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2 years ago

6

if there are 6 people at a party. if each person must shake hands with every other person at the party exactly once, how many ha

ndshakes will there be?

1 answer:

katovenus [111]2 years ago

6 0

One person will exactly shake five hands

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A ball is thrown up in the air, and it's height (in feet) as a function of time (in seconds) can be written as h(t) = -16t2 + 32

olga2289 [7]

Answer:

1) Using properties of the quadratic equation:

Here the height equation is:

h(t) = -16t^2 + 32t + 6

We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.

Then, the vertex of the quadratic equation will be the maximum.

Remember that for a general quadratic equation:

a*x^2 + b*x + c = y

the x-value of the vertex is:

x = -b/2a

Then in our case, the vertex is at:

t = -32/(2*-16) = 1

The maximum height will be the height equation evaluated in this time:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

2) Second method, using physics.

We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).

If the height equation is:

h(t) = -16*t^2 + 32*t + 6

the velocity equation is the first derivation of h(t)

Remember that for a function f(x) = a*x^n

we have that:

df(x)/dx = n*a*x^(n-1)

Then:

v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0

v(t) = -32*t + 32

Now we need to find the value of t such that the velocity is equal to zero:

v(t) = 0 = -32*t + 32

32*t = 32

t = 32/32 = 1

So the maximum height is at t = 1

(same as before)

Now we just need to evaluate the height equation in t = 1:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

4 0

3 years ago

Which of the following is the graph of the inequality y< -2x + 3?

zaharov [31]

Answer:

look at the photo

Step-by-step explanation:

Since the inequality is already written in y=mx+b, you can easily graph the line. +3 is the y intercept, so one point would be (0,3). -2 resembles the slope, so diagonally to the left, you would go up 2 and across 1. Also, since the sign is "<" you would graph with a dotted line. Then to know which side to shade, I always use the coordinate (0,0). I plug in 0 for both x and y to see if (0,0) satisfies the inequality. In this case it does, so you would shade on the side where (0,0) is located.

3 0

3 years ago

What is the explict rule for the geometric sequence? 9,6,4, 8/3 Enter your answer in the box. an=

ad-work [718]

Answer:

an = 9(⅔)^(n-1)

Step-by-step explanation:

The formula for explicit is: An = a1(r)^(n-1)

7 0

2 years ago

zysi [14]

Answer:

The laboure was charging 22% per hour

Step-by-step explanation:

8 0

3 years ago

Which expresión is equivalent to 8x-2y+x+x

Marta_Voda [28]

We can combine x + x and get 2x. So we have:
8x - 2y + 2x. Therefore 10x - 2y is equivalent.

8 0

3 years ago