__________ A ball bounce function is given by $f\left(x\right)=100\mathrm{\times}{0.85}^{x}$ where x is the bounce number and f(x) is the bounce height. Evaluate this function at x = 10 bounces.
__________ A ball bounce function is given by $f\left(x\right)=100\mathrm{\times}{0.85}^{x}$ where x is the bounce number and f(x) is the bounce height. Solve for the bounce number x where f(x) is 8.73542 centimeters high .
__________ The compound interest formula is given by:
$A=P{(1+\frac{r}{n})}^{nt}$
For a principal P of $460, an interest rate r of 0.07, compounded n = 4 times a year, calculate the Amount A after a time t of nineteen years.
__________ The continously compounding interest formula is given by:
$A=P{e}^{rt}$
For a principal P of $460, an interest rate r of 0.05, calculate the Amount A after a time t of ten years.
Transit has a growth rate given by the following table:
Age in months post-conception
Actual mass in kilograms
9.0
3.35
10.2
4.69
11.3
5.97
13.2
7.59
15.3
8.13
21.7
9.29
33.7
10.91
Enter the data in a LibreOffice.org Calc spreadsheet. Insert a logarithmic trend line and show the equation. Write the equation below:
___________ Transit has a growth rate curve given by the equation above. Use the logarithmic equation to predict the mass of the baby at 27 months post-conception.
__________ Transit has a growth rate curve given by the equation above. Use the logarithmic equation to solve for the month in which the baby will have a mass of 10 kilograms.
The soil on Bikini atoll in the Marshall Islands is contaminated by the radioactive element Cesium-137. Like all radioactive elements, Cesium-137 will eventually decay into non-radioactive elements. The rate of decay is an exponential decay given by the formula
$N=P{e}^{\left(-0.023t\right)}$
where P is the starting amount of Cesium in the soil in kilograms, t is the number of years, and N is the remaining amount of radioactive Cesium after that number of years.
__________ If there were 100 kilograms of Cesium-137 in the soil in 1954 as a result of the Castle Bravo thermonuclear hydrogen bomb test, how many kilograms will be in the soil now in 2011?
__________ How many years after 1954 until there is only 1 kilogram of the original 100 kilograms of Cesium-137 left in the soil?
The circle has a radius r = 100. The shape is a seven sided heptagon. The center of the circle is (100,100). The coordinate system is SVG with y values increasing as one moves down the page. θ is theta. φ is phi.
( _____ , _____ ) What are the coordinates of A, the point at the very top of the seven-sided heptagon?
__________ Given r = 100 and θ = 38.57°, calculate the length of B, the adjacent side.
( _____ , _____ ) What are the coordinates of point C?
__________ Given r = 100 and θ = 38.57°, calculate the length of D, the opposite side.
( _____ , _____ ) What are the coordinates of point E?
__________ Given r = 100 and φ = 25.71°, calculate the length of F, the adjacent side.
( _____ , _____ ) What are the coordinates of point G?
__________ Given r = 100 and φ = 25.71°, calculate the length of H, the opposite side.
( _____ , _____ ) What are the coordinates of point I?
A RipStik was ridden across a wet cloth towel soaked in water with food color. The RipStik was then swizzled across a large sheet of presentation paper. The swizzle wave can be seen in the diagram below.
λ = _______________ Determine the wavelength λ of the RipStik swizzle wave.
a = _______________ Determine the amplitude a of the RipStik swizzle wave.
f(x) = ______ sin( _________ x). Given the general form
$f\left(x\right)=a\mathrm{sin}\left(\frac{2\pi x}{\lambda}\right)$,
write the equation for the RipStik swizzle wave.
________ Calculate
$\mathrm{arcsin}\left(\frac{\sqrt{3}}{2}\right)$, report the result in degrees.
__________ For a right triangle with an opposite side of length 140 and a hypotenuse of 221, find the angle θ in degrees.
__________ For a right triangle with an opposite side of length 140 and a hypotenuse of 221, find the length of the adjacent side x.
______, _____ Find the other two numbers in a Pythagorean triple where one of the three numbers is 28.
_________ The equation for a projectile is given by:
$\text{distance}=\frac{2{v}^{2}\mathrm{sin}\left(\text{\theta}\right)\mathrm{cos}\left(\text{\theta}\right)}{\mathrm{9.8}}$
For a velocity v of 28 m/s, and an angle of 45°, calculate the distance d.
_________ Solve for the velocity v:
$\frac{2{v}^{2}\mathrm{sin}\left(40\right)\mathrm{cos}\left(40\right)}{\mathrm{9.8}}=\mathrm{10.0491}$ with the angles given in degrees.
Solve: 49.4109 sin(x) cos(x) = 24.3301 for 0 < x < π/2.
Report the angle x in radians for the solution between 0 and π/2. Find the answer in decimal radians, not in arctan form. If there is more than one answer, report both. Note that π/2 is also equal to 1.57.
__________ For a force F of 30 Newtons, a distance of travel d of 800 meters, and an angle theta θ of 35°, use the dot product to calculate the work done pulling a toy wagon with the handle held at that angle.
__________ For a force F of 30 Newtons, a lever arm distance d of 0.4 meters, and an angle theta θ of 35°, use the cross product to calculate the torque on a toy wagon with the handle held at that angle.
Solve:
(x − 5)² + (y − 4)² = 49,
(x + 5)² + (y + 4)² = 81 for x and y. List all real solutions. Keep only two decimal places!
____________ Calculate the magnitude for the vector {696, 697}.
____________ Calculate the angle relative to the horizontal axis for the vector {696, 697}.
______________________ What is the name of the shape?