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4 years ago

Which is the graph of y = ⌊x⌋ – 2?

Mathematics

1 answer:

Alexandra [31]4 years ago

5 0

Answer:

The third graph

Step-by-step explanation:

The Greatest Integer function (also called "floor" function. is in fact the one depicted on your first graph on the left. It indicates the integer part of the real number x.

So, if one translates such function two units down , as requested by the subtraction of 2 of the function y the problem shows, one ends up with the third graph depicted on the page.

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A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If the hei

ratelena [41]

The movement of the ping pong ball follows a exponential progression.

The expression for the k-th bounce is: $\mathbf{T_k = 235 \times (0.75)^k}$
The height after the 6th bounce is 41.82 ft
The total distance after the 12th bounce is 1584.84ft.
There will be 31457280 bacteria after a day and a half.

1. Ping pong ball

The given parameters are:

$\mathbf{a = 235}$ --- the initial height

$\mathbf{r = 75\%}$ --- the common ratio

(a) The expression after bouncing k times

To do this, we make use of

$\mathbf{T_n = a \times r^n}$

So, we have:

$\mathbf{T_n = 235 \times (0.75)^n}$

In this case; k = n.

So, the equation becomes

$\mathbf{T_k = 235 \times (0.75)^k}$

Hence, the expression for the k-th bounce is: $\mathbf{T_k = 235 \times (0.75)^k}$

(b) The height after bouncing 6 times

This means that k = 6.

So, we have:

$\mathbf{T_k = 235 \times (0.75)^k}$

$\mathbf{T_6 = 235 \times (0.75)^6}$

$\mathbf{T_6 = 41.82}$

Hence, the height after the 6th bounce is 41.82 ft

(c) The total distance after the 12th bounce

First, we calculate the total height after the 12th bounce using:

$\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}$

So, we have:

$\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}$

$\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}$

$\mathbf{S_k = 909.92}$

So, the total distance is:

$\mathbf{Distance = 2 \times S_k - a}$

$\mathbf{Distance = 2 \times 909.92 - 235}$

$\mathbf{Distance = 1584.84}$

Hence, the total distance after the 12th bounce is 1584.84ft.

(2) Cell division

The given parameters are:

$\mathbf{r = 2/2hr}$ --- rate

$\mathbf{a = 120}$ --- initial number of cells

$\mathbf{t = 18}$ --- number of 2 hours is a day and a half

So, the number of bacteria is:

$\mathbf{T_t = ar^t}$

This gives

$\mathbf{T_t = 120 \times 2^{18}}$

$\mathbf{T_t = 31457280}$

Hence, there will be 31457280 bacteria after a day and a half.

Read more about exponential functions at:

brainly.com/question/11487261

6 0

3 years ago

Read 2 more answers

How to solve ×+6y=13. 2×+y=15

saul85 [17]

Answer:

x, y = 7, 1

Step-by-step explanation:

x+6y=13 ............ (i)

2x+y=15 ........... (ii)

We will apply substitute method.

From equation (i), we can get,

x+6y=13

or, x = 13 - 6y .......... (iii)

Putting the value of x in equation (ii), we can get,

2x+y=15

or, 2 × (13 - 6y) + y = 15

or, 26 - 12 y + y = 15 [multiplying]

or, -11 y = 15 - 26 [Subtracting 26 from both the sides]

or, -11 y = -11

or, [(-11 y) ÷ (-11)] = [(-11) ÷ (-11)] [Dividing both the sides by -11]

or, y = 1

Therefore, the value of y = 1

Putting y = 1 in equation (iii), we get,

x = 13 - 6y

or, x = 13 - 6 × 1

or, x = 13 - 6

or, x = 7

Therefore, the value of x = 7.

Answer: x, y = 7, 1

3 0

3 years ago

Jessica is at a charity fundraiser and has a chance of receiving a gift. The odds in favor of receiving a gift are 5/12. Find th

Goryan [66]

Answer:

5/17

Step-by-step explanation:

This is a question to calculate probability from odds. The formula is given as:

A formula for calculating probability from odds is P = Odds / (Odds + 1)

From the question , we are told that the odds of receiving a gift is

= 5:12

The probability of Jessica receiving a gift =

Probability = Odds / (Odds + 1)

P = 5/12 / ( 5/12 + 1)

P = (5/12)/ (17/12)

P = 5/12 × 12/17

= 5/17

Therefore, the probability of Jessica. receiving a gift is 5/17.

3 0

4 years ago

How do you do 8b+12-b=8+7b+4 and plz show how you got it

lawyer [7]

8b+12-b=8+7b+4
7b+12=12+7b
-7b
7b-7b+12=12
-12 -12
0= 12-12
0=0

6 0

3 years ago

What is the volume of the water needed to completely fill the deep section of the pool? 9 ft 20 ft 18 ft 10 ft and 3ft

bulgar [2K]

I think its 97200 i am sorry if it is wrong

8 0

3 years ago