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3 years ago

Plz help question in the picture help me plz

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2 answers:

Aliun [14]3 years ago

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The answer is true, true, true!!

Nina [5.8K]3 years ago

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Answer:

true, false, true

Step-by-step explanation:

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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

What is the equation of the parabola with vertex (6,7) and focus (7,7)?

Delicious77 [7]

Answer:

Step-by-step explanation:

If you plot these points on a coordinate plane, you see that they are on the same horizontal line, y = 7, with the focus 1 unit to the right of the vertex. This means that the parabola is a sideways opening parabola, to the right, to be more specific. That means that it has the basic vertex form

$4p(x-h)=(y-k)^2$

where p is the distance in units from the vertex to the focus, h is the first coordinate in the vertex, and k is the second coordinate in the vertex. For us, p = 1, h = 6, and k = 7. Now we will just fill the vertex form of the equation in with our values:

$4(x-6)=(y-7)^2$