Which is the expression 4 x 4 x4 x 3 x 3 x 2 x 2 x 2 x 2 written using
exponents?

Answer:

The maximum height a rider will experience is 55 feet.

Step-by-step explanation:

Let's start writing the function that defines the path of a seat on the new Ferris wheel. This function will depend of the variable ''t'' which is time.

[tex]X(t)=(x,y)[/tex]

In which [tex]X(t)[/tex] are the coordinates of the seat (the x - coordinate and the y - coordinate) that depend from time.

[tex]''x''[/tex] and [tex]''y''[/tex] are functions that depend from the variable ''t''.

For this exercise :

[tex]X(t)=[-25sin(\frac{\pi}{30}t);-25cos(\frac{\pi}{30}t)+30][/tex]

In order to find the maximum height a rider will experience we will study the behaviour of the y - component from the function [tex]X(t)[/tex].

The function to study is [tex]y(t)=-25cos(\frac{\pi}{30}t)+30[/tex]

To find its maximum, we will derivate this function and equalize it to 0. Doing this, we will find the ''critical points'' from the function.

⇒ [tex]y(t)=-25cos(\frac{\pi}{30}t)+30[/tex]  ⇒

[tex]y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)[/tex]

Now we equalize [tex]y'(t)[/tex] to 0 ⇒

[tex]y'(t)=0[/tex] ⇒ [tex]\frac{5}{6}\pi sin(\frac{\pi}{30}t)=0[/tex]

In this case it is easier to look for the values of ''t'' that verify :

[tex]sin(\frac{\pi}{30}t)=0[/tex]

Now we need to find the values of ''t''. We know that :

[tex]sin(0)=0\\\\sin(\pi)=0\\sin(-\pi)=0[/tex]

Therefore we can write the following equivalent equations :

[tex]\frac{\pi}{30}t=0[/tex] (I)

[tex]\frac{\pi}{30}t=\pi[/tex] (II)

[tex]\frac{\pi}{30}t=-\pi[/tex] (III)

From (I) we obtain [tex]t_{1}=0[/tex]

From (II) we obtain [tex]t_{2}=30[/tex]

And finally from (III) we obtain [tex]t_{3}=-30[/tex]

We found the three critical points of [tex]y(t)[/tex]. To see if they are either maximum or minimum we will use the second derivative test. Let's calculate the second derivate of [tex]y(t)[/tex] :

[tex]y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)[/tex] ⇒

[tex]y''(t)=\frac{\pi ^{2}}{36}cos(\frac{\pi }{30}t)[/tex]

Now given that we have an arbitrary critical point ''[tex]t_{n}[/tex]'' ⇒

If [tex]y''(t_{n})>0[/tex]  then we will have a minimun at [tex]t_{n}[/tex]

If [tex]y''(t_{n})<0[/tex] then we will have a maximum at [tex]t_{n}[/tex]

Using the second derivative test with [tex]t_{1},t_{2}[/tex] and [tex]t_{3}[/tex] ⇒

[tex]y''(t_{1})=y''(0)=\frac{\pi ^{2}}{36} >0[/tex] ⇒ We have a minimum for [tex]t_{1}=0[/tex]

[tex]y''(t_{2})=y''(30)=\frac{-\pi^{2}}{36}<0[/tex] ⇒ We have a maximum for [tex]t_{2}=30[/tex]

[tex]y''(t_{3})=y''(-30)=\frac{-\pi^{2}}{36}<0[/tex] ⇒ We have a maximum for [tex]t_{3}=-30[/tex]

The last step for this exercise will be to find the values of the maximums.

We can do this by replacing in the equation of [tex]y(t)[/tex] the critical points [tex]t_{2}[/tex] and [tex]t_{3}[/tex] ⇒

[tex]y(t_{2})=y(30)=55[/tex]

[tex]y(t_{3})=y(-30)=55[/tex]

We found out that the maximum height a rider will experience is 55 feet.

Answer:

B

Step-by-step explanation:

Answer:

A, C, E

Step-by-step explanation:

Answer:

42 square inches

Step-by-step explanation:

Area of a triangle = (1/2)(base)(height)

A = 1/2(12)(7)

A = 1/2(84)

A = 42

Answer:

10 / 26

Step-by-step explanation:

cos <Z = adjacent / hypotenuse

= YZ / XZ

= 10 / 26

Answer:

Cos of an angle by definition of its ratio is side adjacent/hypotenuse.  The side adjacent to angle Z cannot be the hypotenuse, so it has to be 10. he hypotenuse is 26.  Therefore, cosZ= 10/26 = 5/13

Step-by-step explanation:

MRK ME BRAINLIEST PLZZZZZZZZZZZZz

The probability of drawing a green Skittle, replacing it, and then drawing another green Skittle is 1/36

The distribution of the Skittle is given as:

Red = 6

Orange = 4

Yellow = 7

Purple = 3

Green = 4

The total number of skittle is:

Total = 6 + 4 + 7 + 3 + 4

Evaluate

Total = 24

The probability of selecting a green skittle is:

P(Green) = 4/24

So, the probability of selecting 2 green skittles is:

P = 4/24 * 4/24

Evaluate

P = 1/36

Hence, the probability of drawing a green Skittle, replacing it, and then drawing another green Skittle is 1/36

Read more about probability at:

https://brainly.com/question/25870256

#SPJ1

Answer: 480 in cubed

Step-by-step explanation: volume is length * width * height so 8*5*12=480

Answer:

Students who attend a private college are more likely to travel a farther distance to attend college.

Step-by-step explanation:

Answer:

1 / 9

Step-by-step explanation:

Given the number cube :

(11,12,11,12,20,20)

Spinner : (G, H, J)

Probability = required outcome / Total possible outcomes

P(20) = 2 / 6 = 1/3

P(H) = 1 / 3

P(20 and H) = P(20) * P(H) = 1/3 * 1/3 = 1 /9

Answer: 7.1 yd

Step-by-step explanation:

the formula for arc length is 2πr(x/360),  x being the central angle

input the values, so the equation would be 2π9(45/360), which equals 7.1

Answer:

um I think it's f I'm not sure tho

Answer:

Please check my interpretation of your written equation.

Step-by-step explanation:

f(x) = (-x^2 - 2x - 2)/(x-2)

Wild.  See attached graph.

Answer:

the final score of chase is 170

Step-by-step explanation:

Given that

The chase final score would be double his score after the four rounds

So the chase final score is

= (Round 1 score + round 2 score + round 3 score + round 4 score) × 2

= (-35 + 45  + 90 - 15) × 2

= 170

Hence the final score of chase is 170

The same would be considered and relevant

Answer: 46857578087543677536

4x10=40 16 with a remainder of 1

Answer: I think it is $37.50

Step-by-step explanation: You first have to divide 10 by 4 to know how much money it was for 1 pound and I got 2.5. Then I multiplied 2.5 by 15 to get 37.5 which is $37.50.

Answer: 36

Step-by-step explanation:

Given

The ratio of Mary's to Helen's necklaces is 25:9

Mary has 100 necklaces

Suppose Helen has x necklaces

Therefore the ratio can be written like

[tex]\Rightarrow \dfrac{25}{9}=\dfrac{100}{x}\\\\\Rightarrow x=\dfrac{100}{25}\times 9\\\\\Rightarrow x=4\times 9\\\Rightarrow x=36[/tex]

So, Helen has 36 necklaces

Answer:

ur english is so bad i can barely discern what ur trying to say and the correct answer is 5

Step-by-step explanation:

Answer:

x = -7

Step-by-step explanation:

Seven times a number and seven is equal to six times a number.

Word problems can be tricky no matter what level of math or science you are in.

First look at the question for words that indicate mathematical symbols.

"times" indicates multiplication

"and" indicates addition

"a number" means we have a variable, x, to solve for

Now we can go from left to right and write it in a mathematical equation

7x + 7 = 6x

Then, solve for x

7x + 7 = 6x

7 = 6x - 7x

7 = -1x

7/-1 = x

x = -7

Finally, we check our work.

7x + 7 = 6x

7(-7) + 7 = 6(-7)

-49 + 7 = -42

-42 = -42 √

The answer is x = -7

Answer:

a.option is the correct answer

Answer:

The correct answer is [tex]\frac{2}{16}[/tex].

Step-by-step explanation:

Since there are 8 cards and two sides to the coin, that means there will be a total of 16 different outcomes. Out of the 16 possible outcomes, 2 of them meet the requirement of picking a vowel card and landing on heads, so the fraction to represent the situation would be [tex]\frac{2}{16}[/tex].

Answer:

2/16

Step-by-step explanation:

Answer:

f ' [x] = 0

Step-by-step explanation:

Answer:

wt actual hell

Step-by-step explanation:

Answer:

answering because my account got banned

Step-by-step explanation:

9514 1404 393

Answer:

  C  413.3K

Step-by-step explanation:

Temperature is proportional to volume and pressure. Pressure has decreased by a factor of 2/3, and volume has increased by a factor of 400/200 = 2. So, the new temperature is ...

  (310 K)(2/3)(2) = 413 1/3 K ≈ 413.3 K

Answer:

Hi! I'll just help qwq

The first option should be the correct answer!

Step-by-step explanation:

The sun is in the center, and all other planet orbits/goes around the sun.

The second option is a theory of which old people believed. Now we know for sure that the sun is in the center, and we orbit around it.

Answer:

5

Step-by-step explanation:  1/2 probability, 10 / 2 equals 5

Answer:

The best prediction possible for the number of times it will land on tails is 5 times.

Step-by-step explanation:

Because there are two sides to a coin, that means there will be a 50% chance of landing on a side. Since you are flipping 10 coins, the best prediction to make is that 50% of the flips, or 5 flips, will result in tails.

Answer:

the answer is y=40

Step-by-step explanation:

y/8=5

y=8*5

y=40

Answer:

5

Step-by-step explanation:

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate. Also called "Ordinate"        

I hope this helped!

Answer:

-77x^2 -84x

Step-by-step explanation:

[tex] - {77x}^{2} - 84x[/tex]

just multiply -7 by each number within the parentheses.

Answer:

box-and-whisker plot

line graph

stem-and-leaf plot

scatter plot

histogram

Step-by-step explanation:

Answer:

stem-and-leaf plot

Step-by-step explanation:

trust me this is the right one