Question 139795
1.A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after 1 second is s =160t - 160t^2. For what is the interval of time is the ball less than 336 feet above the ground (after it is tossed until it returns to the ground)
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I think the equation for this type of problem would be s = 160t - 16t^2:
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Find the interval above 336 ft
Arrange as a quadratic equation
-16t^2 + 160t < 336
-16t^2 + 160t - 336 > 0
Simplify and change the signs, divide equation by -16
+t^2 - 10t = 21 = 0
Factor
(t-7)(t-3) = 0
t = 7; t = 3
Here is the graph of the equation  y = -16t^2 + 160t
You can see the ball will be above 336 ft during the 4 sec interval between 3 sec and 7 sec.
{{{ graph( 300, 200, -4, 12, -100, 500, -16x^2 + 160x) }}}
You can also see that the ball will be less than 336 ft during the intervals
0 to 3 sec
7 to 10 sec
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2.Use the compound interest formulas A=P(1 +r/n)^nt and A =P^ert to solve.
Suppose you have 9000 dollars to invest. Which investment yields the greater return over 5 years: 6.25% compounded continuously or 6.3% compounded semi annually?
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Find the interest compounded semi-annually at 6.3% for 5 years
A = 9000 * (1 + .063/2)^(2*5)
A = 9000 * (1.0315)^10; use a calc
A = 9000 * 1.363617
A = 12,272.55
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Find it a continuous interest after 5yrs at 6.25%:
Here I think the continuous interest formula should be P*e^rt
A = 9000 * e^(.0625*5); use a calc
A = 9000 * 1.366838
A = 12,301.54
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3. Graph the polynomial function f(x) = -6x^4 + 9x^3:
If you factor this, it will give you a range of the values of x to plot
-3x^3(2x - 3)= 0
So you have x = 0 and x = +1.5, so plot this from -1 to + 2 at .5 intervals
 x | y
-------
-1 | -15
-.5| -1.5
 0 | 0
+.5|+.75
+1 |+3
1.5| 0
 2 |-24
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Your graph should look like this:
{{{ graph( 300, 200, -2, 3, -20, 6, -6x^4 + 9x^3) }}}
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Hope this helps you out.