11. An object is propelled upward at an angle 0, where 45° initial velocity of vo (measured in feet per second) from the base of a plane that makes an angle
of 45 degrees with the horizontal. If air resistance is ignored, the distance R that it travels up the
inclined plane is given by the function
võvz
R(O) = cos(() [sin(O) - cos(0)]
16
a.
b.
Show that RO)
va va
[sin(20) - cos(20) - 1]
32
In calculus, you will be asked to find the angle that maximizes R by solving the
following equation
sin(20) + cos(20) = 0
Solve the equation for theta:
C. What is the maximum distance R if Vo = 25 feet per second?
d. Graph R = R(O), where 45° more than equal to 90°, and the angle theta maximizes the distance

Which of the following transformations does not preserve congruence? * 5 points a. (x, y) → (y − 3, x − 3) b. (x, y) → (x + 5, y − 1) c. (x, y) → (y + 9, −x + 2) d. (x, y) → (3x + 1, 3y − 2)

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

Prism m and pyramid n have the same base area and the same height. cylinder p and prism q have the same height and the same base perimeter. cone z has the same base area as cylinder y, but its height is three times the height of cylinder y. the figures and have the same volume.