11. Simplify 3/ 2 - /2

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 = 1,4

B = 2,1

C = -4,-5

Step-by-step explanation:

The 90 degree anticlockwise rotation around the origin (0,0) would over lap the y axis around 1 and due to this the formation would show C point at -4,-5

Answer:

x=28.9

Step-by-step explanation:

tan(61)=x/16

Answer:

4

Step-by-step explanation:

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:

1, 3, and 4 would be correct answers

Step-by-step explanation:

1.) -x - 2x - 3y - 2y + 1 + 1 = -3x -5y + 2

2.) -3x + 2y + 3y + 2 = -3x + 5y + 2

3.) -3x - y - y - y - y - y + 2 = -3x - 5y + 2

4.) -x - x - x - y - y - y - y - y + 1 + 1 = -3x - 5y + 2

5.) x + x + x + y + y + y + y + y + 1 + 1 = 3x + 5y + 2

Hope this helps!

Answer:

He might have dropped it.

Step-by-step explanation:

If the manager didn't have any 5 dollar bills then he could have given him 3 dollars in ones and one 2 dollar bill. 2 dollar bills are rare now, he wanted the 2 dollar bill to keep for himself and also dropped one of the single dollar bills.

Answer:

Skateboard costs 125.73$

Step-by-step explanation:

Answer: 36

Step-by-step explanation: using long division you take 11 divide into 398 so first, 11 goes into 39, 3 times

you have 6 left, so keep the 6 and drop down the other 6

next 11 goes into 66, 6 times making it 396/11= 36  

hope this helps

Answer:

36

Step-by-step explanation:

396 divided by 11 is equal to 36

      36

11/[tex]\sqrt{396\\}[/tex]

   - 33

      066

    -  66

         0

This is where the diagonal line crosses the vertical y axis.

The y intercept always occurs when x = 0. The location of the y intercept in (x,y) form is (0,-1)

Answer:

=48

Step-by-step explanation:

Answer:

k/-8=-6

k=-6*-8

k=48

Step-by-step explanation:

Answer:

7.75+1.25x=31.50

Step-by-step explanation:

so in the end the answer is 19

Answer:

19 refills

Step-by-step explanation:

7.75+1.25x=31.50

Subtract the 7.75 on the other side..

1.25x=23.75

Then divide 1.25 from the 23.75

So, x which is the refills equal 19

Answer:

D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

A function is a relation where each input value is assigned to only one output value.

The domain of a function is the set of all input values, or x-values, for which the function is defined.

The range of a function is the set of all output values, or y-values, for which the function is defined.

Which A, B, & C are wrong. So D, is the one that makes the most sense.

Answer:

b

Step-by-step explanation:

Answer:

multiple by pie or 3.14........

Answer:

38 or 37.7 when not rounded

Step-by-step explanation:

12-32+[5-1]x2

-20+4x2

-20+8

=-12

The simplified form of the given expression is -12. Therefore, option A is the correct answer.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

The given expression is 12-32+(5-1)2.

Here, 12-32+4×2

= -20+8

= -12

Therefore, option A is the correct answer.

Learn more about the simplification here:

brainly.com/question/2804192.

#SPJ6

Answer:

$200.00

Step-by-step explanation:

because if you do a ratio:

12=40

60=?        

60 divided by 12 is 5, and whatever you do to the top you must do to the bottom, so then you gotta do 40 times 5=200

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:

8% como un decimal es 0.08%

Espero que te ayude!

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:

Yes

Step-by-step explanation:

Answer:

try doing 18.1

Step-by-step explanation:

hope this helps

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:

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 ♡

Answer:

radius = 17 units

equation of the circle =( x -h)^2 +(y -k) ^2 = r^2

or , (8 -(-7))^2 + (7-(-1))^2 = r^2

or, (8+7)^2 + (7 + 1)^2 = r^2

or, (15)^2 + (8)^2 =r^2

or, 225 + 64 = r^2

or 289 =r^2

or, 17^2 = r^2

or, r = 17 units

Please check the point by inserting centre(-7,-1) in place of (h,k ) and point in (x , y) and radius in r in the following equation

(x-h)^2 + (y - k)^2 = r^ 2.