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LenKa [72]
3 years ago
11

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function

h=-16x^2+36t+5. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
Mathematics
1 answer:
fenix001 [56]3 years ago
3 0
There are many ways to solve this...however without calculus or derivations from physics, the simplest is to find the midpoint of the two zeros of the function:

(*note, that this will occur for -b/(2a), where a and b are from the general quadratic ax^2+bx+c.  So the time when the ball is at its maximum height is -36/(2*-16),  -36/-32, 1.125 seconds.  And the maximum/minimum height will be (4ac-b^2)/(4a), 25.25 ft.  In general the vertex, minimum/maximum point of a parabola will always be (-b/(2a), (4ac-b^2)/(4a) if you care to commit such to memory.)

So back to the midpoint of the zeros.  Simply use the quadratic formula to find when h=0

t=(-b±√(b^2-4ac))/(2a)

t=(-36±√1616)/-32  regardless of what is under the radical the midpoint for t is simply

t=-36/-32=1.125 seconds

You then can plug this value in for t in the equation h(t) to get the maximum height of 25.25 ft.

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3 years ago
Write an equation for the following tile pattern.<br><br> Figure 2<br><br> Figure 3<br><br> Figure 4
oksano4ka [1.4K]

Answer:

The general equation following the pattern becomes is 7 + (n - 1)×2

Where, n = The figure number - 1

Step-by-step explanation:

The pattern in the question can be described as follows;

Figure 2 = (5 + 2) squares boxes = 7 squares boxes

Figure 3 = (5 + 2 + 2) squares boxes

Figure 4 = (5 + 2 + 2 + 2) squares boxes

Therefore, the number of squares boxes per figure, form an arithmetic progression (a + (n - 1)d) with the first term a = 7, the common difference d = 2, and the n = the nth term of the series, such that the general equation following the pattern becomes;

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3 years ago
Estimate using a rate per 100 of 74% of 315. 89% of 195
LiRa [457]
<span><span>1.       </span>Given numbers:
74 % of 315
89% of 195

now, let’s solve the first given numbers:
=> 74% of 315
=> 315 is the 100%
Let’s convert 74% into decimals
=> 74% = .74
=> 315 * .74 = 233.1, the value of 74% of 315
Let’s solve the second given:
=> 89% of 195
where 195 is the 100%
=> 89% = .89
=> 195 * .89
=> 173.55, the value of 89% of 195</span>



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