Find the derivative of f(x) = negative 9 divided by x at x = -8.

Answers

Answer 1

Answer:

[tex]f'(-8)=\frac{9}{64}[/tex]

Step-by-step explanation:

Given the function

[tex]f(x)=\frac{-9}{x}[/tex]

We can rewrite it as

[tex]f(x)=-9x^{-1}[/tex]

Now we can apply the power rule

[tex]f'(x)=9x^{-2}[/tex]

Now we can rewrite it

[tex]f'(x)=\frac{9}{x^{2} }[/tex]

Now we can plug in x=-8

[tex]f'(-8)=\frac{9}{(-8)^{2} }\\f'(-8)=\frac{9}{64}[/tex]

Answer 2
Final answer:

The derivative of f(x) = -9/x at x = -8 is 9/64.

Explanation:

To find the derivative of f(x) = -9/x at x = -8, we can use the power rule for differentiation. The power rule states that if we have a function of the form f(x) = x^n, then the derivative of f(x) is given by f'(x) = n*x^(n-1).

In our case, the function is f(x) = -9/x. Rewriting it as f(x) = -9*x^(-1), we can apply the power rule and find that the derivative is f'(x) = (-1)*(-9)*x^(-1-1) = 9/x^2.

Substituting x = -8 into the derivative formula, we get f'(-8) = 9/(-8)^2 = 9/64.


Related Questions

What is the Greatest Common Factor of the expression 12x4 + 18x2?

Answers

Answer:

6x²

Step-by-step explanation:

to find the GCF we look at the terms and see what they have in common

we see that the greatest number both can be divided by is 6

we also look at the variables. both contain an x², so we can factor out as well

the answer would be 6x²

Tanya have several different ways she likes to walk home. One route takes 20 minutes, two of the routes take 30 minutes, and two take 40 minutes. Tanya randomly chooses a route to walk home. What is the probability, to the nearest percent, that it will take her 30 minutes to walk home?
A.) 20%
B.) 33%
C.) 40%
D.) 67%

Please explain answer for me :)

Answers

Answer:

40%

Step-by-step explanation:

Tanya has a a choice of 5 different routes (1-20 mins, 2-30 mins, 2-40 mins).

How many routes can she take that will take her 30-mins to get home?

The answer is 2.

What's the probability she will take 2 of the 5 routes to get home?

The probability is 2/5 so 40%.

The rounding instruction was there to mislead you in this case :-)

what is 1 2/5 + 2 3/10

Answers

Answer: 3 7/10

Solution by separating parts

Let's rewrite our equation with the parts separated

= 1 + 2/5 + 2 + 3/10

Now, let's add the whole numbers

1 + 2 = 3

Now, let's figure out how to solve the fraction parts

2/5 + 3/10 = ?

You'll need to find the LCD (Lowest Common Denominator) of 2/5 and 3/10.

If you don't know, the LCD is 10

Since 3/10 already has a denominator of 10, we don't need to do anything with it.

However, we need to multiply the numerator and denominator of 2/5 by 2

Why? We need the LCD, which is 10. Also, we can only add fractions if they have the same denominators

Numerator: 2 x 2 = 4

Denominator: 5 x 2 = 10

Fraction: 4/10

Now add the fractions

4/10 + 3/10 = 7/10

Finally, combine the whole numbers with the fractions

3 + 7/10 = 3 7/10

Thank you for any help!

Answers

The answer is D

0 is not less than or equal to -4, and in the second equation, 0 is greater than -1

Answer:

D. No. (0, 0) satisfies [tex]y>2x-1[/tex] but does not satisfy [tex]y\leq x^2-4[/tex].

Step-by-step explanation:

We are given the following system of equations and we are to determine if (0, 0) is its solution or not:

[tex]y\leq x^2-4[/tex]

[tex]y>2x-1[/tex]

Substituting the given point [tex](0, 0)[/tex] in both the equations to check if it satisfies them.

[tex]y\leq x^2-4[/tex] [tex]\implies[/tex] [tex]0\leq (0)^2-4 \implies 0\leq -4[/tex] - False

[tex]y>2x-1 \implies 0 > 2(0)-1 \implies 0>-10[/tex] - True

Therefore, the correct answer option is D. No. (0, 0) satisfies [tex]y>2x-1[/tex] but does not satisfy [tex]y\leq x^2-4[/tex].

Fifteen friends share 20 cups of popcorn equally. Which faction of a cup does each friend get?

Answers

Answer:*fraction

Step-by-step explanation: I hope you get your answer soon

Polygons and Quadrilaterals... Help

Answers

Answer:

That is an octagon (eight sides).

Interior Angle Total = 1,080

EACH interior angle = 180 - (360 / 8) = 135

n + 161 + (n -12) +(n + 30) + n + 134 + (n+16) + 126 = 1,080

5n + 455 = 1,080

5n = 625

n = 78.125

Step-by-step explanation:

I need help please????

Answers

Answer:

(2, 2)

Step-by-step explanation:

To determine which ordered pair is a solution to the equation.

Substitute the x- coordinate into the left side and the y- coordinate into the right side and if both sides are equal then that is the solution.

(2, 2)

3 × 2 = 6 and 8 - 2 = 6 → hence (2, 2) is a solution

(8, 0)

3 × 8 = 24 and 8 - 0 = 8 → hence (8, 0) is not a solution

(3, 1)

3 × 3 = 9 and 8 - 1 = 7 → hence (3, 1) is not a solution

PLEASE HELP!! The line plot shows the amount of liquid fertilizer used on nine plants. What is the total amount of liquid fertilizer used?

Answers

Answer:

4 3/4 or 19/4

Step-by-step explanation:

To answer this question, you must add the values of all of the x's on the line plot. There is 1 x on 1/4 and 2 x's on 3/8. So, add 1/4 + 3/8 + 3/8 to get 1. Next, there are 3 x's on 1/2. So, add 1 + 1/2 + 1/2 + 1/2 to get 2 1/2. Lastly, there's 1 x on 5/8, 1 x on 3/4, and 1 x on 7/8. So add 2 1/2 + 5/8 + 3/4 + 7/8 to get  4 3/4 of 19/4 as your final answer. I hope this helps!!!

which expression can be used to find the value of x?

• (sin 29°)(sin 42°)
____________
9

• 9(sin 42°)
_______
sin 29°


• 9(sin 29°)(sin 42°)


• 9(sin 29°)
________
sin 42°

Answers

Answer:

• 9(sin 42°)

_______

sin 29°

Step-by-step explanation:

The value of x is calculated by the sine rule is 9(sin 42°)/sin 29°. Then the correct option is B.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a triangle.

We know that the sine rule is given as

[tex]\rm \dfrac{a}{sin A} =\dfrac{b}{sin B}=\dfrac{c}{sin C}[/tex]

Then put the values and we have

[tex]\begin{aligned} \rm \dfrac{x}{sin 42^o} &= \rm \dfrac{9}{sin 29^o}\\\\\\\rm x &= \rm \dfrac{9*sin 42^o}{sin 29^o} \end{aligned}[/tex]

More about the trigonometry link is given below.

https://brainly.com/question/22698523

Mack wants to calculate the circumference of a circle with a radius of 7 centimeters.

Answers

So C= dxpi or rx2xpi= c in this case 7x 2 = 14 is diameter do E D and A finds the diameter and the rest do not

PLEASE HELP ME ASAP !!!!​

Answers

Answer:

Same:

A 50% decrease followed by a 100% increase.

A 33 1/3% decrease followed by a 50% increase.

Less:

A $25 increase followed by a $30 decrease.

A 20% increase followed by a 25% decrease.

Greater:

An 80% increase followed by a 40% decrease.

IN ORDER TO FIGURE OUT THE ANSWER CHOOSE A NUMBER AND APPLY WHAT IT IS TELLING YOU. FOR EX: on #1: I chose the number 100 then multiplied it by 1.8 then multiplied that number by 0.6 to get 108 which is greater than 100

80% increase followed by 40% decrease=greater

50% decrease follow by 100% increase=greater

20% increase followed by a 25% decrease=less

$25 increase followed by $30 decrease= less

33 1/3% decrease followed by 50% increase= same

15 POINTS, WILL GIVE BRAINLIEST: simplify x^-4 y^-4 z^-1 * 2yx^3 z^-3 using properties of exponents.

Answers

2\xy³z⁴ is the simplification.

PLZ HELP!! PLZ SHOW WORK AND EXPLAIN

Answers

Answer:

50 miles

Step-by-step explanation:

Addition:

7/8 + 9/4 = 7/8 + 18/8 = 25/8 inches.

Now we have to convert to miles:

25/8 inches *16

Answer = 50 miles.

Last weekend nina mowed 4 lawns and received $60 this weekend she mowed 6 lawns and received $90 what is the constant of proportionality

Answers

Answer: nina is getting $15 for 1 lawn.

Step-by-step explanation:

1      $15

2     $30

3     $45

4     $60

the gestation time for cows is normally distributed with a mean of 284 days and a standard deviation of 12 days. at a local Ranch over the course of a year they're 820 calf births. of these how many would be expected to have a gestation time of less than 270 days​

Answers

Answer:

100 calfs

Step-by-step explanation:

We must calculate the probability that the cows have a gestation time of less than 270 days. If X represents the gestation time of a randomly selected cow, then we look for:

[tex]P (X <270)[/tex]

Acora we calculate the Z-score

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

In this case

[tex]\mu=284\ days\\\\\sigma = 12\ days[/tex]

So

[tex]P (X <270) =P (\frac{X-\mu}{\sigma} <\frac{270-284}{12})=P(Z<-1.167)[/tex]

Looking in the normal standard table we have to

[tex]P(Z<-1.167)=0.1216[/tex]

Finally, the expected number of calf "E" that will have a gestation time of less than 270 days is:

[tex]E=820*P (X <270)\\\\E=820*0.1216[/tex]

E=99.71≈100 Calfs

Please help with math problem

Answers

Answer:

[tex]a_0 = -6[/tex]

[tex]a_1=8[/tex]

[tex]x^2 +y^2 -6x + 8y = 0[/tex]

Step-by-step explanation:

The equation of the circle has the following form

[tex]x^2 + y^2 + a_0x + a_1y=0[/tex]

The equation of the circle has the following form

We know that the circle goes through the following points

(0, 0)

(6, 0)

(0, -8).

Then we substitute the values of x and y in the equation

For (0, 0)

[tex]0^2 + 0^2 + a_0(0) + a_1(0)=0[/tex]

[tex]0=0[/tex]

For  (6, 0)

[tex]6^2 + 0^2 + a_0(6) + a_1(0)=0[/tex]

[tex]36 + 6a_0=0[/tex]

[tex]a_0 = -\frac{36}{6}\\\\a_0 = -6[/tex]

For (0, -8)

[tex]0^2 + (-8)^2 + a_0(0) + a_1(-8)=0[/tex]

[tex](-8)^2 - 8a_1=0[/tex]

[tex](-8)^2 = 8a_1[/tex]

[tex]a_1=8[/tex]

Finally the equation is:

[tex]x^2 +y^2 -6x + 8y = 0[/tex]

What is the variable in this expression?
4b + 2b + 1⁄4

Answers

Answer:

the variable is "b"

Step-by-step explanation:

What’s one way to check the answer to 5x6=30?

Answers

Answer:

5 + 5 + 5 + 5 + 5 + 5 = 30

6 + 6 + 6 + 6 + 6 = 30

5 = 30 ÷ 6

6 = 30 ÷ 5

Translate the following into a math equation:

4 divided by the difference of h and 7

Question 1 options:

a 4 − h ÷ 7

b (h − 7) ÷ 4

c 4 ÷(h − 7)

d 4 ÷ (h + 7)

Answers

Answer:

C

Step-by-step explanation:

4 divided is said first, so it comes first in the equation. Difference means subtraction, meaning h - 7

I. You withdraw $17 from your account. II. A running back loses 17 yards in a game. III. The temperature rises 17 degrees. The integer -17 would BEST represent which of these events? A) I only B) III only C) I and II only D) II and III only

Answers

Withdrawing money from an account is a negative value, losing yards in a game would also be a negative value.

A rise in temperature would be a positive value.

Both 1 and 2 could be written as -17.

The answer is C.

please help!!!!!
Which defines the piecewise function shown?

Answers

Hello!

The answer is:

The second piecewise function,

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]

Why?

To answer the question, we need to find which piecewise function contains the graphs shown in the picture, we have that first line shown, is decreasing and exists from the negative numbers to 0,  and the line cuts the x-axis and the y-axis at "-2", for the second line shown,  we have that is decreasing but exists from 0 (including it) to the the positive numbers.

So, finding which piecewise satisfies the function shown, we have:

- First piecewise function:

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {\frac{x}{2} }\geq 0} \right.[/tex]

First line,

We have the first line,

[tex]-x-2<0\\[/tex]

The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exists from all the numbers less than 0, to 0, and it cuts the x-axis at -2 and the y-axis at -2.

Second line,

[tex]\frac{x}{2}\geq 0[/tex]

The variable has positive coefficient, meaning that the function (line) is increasing.

Hence, since the second line is not decreasing, the piecewise function is not the piecewise function shown in the picture.

- Second piecewise function,

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]

First line,

We have the first line,

[tex]-x-2<0\\[/tex]

The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exist from all the numbers less than 0, to 0.

Second line,

[tex]-\frac{x}{2}\geq 0[/tex]

The variable has a negative coefficient ([tex](-\frac{1}{2})[/tex], meaning the the unction (line) is decreasing, also we can see that the function does exists from 0 (including it) to the positive numbers.

Hence, we have that the correct option is the second piecewise function,

[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]

Note: I have attached a picture for better understanding.

Have a nice day!

find the distance between the two points 4,1 and -3,-2. Show your work​

Answers

Answer:

The distance between two points is √58 or 7.61.

Step-by-step explanation:

In the question we need to find the distance between two points 4,1 and -3,-2 given.

Distance between two points can be found using the formula:

[tex]d(P1,P2) = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex]

Putting the given points in the formula we get,

x₂ = -3, x₁ = 4, y₂= -2, y₁= 1

[tex]=\sqrt{(-3-(4))^2 + (-2-(1))^2} \\=\sqrt{(-3-4)^2 + (-2-1)^2}\\=\sqrt{(-7)^2 + (-3)^2}\\=\sqrt{49 + 9}\\=\sqrt{58}\\=7.61[/tex]

So, the distance between two points is √58 or 7.61.

The density of an object is its mass per unit volume. An object has a mass of 4.2 grams and a volume of 2 cm3. What is the density of the object?
A. 8.4 g/cm^3
B. 0.5 g/cm^3
C. 2.1 g/cm^3
D. 2.2 g/cm^3

Answers

Answer:

C. 2.1 g/cm^3

Step-by-step explanation:

The density of an object is its mass per unit volume.

The formula for density is:

[tex]D=\frac{M}{V}[/tex]

The object has a mass of 4.2 grams.

[tex]\implies M=4.2g[/tex]

and a volume of 2 cubic centimeters

[tex]\implies V=2cm^3[/tex]

We substitute the known values into the formula to get:

[tex]D=\frac{4.2}{2}gcm^{-3}[/tex]

We simplify to obtain:

[tex]D=2.1gcm^{-3}[/tex]

Answer:

2.1 g/cm^3 so its c

Select all the equations where c=9 is a solution. Choose 2 answers:

A. 4 - c =5

B. 20 = 14 + c

C. 15 = c - 6

D. C/3 = 3

E. 36 = 4c

Answers

Answer is D and E

Since 9 divided by 3 is three it would be correct and 4 multiplied by 9 is E would be correct. The others just don’t add up.

The equation where c = 9 should be option D and option E.

Given information:

C = 9

Equation selection:

If [tex]C \div 3 = 3\\\\[/tex]

So this should be correct as 3 = 3

And,

36 = 4c

c = 9

Learn more about the equation here: https://brainly.com/question/18715058

Convert the complex number z = 4 - 10i from rectangular form to polar form.​

Answers

ANSWER

[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]

EXPLANATION

The polar form of a complex number ,

[tex]z = x + yi[/tex]

is given by:

[tex]z = r( \cos( \theta) + i \sin( \theta) )[/tex]

where

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

The given complex number is:

[tex]z = 4 - 10i[/tex]

[tex]r = \sqrt{ {4}^{2} + {( - 10)}^{2} } [/tex]

[tex]r = \sqrt{16 + 100} [/tex]

[tex]r = \sqrt{116} = 2 \sqrt{29} [/tex]

And

[tex]\theta= \tan^{ - 1}(\frac{ y}{x} )[/tex]

[tex]\theta= \tan^{ - 1}(\frac{ - 10}{4} )[/tex]

[tex]\theta= 292 \degree[/tex]

Hence the polar form is :

[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]

please help answer all please!!!!The graph below represent a trip taken by bicycle. Use the graph to answer questions


11. During the trip the cyclist stops for a time. During which labeled section-A, B, C, or D- did he stop? ________

12. During which labeled section was he traveling the slowest? _______

13. During which labeled section was he traveling the fastest? ______

14 Calculate the speed of the cyclist during section D _______

15. How far away was the cyclist when he turned around and headed home? _______

Answers

Answer:

Part 11) The cyclist stops for a time during the section B

Part 12) He traveling slowest in section A

Part 13) He traveling fastest in section C

Part 14) The speed in section D is 20 km/h

Part 15) The cyclist was 60 km from home when he turned around

Step-by-step explanation:

we know that

The speed is the ratio of the distance by the time

s=d/t

The slope of the graph is equal to the speed of the cyclist

Part 11. During the trip the cyclist stops for a time. During which labeled section-A, B, C, or D- did he stop?

The cyclist stops for a time during the section B

Because, during section B the distance is a constant (d=30 km)

therefore

The speed is equal to zero (Remember that the slope of a horizontal line is equal to zero)

Part 12. During which labeled section was he traveling the slowest?

Find the slope (speed) in each section

Find the slope in section A

Let

A(0,0) and B(4,30)

the slope is equal to

m=(30-0)/(4-0)=7.5 km/h

Find the slope in section B

Is a horizontal line

therefore

the slope is equal to

m=0 km/h

Find the slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h

Find the slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

He traveling slowest in section A

Part 13. During which labeled section was he traveling the fastest?

Remember part 12)

Slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h ----> is the greater slope

therefore

He traveling fastest in section C

Part 14. Calculate the speed of the cyclist during section D

Remember part 12)

Slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

The speed in section D is 20 km/h

Part 15. How far away was the cyclist when he turned around and headed home

Observing the graph

we know that the cyclist turned around at point (7,60)

therefore

The cyclist was 60 km from home when he turned around

the probability of getting number 2 when a die is rolled​

Answers

1/6 Of A Chance So UnlikelyIf There Are Only 6 Sides On A Dice, Rolling A Number 2 Would Be Unlikely But Possible.

A pharmacist weighed eight different capsules of the same compound and recorded these measurements: 2312 mg, 2313 mg, 2315 mg, 2321 mg, 2325 mg, 2310 mg, 2320 mg, and 2319 mg. What is the median measurement? What is the mean measurement?

Answers

Final answer:

The median measurement of the capsules is 2317 mg, which is the average of the fourth and fifth values when listed in order. The mean measurement is also 2317 mg, found by summing all measurements and dividing by the total number of samples.

Explanation:

To find the median measurement of the pharmacist's recorded capsule weights, we first list the measurements in numerical order: 2310 mg, 2312 mg, 2313 mg, 2315 mg, 2319 mg, 2320 mg, 2321 mg, 2325 mg. Since there are eight measurements (an even number), the median is the average of the fourth and fifth measurements: (2315 mg + 2319 mg) / 2 = 4634 mg / 2 = 2317 mg. Therefore, the median measurement is 2317 mg.

To calculate the mean measurement, we sum all the measurements and then divide by the number of measurements: (2312 mg + 2313 mg + 2315 mg + 2321 mg + 2325 mg + 2310 mg + 2320 mg + 2319 mg) / 8 = 18535 mg / 8 = 2316.875 mg. The mean measurement, rounded to the nearest milligram, is 2317 mg.

Choose the answer that correctly solves the equation: 6 x 4 + 3 = ?

Answers

Answer:

27

Step-by-step explanation:

because 6×4 is 24 and 24+3 =27

Answer:

The answer is 27

Step-by-step explanation:

Using Pemdas (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) 6 x 4= 24 then 24 + 3= 27.

Hope this helps. Please name me Brainliest

How many solutions are there to the equation below 9x+16=4x

Answers

Answer:

one solution

Step-by-step explanation:

9x+16=4x

16=4x-9x

16/-5=x

x=-3.2

Other Questions
save hangman by figuring out what these word are...CO_ _ T D_ _ C _ L _A.a popular tourist attraction. B.an item of food.C.a character from a book or movie. D.a song. Triangle ABC is similar to triangle DEF. The length of AC is 10cm. The length of BC is 16 cm. The length of DF is 8cm. What is the length of EF? The average power dissipated by a resistor connected to a sinusoidal emf is 5.0 W.a) What is Pavg if the resistance R is doubled?Pavg=IR2RPavg=IR22R =IR2R Pavg=2.5 Wb) What is P_{\rm avg} if the peak emf {\cal{E}}_0 is doubled?c) What is P_{\rm avg} if both are doubled simultaneously? What is pH?A. How basic a solution isB. The concentration of potassium ions in solutionC. How acidic a solution isD. The concentration ions in a solution Enrique, porqu __________ enojado ayer?EstabasEstabaisEstabanEstabamos George measured the capacity of a cardboard box as 400 in3. The true capacity of the cardboard box is 450 in3. What is the percent error in Georges measurement? If necessary, round to the nearest percent. A comparative box plot is shown for two data sets. Which statement is true? (Please help me and please if you're not 100% sure)Answer Choices A. At least 50% of the data for each set is between 13 and 16.B. Less than 25% of the data for the sets overlap.C. More than 25% of the data for each set is greater than 15.D. At least 75% of the data is greater than 16. French True or False What mainly does Ashe identify as the reason for the lack of historical documentation for King Arthurs conquests in Conversation with Geoffrey Ashe?A. War journalism did not exist at the time of King Arthur.B. King Arthur is an entirely fictional character.C. The documentation of King Arthur was likely destroyed.D. King Arthurs conquests were recorded in French. Immigrants from Southern Europe who arrived in U.S during the late 19th and the early 20th century tended to settle in Toms es el____artista de la clase. Dibuja super bien.msmenosmejorpeor Which process has been largely responsible for increasing the amount of co2 in the last 200 years? increasing cattle ranching worldwide burning of fossil fuels? Find the value of the matrices A) 17B) 12C) 15D) 13 At an elementary school carnival, students can draw a rubber duck out of a tub of water. Each duck has a number written on the bottom of it which correlates with a prize. There are a total of 8 ducks in the tub. Two ducks have a 5 on them, four ducks have a 6 on them, and two duck has a 7 on it. What is the expected value of a duck?a. 8.25b. 6.85 c. 25d. 4Please help!!!! Eight less than seven times a number is the same as for l four more than three times a number. Find the number. In a species of ground finch that inhabits the galapagos islands, the average beak size increased over several generations from 9 mm to 10 mm after a drought that left only large hard seeds for the finches' food source. this is Which is the advantage of waters heat capacity The density of an object is its mass per unit volume. An object has a mass of 4.2 grams and a volume of 2 cm3. What is the density of the object?A. 8.4 g/cm^3B. 0.5 g/cm^3C. 2.1 g/cm^3D. 2.2 g/cm^3 Fifteen friends share 20 cups of popcorn equally. Which faction of a cup does each friend get? In a short paragraph of at least five sentences, describe the three common forms of city government.