1. The function H= -16T^2+80T+5 is a parabola of the form , so to find the maximum height of the ball, we are going to find the y-coordinate of the vertex of the parabola. To find the y-coordinate of the vertex we are going to evaluate the function at the point . From our function we can infer that and , so the point \frac{-b}{2a} [/tex]will be . Lets evaluate the function at that point:
We can conclude that the ball reaches a maximum height of 105 feet.
2. Since we now know that the maximum height the ball reaches is 105 feet, we are going to replace with 105 in our function, then we are going to solve for to find how long the ball takes to reach its maximum height:
We can conclude that the ball reaches its maximum height in 2.5 seconds.
3. Just like before, we are going to replace with 5 in our original function, then we are going to solve for to find how long will take for the ball to be caught 5 feet off the ground:
We can conclude that it takes 5 seconds for the ball to be caught 5 feet off the ground.
The answer is: " 2 :5 " ; or, write as: " 2/5 " . ________________________________________________________ The ratio of 'girls' to 'all students' is: "2: 5 " ; or, write as: " 2/5 ". ________________________________________________________ Explanation: ________________________________________________________ Given: The ratio of boys to girls is: " 3:2 " .
Problem: Find the ratio of "girls" to "all students: ________________________________________________________ Note: This ratio of "boys to girls", which is " 3 : 2 " ; ________________________________________________________ → can be expressed as " 3x: 2x" ;
in which the total number of students is: " 3x + 2x " = 5x " .
→ The total number of students is represented as: " 5x " . ________________________________________________________ → The ratio of "girls to boys" is: "2x : 3x" .
→ {that is; the "inverse" of the ratio of "boys to girls"} ; →{that is; the "inverse" of " 3x: 2x" } ; → which is: " 2x : 3x " . ________________________________________________________
The ratio of "girls" to "all students" is: "2x : 5x " ; or " 2x/5x " ; → Both "x" values cancel ; {since: " x/x = 1 "} ; _________________________________________________________ → and we have the answer: " 2 :5 " ; or, write as: " 2/5 " . _________________________________________________________ The ratio of 'girls' to 'all students' is: " 2 :5 " ; or, write as: " 2/5 ". _________________________________________________________
The two base angles cannot both be 92 degrees because they would add up to 184 which is more degrees than any triangle has. The apex angle (the top angle) therefore has 92 degrees.