the lateral surface area of cylinder R is 33π find the height of the cylinder​

To make sure the flip is in unison, after 4  seconds should the flip occur, as given by the option C: 4 seconds.

Synchronized motion is a motion of two or more system which goes in syncronization with each other.

For this case, the flip will occur such that both gymnasts are synchronized and flip is unison (simultaneous).

For that, we need the time(x) and the height (y) same.

Since the motion paths are:

[tex]y= -(x-5)^2 + 3\\\\y = -3(x-3)^2 + x + 1[/tex]

Therefore, we need to find the values of x for which same y comes as output.

Let  x =  t be the time for which the height y is same, then:

[tex]-(t-5)^2 + 3 = -3(t-3)^2 + t + 1[/tex] = height achieved by both gymnasts.

Solving it further:

[tex]-(t-5)^2 + 3 = -3(t-3)^2 + t + 1\\3(t^2 + 9 -6t) -(t^2 + 25 -10t) -t + 2 = 0\\\\2t^2 -9t + 4 = 0\\2t^2 -8t - t + 4 = 0\\2t(t-4) -1(t-4) = 0\\(2t -1)(t-4) = 0\\\\t = 4, t = 1/2[/tex]

Assuming they planned to do flip after integral number of time in seconds, the correct option is t = 4 seconds.

Thus, to make sure the flip is in unison, after 4  seconds should the flip occur, as given by the option C: 4 seconds.

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Answer:

5 seconds

Step-by-step explanation:

Put the equations in desmos and you will see they intersect at 5 seconds.

This is definitely correct.  Here is proof:

(i) 1.272727...

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1.\overline{27}}}}[/tex] [tex]\bf{i.}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{Let\:x\:be\:1.\overline{27}}}}[/tex]

Multiplying both the sides by 100.

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{x\:*\:100=1.\overline{27}\:*\:100}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{100x=127.\overline{27}}}}[/tex] [tex]\bf{ii.}[/tex]

Subtracting [tex]\bf{i.}[/tex] from [tex]\bf{ii.}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{100x\:-\:x=127.\overline{27}\:-\:1.\overline{27}}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{99x=126}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{126}{99}}}}[/tex]

Reducing it to lowest form

[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{14}{11}}}}[/tex]

[tex]\gray{\rule{300pt}{0.3em}}[/tex]

(ii) 0.1282828...

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{0.1\overline{28}}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{Let\:x\:be\:0.1\overline{28}}}}[/tex]

Multiplying both sides by 10

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{x\:*\:10=0.1\overline{28}\:*\:10}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{10x=1.\overline{28}}}}[/tex] [tex]\bf{i.}[/tex]

Multiplying both sides by 100

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{10x\:*\:100=1.\overline{28}\:*\:100}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1000x=128.\overline{28}}}}[/tex] [tex]\bf{ii.}[/tex]

Subtracting [tex]\bf{i.}[/tex] from [tex]\bf{ii.}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1000x\:-\:10x=128.\overline{28}\:-\:1.\overline{28}}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{990x=127}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{127}{990}}}}[/tex]

[tex]\gray{\rule{300pt}{0.3em}}[/tex]

Step-by-step explanation:

108 x 9 = 972

so it's 972 dollars

The product  (y−4x)(y^2 + 4y + 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x then the value of a is 16.

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

First let w = y-4x make distribution a bit easier

(y−4x)(y^2 + 4y + 16)

[tex]w(y^2 + 4y + 16)\\wy^2 + w4y + w16\\[/tex]

now put the values of w in the equation

[tex](y-4x)y^2 + (y-4x)4y + (y-4x)16\\y^3-4xy^2 + 4y^2-16xy+16y-64x\\[/tex]

Here the value of a is 16.

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Answer:

16

Step-by-step explanation:

The quotient of the equation is x-2.

The quotient is the number that is generated when we perform division operations on two numbers. Basically, it is the result of the division method.

The given equation is;

[tex]\rm \dfrac {x^3 - 3x^2 + 3x -2}{ x^2 - x + 1}\\\\[/tex]

By fraction, a quotient is a number obtained by dividing the dividend by the divisor which is a simple division of numerator and denominator.

The solution of the equation is determined in the following steps given below.

[tex]\rm = \dfrac {x^3 - 3x^2 + 3x -2}{ x^2 - x + 1}\\\\\rm = \dfrac {( x^2 - x + 1)(x-2)}{ x^2 - x + 1}\\\\=x-2[/tex]

Hence, the quotient of the equation is x-2 .

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Answer:75% percent chance of picking a card greater than 1 and a 50% chance of picking a card greater than 2

Step-by-step explanation:

please pick me as brainliest

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{h(x)}{y}~~ = ~~6\sqrt[3]{2x+5}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~6\sqrt[3]{2y+5}-1} \\\\\\ x+1=6\sqrt[3]{2y+5}\implies \cfrac{x+1}{6}=\sqrt[3]{2y+5}\implies \left( \cfrac{x+1}{6} \right)^3=\left( \sqrt[3]{2y+5} \right)^3[/tex]

[tex]\left( \cfrac{x+1}{6} \right)^3=2y+5\implies \left( \cfrac{x+1}{6} \right)^3-5=2y\implies \cfrac{\left( \frac{x+1}{6} \right)^3-5}{2}=y \\\\\\ \cfrac{\left( \frac{x+1}{6} \right)^3}{2}-\cfrac{5}{2}=y\implies \cfrac{~~ \frac{(x+1)^3}{6^3}~~}{2}-\cfrac{5}{2}=y\implies \cfrac{(x+1)^3}{432}-\cfrac{5}{2}=\stackrel{y}{h^{-1}(x)}[/tex]

Answer:

180 more students than parents at the game

Step-by-step explanation:

There are 5 students for every 2 parents equalling 7 people in one set of students to parents ratio.

There are 420 fans at the game. Divide the 420 by the 7 people per set.

420 / 7 = 60 (There are 60 sets of 5 students to 2 parents ratio)

Multiply the 60 sets by 5 students and 2 parents, respectively:

60 x 5 = 300 students

60 x 2 = 120 parents

Subtract the number of parents from number of students:

300 students - 120 parents = 180 more students

Answer:

B. rotation

Step-by-step explanation:

A reflection would mean that the shape would be mirrored across the y-axis or the x-axis. A translation means that nothing about the shape changes except for the location. A dilation (not an answer option but still helpful to know) is the change in size of the shape. And finally, the correct answer for this problem, a rotation means that the shape is rotated at a specific point.

I included a picture that uses a shape to help explain this idea. I hope this helps! Have a lovely day!! :)

Answer:

Friday: 18 tickets  Saturday:24 tickets  Sunday: 2 tickets

Step-by-step explanation:

120-102=18 tickets

120-96=24 tickets

120-118=2 tickets

TYSM I REALLY NEEDED IT TY!!

it helped me

Answer:

Perpendicular cross section of a pyramid -------   triangle.

Perpendicular cross section of a cylinder -------  rectangle

parallel cross section of a sphere ------ circle

shape create....    -----    cylinder.  

Step-by-step explanation:

Imagine you cut pyramid like that. Height of pyramid would be height of your triangle. and sides of pyramid would be sides of triangle.

diameter of a base of cylinder would be one side of rectangle and height of cylinder would be other side of rectangle. (pair of sides)

when you cut sphere a side would apear with shape of circle.

one side of rectangle would be hight of cylinder and other would be radius of it.

last one is cone.  If you place right angle in coordinate beginning (0.0) and one of shorter sides to lie on y axis other would be on x axis. when rotated you get cone.

Answer:

81

Step-by-step explanation:

f ( x ) = ( x - 3 )² + 17

To find : f ( - 5 )

f ( - 5 ) = f ( x )

Here,

x = - 5

f ( - 5 ) = ( - 5 - 3 )² + 17

          = ( - 8 )² + 17

          = 64 + 17

f ( - 5 ) = 81

Answer:

x = log 17frac 23 (3)

(50)

Step-by-step explanation:

500 x 0.85 x at the top =30x1.15 x at the top again.

Answer:

5 1/3 bags

Step-by-step explanation:

12/9 = 1 1/3 bags per pot

4 * 1 1/3 = 5 1/3 bags to fill the pots

Answer:

3 bags

Step-by-step explanation:

Given

Solving

Answer:

22/29

Step-by-step explanation:

First, add up all of the numbers given:

16 + 4 + 6 + 3 = 29

Now since there are 16 students who have a dog and a cat, and 6 who only have a dog, we add those numbers:

16 + 6 = 22

Now since there are 29 total numbers, that will be the number of outcomes out of the 22 people with dogs:

22/29

The answer is "no solution"

Answer:

113°

Step-by-step explanation:

1) according to the condition m(∠B)=m(∠D)=67°;

2) m(∠C)=180°-m(∠B)=180°-m(∠D);

m(∠C)=180-67=113°.

The spinner illustrates probability, and it is expected that a vowel will be spun approximately 10 times

In the spinner, we have:

Sections = 6

Vowels = 2 i.e. A and E

The expected number of vowels in 30 spins is:

Expected = Vowels/Sections * 30

This gives

Expected = 2/6* 30

Evaluate the product

Expected = 10

Hence, it is expected that a vowel will be spun approximately 10 times

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Answer:

the answer is 10

Step-by-step explanation:

Answer:

y = - 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (7, - 9 ) into the partial equation

- 9 = - 14 + c ⇒ c = - 9 + 14 = 5

y = - 2x + 5 ← equation of line

Answer:

I believe its D

If correct please give brainliest

Step-by-step explanation:

Answer:

C)

Step-by-step explanation:

The first inequality, y ≥ 2x + 1 has no solution below the function since it is  greater than OR EQUAL to it. Similarly, the second inequality, y > 1/2x - 1 has no solution at or below the function since it is only GREATER THAN this value.

If we look at the graph of these inequalities, we see that they don't overlap at all in quadrant IV. For that reason, this area of the graph there will have no solution, or empty set.

Hope this helps and God bless!

At a local high school, enrollment in the drama club increases by 5%. the common ratio will be 1.05.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

At a local high school, enrollment in the drama club increases by 5%.

Let an initial number of students in high school be 'a'.

so next year increase in students will be = 5% of a

                                                                   = 5/100 × a

                                                                   = 0.05a

and total number of the students will be  = ( a + 0.05a )

                                                                   = ( 1.05a )

So common ratio of the geometric square formed

( 1.05a )/ a =  1.05

Therefore, the common ratio will be 1.05.

Learn more about percentages;

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Answer:

6/14 or simplify it to 3/7

Step-by-step explanation:

this is because you have a total of 14 marbles

Answer:

look below

Step-by-step explanation:

Slope =  materials cost per student

Y—intercept = cost of renting the classroom

Answer:

  3334 N·m

Step-by-step explanation:

Work is the product of force and distance. The force used in the product is the force that is in the direction of motion.

__

The horizontal component of the applied force is ...

  F = (35 N)cos(30°) ≈ 30.311 N

Then the work done is ...

  W = Fd

  W = (30.311 N)(110 m) = 3334 N·m

Answer:

✏If the rod is held straight then the angle alpha equals 90°,therefore the required solution is 45°

Step-by-step explanation:

Answer:

8 :)

Step-by-step explanation:

Side 1: 15

Side 2: 14

Side 3: 7 + x

Side 1 and 3 are the same length so we subtract :D

15 - 7 = 8

Have an amazing day!!

Please rate and mark brainliest!!

A Circle is a closed plane geometric shape figure. The diameter of a circle is the longest chord of a circle. The radius drawn perpendicular to the chord bisects the chord. A Circle is always lie at an equal distance from a center point. Circles having different radius are similar.

The circumference of a circle is the product of pi and length of the diameter of a circle. Mathematically;

[tex]\longrightarrow \tt{Circumference_{(circle)} = \pi{D}}[/tex]

Here, D is the diameter of the circle or distance between the circle.

We are asked to find the circumference of the circle if the diameter is 8 inches.

We know that, The circumference of a circle is the product of pi and length of the diameter of a circle. Therefore;

[tex]\implies \tt{Circumference_{(circle)} = \pi{D}}[/tex]

[tex]\implies \tt{Circumference_{(circle)} = 3.14 \times 8}[/tex]

[tex]\implies \boxed{\pmb{\tt{Circumference_{(circle)} = 25.12}}}[/tex]

Hence, the circumference of the circle is 25.12 inches. So option (B) is correct.

Answer:

Step-by-step explanation:

In the question we are given that diameter of circle is of 8 inches . And we have asked to find the circumference of the circle .

For finding circumference of circle we must have to know that what is the formula for finding circumference of circle. So :

[tex] \quad \quad \: \red{\underline{\pink{ \boxed{ \frak{Circumference \: of \: Circle =2 \pi r }}}}}[/tex]

Where ,

Solution : -

As in the question we are given length of diameter . So for finding circumference we need to find the radius of circle .

We know that diameter of circle is two times its radius ,

[tex] \qquad \: \rm {Diameter = 2 × Radius }[/tex]

So for radius we are dividing both side with 2 :

[tex]\qquad \: \rm { \dfrac{Diameter}{2} = \dfrac{ \cancel{2} × Radius}{ \cancel{2}} }[/tex]

We get that ,

[tex] \qquad \: \rm {Radius = \dfrac{Diameter}{2} }[/tex]

Therefore , we can say that radius of circle is half of its diameter .

Now using this , firstly we are finding radius of circle . So :

[tex] \longmapsto \quad \: \boxed{\rm{ Radius = \frac{8}{2} \: \: inches}}[/tex]

Now , we are moving towards our final solution .

So ,

[tex] \longmapsto \quad Circumference_ { (Circle)} =2 \times 3.14 \times 4 [/tex]

Multiplying 2 with 3.14 :

[tex]\longrightarrow \quad Circumference_ { (Circle)} = 6.28 \times 4 [/tex]

Multiplying 4 and 6.28 :

[tex]\longrightarrow \quad \purple{{\boxed{\frak{Circumference_ { (Circle)} = 25.12\: inches }}}}[/tex]

Answer:

B: Every input value corresponds to only one output value.