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wolverine [178]
3 years ago
10

A ball is thrown vertically upward with an initial velocity of 48 feet per second. The distance s​ (in feet) of the ball from th

e ground after t seconds is s = 48 t -16 t ^2. ​(a) At what time t will the ball strike the​ ground? ​(b) For what time t is the ball more than 32 feet above the​ ground?

Mathematics
1 answer:
ra1l [238]3 years ago
5 0
Hello,

s=48t-16t²

a)
s=0==>16t(3-t)=0==>t=0 or t=3

b)
s>32==>48t-16t²>32===>16(t²-3t+2)<0
Δ=9-8=1
==>16(t-1)(t-2)<0

==>1<t<2 (negative between the roots)

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hodyreva [135]

Answer:

Final graph is attached.

Solution is x=2, y=3

Step-by-step explanation:

As we have to solve by graphing to let's graph y=2x-1 first.

we are free to plug any number for x say x=0 and x=2

when x=0 then y=2x-1 changes to

y=2(0)-1=0-1=-1

Hence point is (0,-1)

Similarly

when x=2 then y=2x-1 changes to

y=2(2)-1=4-1=3

Hence point is (2,3).

Now we graph both points (0,-1) and (2,3) then join them by a straight line.


We repeat exactly same process for other line y=-x+5 and get points (0,5) and (2,3)

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6 0
2 years ago
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9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?
ZanzabumX [31]
<h3>Answer:  17,280</h3>

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

=========================================================

Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

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Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.

6 0
3 years ago
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Gwar [14]

Answer:

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Collect like terms

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Answer:

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