GIVING BRAINLIEST, EASY 7TH GRADE MATH PROBLEM.

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:

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: 480 in cubed

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

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:

-77x^2 -84x

Step-by-step explanation:

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

just multiply -7 by each number within the parentheses.

Answer:

f ' [x] = 0

Step-by-step explanation:

Answer:

third option mechanical weathering

Step-by-step explanation:

in mechanical weathering it breaks the rock into smaller pieces . these smaller pieces are just like the bigger rock , just smaller .

Answer: Mechanical weathering

Step-by-step explanation:

Answer:

A, C, E

Step-by-step explanation:

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:

B is correct option

Step-by-step explanation:

The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.

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:

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:

4

Step-by-step explanation:

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:

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

Answer:

10/3 or 3 1/3

Step-by-step explanation:

-2 1/3=-5/3

-5/3-(-5)

-5/3+5

-5/3+15/3

10/3

answer : -2 1/3 - (-5) = [tex]2\frac{2}{3}[/tex]

explanation : we need to convert the mixed numbers to improper fractions, then find the LCD and combine.

step 1 : convert the mixed number to an improper fraction

ex: [tex]-\frac{7}{3}-(-5)[/tex]

step 2 : when there is a - in front of an expression in parentheses, change the sign of each term in the expression

ex : [tex]-\frac{7}{3}+5[/tex]

step 3 : calculate the sum

ex : [tex]\frac{8}{3}[/tex]

solution : [tex]\frac{8}{3}[/tex]

simplify: [tex]2\frac{2}{3}[/tex]

exact form : [tex]\frac{8}{3}[/tex]

decimal form : 2.66666666 (repeating)

mixed number form : [tex]2\frac{2}{3}[/tex]

hope this helps !

- audrey ♡

I just answered a so let's start with b :

______________________________

b. The equivalent resistance of series

resistances is equal to their sum

Thus :

equivalent resistance = 480 + 360

equivalent resistance = 840

_______________________________

c.

I = V ÷ R

I = 120 ÷ 840

I = 0.1428 A

_______________________________

d. 0.1428 A

_______________________________

e. 480 ===》 120 - ( 480 × 0.1428 ) =

120 - 68.544 =

51.456

360 ===》 120 - ( 360 × 0.1428 ) =

120 - 51.408 =

68.592

_______________________________

f. 480 ===》68.544 lower than battery

360 ===》 51.408 lower than battery

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:

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:

Yes

Step-by-step explanation:

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

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:

Step-by-step explanation:

6: 6, 12, 18, 24, 30, 36, 42, 48, 54

14: 14, 28, 42, 56

the LCM (least common multiple) is 42.

Answer:

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

Step-by-step explanation:

Answer:

wt actual hell

Step-by-step explanation:

Answer:

answering because my account got banned

Step-by-step explanation:

Answer:

8% como un decimal es 0.08%

Espero que te ayude!