A seat on a Ferris wheel is level with the center of the wheel.The diameter of the wheel is 200 feet. Suppose the wheel rotated 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation

Answers

Answer 1

Answer: 86.6ft closer to the ground.

Step-by-step explanation:

The diameter of the wheel is 200ft

Then the radius, half of the diameter, is: r = 200ft/2 = 100ft.

Initially, the seat is at the same level that the center of the wheel.

And the distance between the center of the wheel and the bottom is the radius.

Then the initial position is at an angle of 0° from the x-axis. (where the (0,0) of this axis coincides with the center of the wheel=

Now, the wheel rotates 60°. (downwards, so we actually could use -60° measuring from the positive x-axis)

And thinking in this as a triangle rectangle, where the opposite angle is 60°, we can calculate the displacement in the vertical direction as:

y = sin(-60°)*R

y = sin(-60°)*100ft = -86.6ft

So the seat is 86.6ft closer to the ground.

Answer 2

The seat is [tex]86.6feet[/tex] closer to the ground

The seat will be closer by the height it drops when the Ferris wheel turns downwards by [tex]60^{\circ}[/tex].

The height, and the radius of the Ferris wheel form the opposite and the hypotenuse of a [tex]60^{\circ}[/tex] right-angled triangle. Since the diameter of the Ferris wheel is 200feet, the radius will be 100feet. So we have

[tex]sin60^{\circ}=\frac{opp}{hyp}=\frac{h}{100}\\\\h=100\times sin60^{\circ}\\=100\times 0.8660\\=86.6[/tex]

So the seat is [tex]86.6feet[/tex] closer to the ground

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Related Questions

Please answer asapWhat is the measure of an exterior angle of a regular 13-sided polygon? Enter your answer as a decimal in the box. Round to the nearest tenth of a degree.

Answers

Answer:

Step-by-step explanation:

it is given by the formula=4× 90/ n

where n = number of sides

exterior angle= 4 x 90/13

=360/13=[tex]27.7[/tex]°

                                               

                                     

Given segment XZ and point Y that lies on XZ find XZ if XY = 7 and YZ = 17

Answers

Answer:

24

Step-by-step explanation:

We are given segment XZ and point Y. First, draw a number line. Draw X and Z on either side of the number line. We know that Y is between X and Z since there are the distances of XY and YZ. To find XZ, add the distance of XY and YZ, which are respectively 7 and 17. Adding 7 and 17, we get 24 as the answer.

The value of XZ is 24.

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

What is a Line Segment?

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment XZ, where the length of line segment XZ refers to the distance between its endpoints, X and Z.

Given that a line segment XZ and point Y that lies on XZ

XY = 7 and YZ = 17

Here XZ = XY + YZ

X_____________Y_______________Z

⇒ XZ = XY + YZ

Substitute the values of  XY = 7 and YZ = 17, we get

⇒ XZ = 7 +  17

Apply the addition operation in the above equation,  

⇒ XZ = 24

Therefore, the value of XZ is 24.

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−0.75 − (−
5
2

)+0.4+(−
4
3

)

Answers

Answer:

-13

Step-by-step explanation:

You roll a single die numbered from 1 to 6 twice. The probability of rolling an even number the first time and a 6 the second is the setup. What is the probability "rolling an even number the first time"? (Answer in percentage)

Answers

Answer:

The answer is 50%

Step-by-step explanation:

step one :

first and foremost we are going to list the sample space related to a die

the same space is  S= {1,2,3,4,5,6}= 6

step two:

now the even numbers in the sample space are ={2,4,6}= 3

hence we can solve for the probability of obtaining an even number to be

Pr(even number)= 3/6= 1/2.

step three:

since we are to provide the answer in percentage format, we can easily do this by multiplying the answer by 100 to get the percentage

(1/2)*100= 0.5*100= 50%

Solve for x: 5x +1(3x + 6) > 14

Answers

Answer:

5x+3x+6>14

8x>14-6

8x>8

divide both sides by 8

x>1

What is rhe price of the computer be after the mark down?​

Answers

Answer:

C.$150

Step-by-step explanation:

The sales man told her that he would sell it to he for ⅓ of the marked price.

Given:

Marked Price= $450

Required:

of the marked price or $450

Formula:

*$450

Solution:

⅓ of $450

⅓*$450

$450/3

$150

Hope this help ;) ❤❤❤

Answer:

A.180

Step-by-step explanation:

Let x, y, z be numbers. (x2 yz4)3 =​

Answers

I’m not sure I think it ended up being x2yz4

Yesterday at 4pmn, I was 95 degrees outside. Every hour after that, the temperature dropped 3 degrees. What was the temperature at 8pm

Answers

Answer:

83 degress

Step-by-step explanation:

We know that every hour it dropped 8 degress. If it dropped from 4pm to 8pm, that means it dropped 4 times. 3x4=12 so we do 95-12 which equals 83.

How can you determine what type of solution an equation has when solving? Explain.

Answers

Answer: Answer is in the steps

Step-by-step explanation:

If the system of equations have the same slope and same y-intercepts then it means that they have infinitely many solutions.

if the system of equations have the same slope but different y-intercepts it means that they have no solution because they will never intersect but will always form parallel lines.

If the system of equations have different slopes and different y-intercepts or have same y-intercepts and different slopes it means that they have exactly on solution.

Which option best completes the following statement?
As a unit of account, money provides a way to determine and compare
OA) money over time.
B) apples.
O C) value.
OD) people.

Answers

Answer: C) Value

Apples and people don't make much sense as an answer here, so we can rule out B and D. Choice A can be ruled out as it seems redundant to say "money compares money over time". It makes more sense to say "Money compares value (over time)".

Which point is located in quadrant IV?

Answers

Quadrant General Form of Point in this Quadrant Example
I (+, +) (5, 4)
II (−, +) (−5, 4)
III (−, −) (−5, −4)
IV (+, −) (5, −4)

Can anyone explain to me why I got this wrong

Answers

Answer:

I think your suppose to multiply the lengths together then you multiply the width together and the add those two

Step-by-step explanation:

srry if i am wrong lol

please answer ASAP ......

Answers

10 cm same length as UT

If a = 3 and b = 4, then find the value of 2a + 3b A. 15 B. 16 C. 17 D. 18

Answers

Answer:

18

Step-by-step explanation:

2a+3b

2•3+3•4

6+12

18

Answer:

2124+272cd

Step-by-step explanation:

Explain why it might be easier to solve the multiplication problem by changing it from this: 5×87×2, to this: 5×2×87. Use a property of multiplication to justify your reasoning.

Answers

Answer:

It makes the calculation easy and quick.

Step-by-step explanation:

Commutative Property of multiplicationThe product of two or more real numbers is not affected by the order in which they are being multiplied. In other words, real numbers can be multiplied in any order because the product remains the same.

When you multiply as it is given:

5×87×2=870Step 1)  5×87 = 435Step 2) 435×2 = 870

Using the commutative property makes it much easier:

5×2×87 = 870Step 1) 5×2 = 10Step 2) 10* 87 = 870

Answer:

see below.

Step-by-step explanation:

its a commutative property of multiplication.

it doesn't matter in order or not... the result will always be the same.

form your example 5×87×2, if you use a calculator it doesn't matter which number you start.

say 2 x 87 x 5 = 870

or 87 x 5 x 2 = 870

or 5 x 2 x 87 = 870

see the results are all the same no matter which way you go.

Which are examples of unit rates? Check all that apply.
100 students for every 2 buses
1 teacher per 25 students
4 pencils for each student
8 students per team

Answers

Answer: 8 students per team and 4 pencils each student

Step-by-step explanation:

Answer:

Both C and D

Step-by-step explanation:

What is the value of a if (2a+3)−(4a−8)=7?

Answers

Answer:

Step-by-step explanation:

2a + 3 - 4a + 8 = 7

-2a + 11 = 7

-2a = -4

a = 2

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(2a + 3) - (4a - 8) = 7}[/tex]

When there is a ( - ) in front of an expression in parentheses , change the sign of sign of each term in the expression

[tex] \longrightarrow{ \sf{2a + 3 - 4a + 8 = 7}}[/tex]

Collect like terms

[tex] \longrightarrow{ \sf{ - 2a + 3 + 8 = 7}}[/tex]

Add the numbers: 3 and 8

[tex] \longrightarrow{ \sf{ - 2a + 11 = 7}}[/tex]

Move 11 to right hand side and change it's sign

[tex] \longrightarrow{ \sf{ - 2a = 7 - 11}}[/tex]

Subtract 11 from 7

[tex] \longrightarrow{ \sf{ - 2a = - 4}}[/tex]

Divide both sides by -2

[tex] \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{ - 4}{ - 2} }}[/tex]

Calculate

[tex] \longrightarrow{ \sf{a = 2}}[/tex]

Hope I helped!

Best regards! :D

Can I write (3x-1)(3x+1) as (x-1/3)(x+1/3)?

Answers

Answer:

yes

Step-by-step explanation:

[tex](3x-1)(3x+1)=9x^{2}-1[/tex] [tex]=\frac{9x^{2} }{9}-\frac{1}{9}=[/tex] [tex]x^{2} -\frac{1}{9}[/tex]

[tex](x-1/3)(x+1/3)=x^{2} -\frac{1}{9}[/tex]

aaron walks 2 1/8 miles to his friends house. then, they walk 5/6 miles to the park .finally, aaron walks 1 3/4 miles to get back home.how far did aaron walk today

Answers

Answer:did you check and see if anybody asked this question before??

Step-by-step explanation:

The total distance did Aaron walk today is 4.70 miles.

It is required to find the total distance.

What is distance?

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given :

Aaron walks 2 1/8 miles to his friends.

He walk 5/6 miles to the park.

Again he walks 1 3/4 miles to get back home.

Total distance=

2 1/8 miles+5/6 miles+ 1 3/4 miles

=17/8+5/6+7/4

=4.70 miles

Therefore, the total distance did Aaron walk today is 4.70 miles.

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Alex’s house (point F) lies on the same street as her school (point H). Alex’s bus stop (point G) lies between her house and her school.

Given FG = (2x) meters, GH = 1,000 meters, and FH = 1,200 meters, what is x?

Answers

2X+1000=1200
=> 2X = 1200 - 1000
=> 2X = 200
=> X = 100 meters
Because FG + GH = FH
Or : 2X + 1000= 1200

The value of x in the expression will be 100.

What is a line segment?

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that FG = (2x) meters, GH = 1,000 meters, and FH = 1,200 meters,

The value of x will be calculated by making an equation for the line segment below:-

FG + GH = FH

2X+1000=1200

2X = 1200 - 1000

2X = 200

X = 100 meters

2X + 1000= 1200

Therefore, the value of x in the expression will be 100.

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Evaluate the following function over the domain {0,1,2,3}. What is the range?

Answers

Answer:Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

range is The zero doesn't matter. You still subtract the lowest number from the highest. If zero is the lowest number, then the highest number is the range. If the set consists of negative numbers, and zero is the highest number, then the lowest number (without its negative sign) is the range.

0


[tex]5(m - 1) = - 25[/tex]
can u help me solve it?​

Answers

Answer:

-4.

Step-by-step explanation:

5(m - 1) = -25

m - 1 = -5

m = -4.

Answer:

m = -4

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

m = -4

Help please! Any help is appreciated

Answers

Answer: The answer is (-∞, ∞)

Step-by-step explanation:I hope this helps!

Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The graph of f has a vertical asymptote at x=1, and f has a removable discontinuity at x=−2. (a) Show that a=2 and b=−4. (b) Find the value of c. Justify your answer. (c) To make f continuous at x=−2, f(−2) should be defined as what value? Justify your answer. (d) Write an equation for the horizontal asymptote to the graph of f. Show the work that leads to your answer.

Answers

Answer:

a) [tex]a = 2[/tex] and [tex]b = -4[/tex], b) [tex]c = -10[/tex], c) [tex]f(-2) = -\frac{5}{3}[/tex], d) [tex]y = -\frac{5}{2}[/tex].

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex].

Denominator

i) [tex](x+2)\cdot (x-1) = 0[/tex] Given

ii) [tex]x^{2} + x-2 = 0[/tex] Factorization

iii) [tex]2\cdot x^{2}+2\cdot x -4 = 0[/tex] Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that [tex]a = 2[/tex] and [tex]b = -4[/tex]

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) [tex]c\cdot x - 5\cdot x^{2} = 0[/tex] Given

ii) [tex]x \cdot (c-5\cdot x) = 0[/tex] Distributive Property

iii) [tex](-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0[/tex] Distributive and Associative Properties/[tex](-a)\cdot b = -a\cdot b[/tex]/Result

As we know, this polynomial has [tex]x = -2[/tex] as one of its roots and therefore, the following identity must be met:

i) [tex]\left(x -\frac{c}{5}\right) = (x+2)[/tex] Given

ii) [tex]\frac{c}{5} = -2[/tex] Compatibility with addition/Modulative property/Existence of additive inverse.

iii) [tex]c = -10[/tex] Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of [tex]c[/tex] is -10.

c) We can rewrite the rational function as:

[tex]f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}[/tex]

After eliminating the removable discontinuity, the function becomes:

[tex]f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)[/tex]

At [tex]x = -2[/tex], we find that [tex]f(-2)[/tex] is:

[tex]f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right][/tex]

[tex]f(-2) = -\frac{5}{3}[/tex]

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward [tex]\pm \infty[/tex]. That is:

[tex]y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}[/tex] Given

[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right][/tex] Modulative Property

[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right][/tex] Existence of Multiplicative Inverse/Definition of Division

[tex]y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)[/tex]   [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]

[tex]y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)[/tex]   [tex]\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}[/tex]/[tex]x^{m}\cdot x^{n} = x^{m+n}[/tex]

[tex]y = -\frac{5}{2}[/tex] Limit properties/[tex]\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0[/tex], for [tex]n \geq 1[/tex]

The horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex].

Using asymptote concepts, it is found that:

a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.

b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.

c) Simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex].

d) The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]

-------------------------

Item a:

Vertical asymptote at [tex]x = 1[/tex] and discontinuity at [tex]x = -2[/tex] means that the the roots of the quadratic function at the denominator are [tex]x = 1[/tex] and [tex]x = -2[/tex].The leading coefficient is given as 2, thus, we build the equation to find coefficients a and b.

[tex]2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4[/tex]

[tex]2x^2 + ax + b = 2x^2 - 2x - 4[/tex]

Thus a = 2, b = -4.

-------------------------

Item b:

Removable discontinuity at [tex]x = -2[/tex] means that the numerator when [tex]x = -2[/tex] is 0, thus:

[tex]-2c - 5(-2)^2 = 0[/tex]

[tex]-2c - 20 = 0[/tex]

[tex]2c = -20[/tex]

[tex]c = -\frac{20}{2}[/tex]

[tex]c = -10[/tex]

-------------------------

Item c:

With the coefficients, the function is:

[tex]f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}[/tex]

At x = -2:

[tex]-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}[/tex]

Thus, simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex]

-------------------------

Item d:

The horizontal asymptote of a function is:

[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]

Thus:

[tex]y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}[/tex]

The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]

A similar problem is given at https://brainly.com/question/23535769

Is the expression 2 • 4x equal to the expression 8x?

Answers

Answer:

YES

Step-by-step explanation:

[tex]2 . 4x =\\2 \times 4x\\\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8\\\\= 8x[/tex]

I think the answer is yes

5/k = 15/20 what would the k be?

Answers

Answer:

20/3

Step-by-step explanation:

5/k=15/20

5/k=3/4

5 x 4/3 = k

k=20/3

What is the solution of this equation -4z = 24

Answers

Answer:

z = -6

Step-by-step explanation:

[tex]-4z=24\\\\\frac{-4z=24}{-4}\\\\ \boxed{z=-6}[/tex]

Hope this helps.

19. Amy has 8 coins worth $1.40. Some of the coins are nickels and some are quarters. How
many of each coin does Amy have?

Answers

Answer:

5 quarters and 3 nickels

Step-by-step explanation:

x = nickels

y = quarters

x + y = 8

x(0.05) + y(0.25) = 1.40

3 + 5 = 8

3(0.05) + 5(0.25) = 1.40

0.15 + 1.25 = 1.40

1.25 + 0.15 = 1.40


Which value of x is the solution of the equation (2/3)x+(1/2) =(5/6)

Answers

Answer:

1/2

Step-by-step explanation:

Step 1:

4/6x + 3/6 + 5/6

Step 2:

4/6x = 2/6

Step 3:

2/6 times 6/4

Answer:

1/2

Hope This Helps :)

What integer describes gaining 14 pounds ?

Answers

Answer:

14

Step-by-step explanation:

Since gaining fourteen pounds means going in a positive direction, we can say the gain of fourteen pounds numerically as 14.

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Find the focus and directrix of the parabola y= 1/2 (x+2)^2 - 3 A. The focus is at (2,2) and the directrix is at y = 4. B. The focus is at (2,3) and the directrix is at y = 5. C.The focus is at (2,2 1/2) and the directrix is at y = 3 1/2. D. The focus is at (2,1 1/2) and the directrix is at y = 2 1/2. Explain how judicial review can be used by the Supreme Court to check the power of the executive and legislative branches. The formula D =3/2 (100 C) relates D,the temperature measured on the Delislescale, in degrees, and C, the temperaturemeasured on the Celsius scale, also indegrees. What is the temperature indegrees Celsius when the temperature indegrees Delisle is 78?BO missing angle for triangle PLEASE HELP I HAVE UNTIL TOMORROW Write a short summary of this story. The city of Syracuse in Sicily . . . was ruled by a man . . . whose name was Dionysius. [He] had seized power by force, and kept his authority by exercising the greatest severity. He was always surrounded by guards, who at a mere sign from him were ready to put anyone to death.Dionysius was therefore feared and hated by the people whom he governed, but who would have been very glad to get rid of him. No honest man cared to come near such a bloodthirsty wretch, and there were soon none but wicked men to be found in his court.These men, hoping to win his favor and get rich gifts, used to flatter him constantly. They never told him the truth, but only praised him, and made believe to admire all he said and did.Of course, even though they were wicked too, they could really admire him, but secretly hated and despised him. Their praise, therefore, was as false as they and their advice was always as bad as bad could be.Now, Dionysius was as conceited as he was cruel, and fancied that there was nothing he could not do. Among other things, he thought he could write beautiful poetry. Whenever he wrote a poem, therefore, he read it aloud to all his courtiers, who went into raptures over it, although they made great fun of it behind his back.Dionysius was highly flattered by their praise, but thought he would like to have it confirmed by the philosopher Philoxenus, the most learned man of Syracuse.He therefore sent for Philoxenus, and bade him give his candid opinion of the verse. Now, Philoxenus was far too noble a man to tell a lie: and whenever he was consulted by Dionysius, he always boldly told the truth, whether it was agreeable or not.When the tyrant asked his opinion about the poems, therefore, he unhesitatingly answered that they were trash, and did not deserve the name of poetry at all.This answer so angered Dionysius, and so sorely wounded his vanity, that he called his guards, and bade them put the philosopher into a prison hewn out of the living rock, and hence known as "The Quarries."Here Philoxenus was a prisoner for many a day, although his only fault was having told the tyrant an unwelcome truth when asked to speak.The philosopher_s friends were indignant on hearing that he was in prison, and signed a petition asking Dionysius to set him free. The tyrant read the petition, and promised to grant their request on condition that the philosopher would sup with him.Dionysius' table was well decked, as usual, and at dessert he again read aloud some new verses he had composed. All the courtiers went in to ecstasies over them, but the philosopher did not say a word.Dionysius, however, fancied that his long imprisonment had broken his spirit, and that he would not now dare refuse to give a few words of praise: so he pointedly asked Philoxenus what he thought of the poem. Instead of answering, the philosopher gravely turned toward the guards, and in a firm voice cried aloud, "Take me back to The Quarries." thus showing very plainly that he preferred suffering to telling an untruth.The courtiers were aghast at his rashness, and fully expected that the tyrant would take him at his word and put him in prison, if nothing worse; but Dionysius was struck by the moral courage which made Philoxenus tell the truth at the risk of his life, and he bade him go home in peace. (1 point) Find the antiderivative F of f(x)=43(1+x2)1 that satisfies F(1)=3. assume this car is driven off a cliff. How many arrows of force need to be drawn in the free body diagram? Assum no air resistance Answers: five one four three Which of the following is not true about a thesis statement?O is the last sentence of an introductionstates a fact about the topicO includes a subject and commentarystates an opinion on the topic Based on ppc, if a country is producing 6 coconuts and 4 fish, and they want to increase coconut production to 8. What is the opportunity cost of doing so? A. 2 fish B. 2 coconutsC. 4 fish D. 4 coconuts 59:52 In an oil spill, why does the oil not mix with the seawater? Did the framers of the Constitution meet in Philadelphia to tear up the Articles of Confederation? Why did farming tribes plant their crops on hillsides? What is the man Idea?Whe Chocolate ganache is made from chocolate and cream in a3:2 ratio, respectively. If one batch of ganache requires 240 grams of chocolate, how many grams of cream is required? Tammy is recording the percentages she earned on each quiz in her math class. Here are her results for the last quizzes. 91, 86, 85, 74, 90, 87,86 Find the range of the data set. PLZ HELP Which mountain region is known for its carpet and textile industry? Appalachian Plateau Ridge and Valley Blue Ridge Piedmont Do sunflowers grow better in fields or individually? 7x(15+4) = (7x ) + (7+4) An airport offers 2 shuttles that run on different schedules. If both shuttles leave the airport at 4.00 pm at what time will they leave the airport together