Given the vectors ⃗⃗ = 〈2, 3, 5〉, ⃗ = 〈−2, 5, 0〉, ⃗⃗ = 〈−3, 2, 7〉 calculate:
a) ⃗⃗ + ⃗ + ⃗⃗

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

1. Ping pong ball

The given parameters are:

[tex]\mathbf{a = 235}[/tex] --- the initial height

[tex]\mathbf{r = 75\%}[/tex] --- the common ratio

(a) The expression after bouncing k times

To do this, we make use of

[tex]\mathbf{T_n = a \times r^n}[/tex]

So, we have:

[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]

In this case; k = n.

So, the equation becomes

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

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

(b) The height after bouncing 6 times

This means that k = 6.

So, we have:

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]

[tex]\mathbf{T_6 = 41.82}[/tex]

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:

[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]

[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]

[tex]\mathbf{S_k = 909.92}[/tex]

So, the total distance is:

[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]

[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]

[tex]\mathbf{Distance = 1584.84}[/tex]

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

(2) Cell division

The given parameters are:

[tex]\mathbf{r = 2/2hr}[/tex] --- rate

[tex]\mathbf{a = 120}[/tex] --- initial number of cells

[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half

So, the number of bacteria is:

[tex]\mathbf{T_t = ar^t}[/tex]

This gives

[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]

[tex]\mathbf{T_t = 31457280}[/tex]

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

Read more about exponential functions at:

https://brainly.com/question/11487261

Answer:

2a) because they are continuous lines that don't intercept

Step-by-step explanation:

Answer:

2a) They all have the slope of 2x.

2b) R) y = 2x-3

2c) R is the lowest line because the b value (-3) has the least value out of the 3 choices.

Answer:

C) Exponential

Step-by-step explanation:

If you divide the consecutive y-values, you'll get a consistent result of 2:

16/8 = 2

8/4 = 2

4/2 = 2

2/1 = 2

This type of pattern corresponds to an Exponential Function.        

Answer:

To divide two fractions, flip the second fraction and change the operation from division to multiplication. Therefore, there are 20 fifths in four wholes

(A)

Answer:

43

Step-by-step explanation:

274 would be absurd and 83 would be close to a right angle which that angle is no where near. It looks like half a right angle meaning 45 and 43 is the closest to that so I think its 43

Answer:

See below:

Step-by-step explanation:

The first one is 4 since if we turn if 90 degrees 4 times we will get the same shape 4 times.

The second one is 1 since we will only get it after a 360 degree rotation once,

The third one is once since we wont ever get the same shape since the arrow but only after a 360 degree rotation.

The fourth one is only once since we cant rotate a 3 sided object in 4 ways, hence its only once

The fifth one is twice since it will be the same at 180 and 360 degrees.

Answer:

d

y

d

x

=

−

4

3

x

3

Explanation:

y

=

2

3

x

2

=

2

3

x

−

2

Applying the power rule:

d

y

d

x

=

2

3

⋅

(

−

2

)

x

−

3

=

−

4

3

x

3

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

A is equal to the amount of students that were absent.

Answer:

Olivia typed speed per minutes is 54 words

Step-by-step explanation:

Given:

Olivia typed 36 word in 2/3

Solution:

By Unitary method, calculate the speed of typing by Olivia as-

2/3 Minutes → 36 Words

1 Minutes → 36 ÷(2/3) Words

1 Minutes → 36x3÷2 Words

1 Minutes → 54 Words

Therefore Olivia typed speed is 54 word.

Answer:

3125

Step-by-step explanation:

5*5*5*5*5

Answer:

8

Step-by-step explanation:

Answer:

x= 98

First, you have to find what the third angle is so;

180-53-45=82

The third angle in 82.  

A straight line is 180º. So you need to subtract 180-82 to get 98.

Step-by-step explanation:

Answer:

Orange and apple

Step-by-step explanation:

Mark brainliest, isaac farts all the time u don’t want him to fart on u next

Explanation:

A solution is where the lines intersect. Graph A shows exactly one solution, and it is at (-2,2)

Graph B doesn't have any solutions since the lines are parallel, and parallel lines never intersect. We consider this system to be inconsistent.

Graph C has infinitely many solutions. The two lines perfectly overlap, meaning there are infinitely many intersection points. All solutions here are of the form (x,y) = (x,2x-1)

Answer:

$135

Step-by-step explanation:

120+(12*1.25)

120+15

135

Answer:

-28

Step-by-step explanation:

You have to do the parenthesis 1st, then the [tex]\frac{8}{3}[/tex], and multiply the result :D

Answer:

134

Step-by-step explanation:

So assuming x is the score on the computer science exam, it would take 300*0.32+x=500*0.46=230 to get x=134

Answer:  The lines WX and YZ are parallel.

Step-by-step explanation:  We are given to check whether the lines WX and YZ are parallel, perpendicular or neither if the co-ordinates of the endpoints of both the lines are

W(3,4), X(5,7), Y(8,2) and Z(6,-1).

We know that the slope of a straight line passing through the points (a, b) and (c, d) is given by

m = d-b/c-a

So, the slope of the line WX is

m1 = 7-4/5-3 = 3/2

and the slope of line YZ is

m2 = -1-2/6-8 = -3/-2 = 3/2

Since , we get  m1 = m2, so the two lines WX and YZ are parallel.

Thus, the lines WX and YZ are parallel.

They are not perpendicular, so if you mistyped something and it was parallel that would be the answer, or the answer is neither the mysterious angle form or perpendicular. Hope this helps.

Her score in computer to get a proportionally weighted average of 46% will be 134.

The total score for both subjects = 200 + 300 = 500

Since the proportionally weighted average is 46%, then her score will be:

= 46% × 500

= 0.46 × 500

= 230

Since she had 32% for her statistics test, which was out of a total of 300. Her score will be:

= 32% × 300

= 0.32 × 300

= 96

Therefore, her score in computer will be:

= 230 - 96

= 134

Read related link on:

https://brainly.com/question/24429956

Answer:

square root of 25 is 5

Step-by-step explanation:

when you take the numbers that multiply together to make 25 which in this case is 5 5*5=25

Answer:

side HG would be proud of the side EF and parallelogram EFGH

Answer:

4^-14

Step-by-step explanation:

4^-5 x 4^-4 x 4^-5 = 4^-14

1/4^14

Answer:

[tex] \rm y = x + 16 [/tex]

Step-by-step explanation:

A function is given to us and we need to write the inverse of the function in slope intercept form . The given function is ,

[tex]\rm\implies f(x) = x - 16 [/tex]

Let ,

[tex]\rm\implies y = f(x)[/tex]

So that ,

[tex]\rm\implies y = x - 16 [/tex]

Interchange x and y ,

[tex]\rm\implies x = y - 16 [/tex]

Solve for y ,

[tex]\rm\implies y = x + 16[/tex]

Now replace ,

[tex]\rm\implies y = f^{-1}(x) [/tex]

We have ,

[tex]\rm\implies f^{-1}(x) = x+16 [/tex]

And in slope intercept form ,

[tex]\rm\implies \boxed{\pink{\frak {y = x +16}}}[/tex]

Answer:

i dont get it

Step-by-step explanation:

Answer:

3a^2

Step-by-step explanation:

2a-2a is equivalent to 0 there by making 3a^2 remaining

Answer:

3/8"

Step-by-step explanation:

Reduce the fraction.  The numerator and denominator are both divizable by 2 which leaves 3/8