V=\pi r^{2}h.$ Using the symbol $\pi$ in your answer, find the volume of a cylinder with a radius, $r,$ of 4 cm and a height of 14 cm.

Solve for h: $V=\pi r^{2}h$

Use the formula from the previous question to find the height of a cylinder with a radius of 8 and a volume of $16\pi$

Solve for r: $V=\pi r^{2}h$

Use the formula from the previous question to find the radius of a cylinder with a height of 36 and a volume of $324\pi .$

The formula for the circumference of a circle is $C=2\pi r.$ Find the circumference of a circle with a diameter of 12 in. (diameter = 2 r ). Use the symbol $\pi$ in your final answer.

Solve the formula from the previous question for $\pi .$ Notice why $\pi$ is sometimes defined as the ratio of the circumference to its diameter.