"If an average-sized man with a parachute jumps from an airplane, he will fall 12.5(0.2^t-1) +20t feet in t seconds. How long will it take him to fall 140 feet? (Round your answer to two decimal places.)"
Unless you are familiar with the standard formula for the solution of a cubic equation, you will need to use a numerical method here, such as the following:
"What is the equation of the line that passes through the point (5,1) and has a slope of 6/5?"
Straight line equation: y = (6/5)x + c
Find c by substituting the (x,y) vaues of the given point:
1 = (6/5)*5 + c
I'm sure you can continue from here.
"During a football/soccer match, a goalkeepers save rate was 33 1/3%. .After saving the next shot, it rose to 40%. How many more consecutive shots on target must be saved to raise the save rate to 60%?"
Somewhat unclear question (e.g. what's the significance of the word 'respectively' here?). However, one interpretation is as follows where the largest area is between the radius 7 and radius 1 circles:
Rewrite \(p^2-9s^2+6pq+9q^2\) as \(p^2+6pq+(3q)^2-9s^2\). Rewrite the first three terms: \((p+3q)^2-9s^2\)
This is the difference of two squares, so can be written as \((p+3q+3s)(p+3q-3s)\)
"In a set of four numbers, the first three are in a geometric sequence and the last three are in an arithmetic sequence with a common difference of 6. If the first number is the same as the fourth, find the four numbers."
Set h = 0, (because the ground is at zero height here) then solve the quadratic -16t2 + 32t + 128 = 0 for t. There will be two values, one negative and one positive. Take the positive value.
Let the two numbers be a and b:
a = 5b + 6
a + b = 24
Replace a in the second equation using the first equation, then simplify to find b. Substitute b back into the the first equation to find a.
Can you take it from here?
This is unclear!
+33652 
