Tough math problem solving help

1. matt has a total of $580 in bills. he has 76 bills consisting of $5 and $10 bills. how many of each does he have?

^ is it 38?

this is the hardest one: a golf ball is hit and its height is given by h=-4.9t^2 + 29.4t. where h is the height in metres, and t is the time in seconds.

a) at what time is the golf ball on the ground
b) at what time does the golf ball reach its max height
c) what is the balls max height?

matt has a total of $580 in bills. he has 76 bills consisting of $5 and $10 bills. how many of each does he have?

let x = # of $ 10 bills
let y = # of $ 5 bills

then,

x + y = 76 [he has 76 bills]
10x + 5y = 580 [matt has a total of $580 in bills]

solve the system...

10(76 - y) + 5y = 580
760 - 10y + 5y = 580
5y = 180
y = 36
x = 40

check: 10(40) + 5(36) = 400 + 180 = $580

why did you say 38...guessing is not recommended !

one problem at a time...read your textbook...practice

By using a graphing calculator....

a) when the ball hits the ball (or the height/ y value is 0), the time is 6 seconds
b) Time is 2.9 repeating seconds (or 3 seconds if you wish to round)
c)Max height is 44.1 meters.

For b and c, you must graph the equation, calculate the max value and you will get a coordinate pair.
The coordinate pair is (2.9 repeating, 44.1) x is time so 2.9 seconds while y is height so 44.1 meters.

1) Let f = # of $5 bills and t = # of $10 bills.
5f + 10t = 580
f + t = 76
solve the system of equations:
f = 76 - t
5(76 - t) + 10t = 580
380 + 5t = 580
5t = 200
t = 40
f = 76 - 40 = 36

2)
a) ball is on the ground when h = 0
0 = -4.9t^2 + 29.4t
0 = -4.9t(t - 6)
-4.9t = 0 or t - 6 = 0
t = 0 or t = 6
Note that the ball is on the ground twice, when it is hit and when it lands.
b) max height occurs when h '(t) = 0 and h ''(t) < 0.
h '(t) = -9.8t + 29.4
0 = -9.8t + 29.4
t = 3
h ''(t) = -9.8 < 0 for all t so we know height is at a maximum when t = 3.
c) maximum height = h(3) = -4.9(3^2) + 29.4(3) = 44.1m

1) F+T=76 so 5F+5T=380
5F+10T=580 subtract
5T = 200
T = 40
F = 36
40 $10 bills and 36 $5 bills
2) h=-4.9t^2 + 29.4t
a) 0 = -4.9t^2 + 29.4t
0 = t(29.4-4.9t)
t = 0 seconds and 6 seconds
b)dh/dt = -9.8t+29.4 = 0 for maximum
t = 3 seconds
c) h(3) = -4.9*9+29.4*3 =
44.1 feet

1) x+y = 76
5x+10y = 580

2a)h = o
b) t=-b/2a
c)t=-b/2a substitute to find h