Pls help me it’s for my grade

The volume of the described solid is V = 16r³/3

Given,

A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)

Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = [tex]\int\limits^b_a {A(x)} \, dx[/tex]

The equation of circle x² + y² = r² where r is the radius of the circle.

Equation of upper semicircle yu= √(r²-x²)  and

Equation of lower semicircle yl = -√(r²-x²)

Area of cross-section A(x) = (yu² - yl²)

Substitute yu and yl values

A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²)        (1)

The limit for volume v varies from -r to r

Thus Volume v = ₋[tex]\int\limits^r_r {A(x)} \, dx[/tex]

Substitute A(x) from (1)

V = ₋[tex]\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx[/tex]

⇒V = 4[r²x - x³/3 ]

⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3

The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3

Learn more about volume of solid here;

https://brainly.com/question/29061740

#SPJ4

The population of the city in 2000 = 23.1 million

In 2006 the population will be equal to 28.3 million

Compound interest may be used in a variety of situations, including increasing or decreasing population, Increasing the count of bacteria increasing an item's value, and a decrease in an item's worth.  

The formula for Compound interest is given by

Where P = Principal amount or Initial value

r = rate of interest or increase

t = time period

Here we have

The formula [tex]A = 23.1 e^{(0.0152t)}[/tex] represents the population of a US state, A, in millions, 't' years after 2000.  

Here we need to solve the following questions

a. What was the population of the state in 2000

Compare the given formula with A = Pe^rt  

=>  [tex]23.1 e^{0.0152t} = Pe^{rt}[/tex]    

=> Initial value or initial population, P = 23.1 and

rate of increase r = 0.0152  

Therefore,

The population of the city in 2000 = 23.1 million

b. When will the population of the state reach 28.3 million?

As we know in 2002 the population = 23.1 million

Let's assume that after 'n' year the population will become 28.3 million

As we know Rate of increase = 0.0152    

From the given formula

Population of the city after n, A = 23.1 e^(0.0152n)  

As we assumed the population after n years = 28.3

=>  23.1 e^(0.0152n)  = 28.3

=> e^(0.0152n)  = 28.3/23.1

=> e^(0.0152n) = 1.225  

Apply log on both sides

=> log e^(0.0152n) = log 1.225  

=> 0.0152n log e = log 1.225  

=> 0.0152n (1) = 0.0881    

=> n = 0.0881/0.0152

=> n = 5.8 ≅ 6

After 6 years the population will be 28.3 million

After 6 years i.e 2000 + 6 = 2006  

Therefore,

In 2006 the population will be equal to 28.3 million

Learn more about Population Problems at

https://brainly.com/question/13945651

#SPJ4

The linear expression 6(y + 2) + 9 in the simplified form will be 6y + 27.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear expression is given as,

⇒ 6(y + 2) + 9

Simplify the expression, then we have

⇒ 6(y + 2) + 9

⇒ 6y + 18 + 9

⇒ 6y + 27

The linear expression 6(y + 2) + 9 in the simplified form will be 6y + 27.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

The value of each variable iS

x = 6

y = 4

What is angle bisector theorem?

The angle bisector theorem in geometry is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into. It compares their proportional lengths to the proportional lengths of the triangle's other two sides.

Apply the angle bisector theorem to solve for x and y respectively.

✔️4/(9 - x) = 8/x

Cross multiply

4*x = 8(9 - x)

4x = 72 - 8x

Add 8x to both sides

4x + 8x = 72

12x = 72

12x/12 = 72/12

x = 6

✔️y/2 = 6/3

Cross multiply

3*y = 6*2

3y = 12

3y/3 = 12/3

y = 4

To learn more about angle bisector theorem visit:https://brainly.com/question/10433817

#SPJ1

Answer:

B) Elias sold one-fourth the number of books Lena sold.

Step-by-step explanation:

How is this the answer? Well after I looked at the problem again, I realized what I needed to do. I needed to do 4,832*1/4 which is 1208.

I got this from the line that says "Elias sold 4,832 times one-fourth copies"

I hope this helps!!!!

Answer:

1st

Step-by-step explanation:

-400 degrees can also be seen as positive 40 degrees

The diagram that shows a valid approach to the given construction is option a for the perpendicular bisector.

A perpendicular bisector is a section of a line that divides a straight segment into two congruent or equal segments. At exactly its midpoint, they split the line section. With the line segment it divides, a perpendicular bisector produces a 90° angle. A line segment that bisects another line segment at an angle of 90 degrees is referred to as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal pieces by intersecting it at a 90° angle. The term "perpendicular bisector" refers to a precise drawing in which a line is accurately divided in half by another line that is perpendicular to the first line. To divide into two equal portions, or bisect, is a verb.

Therefore, The diagram that shows a valid approach to the f=given construction is option a.

To know more about perpendicular bisector, visit:

https://brainly.com/question/24753075

#SPJ1

Answer: 4 2/3

Step-by-step explanation:

Answer:

[tex]f(x)=3^{x+1}-3[/tex]

Step-by-step explanation:

The curve of the graph shows it is Exponential:  [tex]f(x)=b^{x-h}+k[/tex]

To find b, h, and k, we need to "un-transform" the graph from  [tex]f(x)=b^{x}[/tex]

1. h = horizontal shift/translation;  k = vertical translation:

  (0,1) ⇒ (-1,-2), so h = -1  and  k = -3  and  [tex]f(x)=b^{x+1}-3[/tex]

2. Given the points (-1,-2), (0,0), and (1,6), use one of them to find b:

     [tex]f(x)=b^{x+1}-3\\0=b^{0+1}-3\\0=b^{1}-3\\3=b^1\\3=b[/tex]

3. Place b, h, and k in their correct places in the function.

A balloon payment is a one-time, large-scale principal payment made near the end of the loan term.

To learn more about demand curve demonstrate refer to:

https://brainly.com/question/5687758

#SPJ1

Answer:5

Step-by-step explanation:

5 2 . 3 8

5= tens

2= ones

3= tenths

8= hundreths

The requested value of f(4) is -10.

What is an expression?

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Here, we have

Given:  f(x) =(7x+7, if x ≤ 0

2-3x, if 0 =X, if x ≥ 3

f(4) means the value of f(x) when x = 4.

Which expression on the right applies when x = 4?  

The first one because it applies only when x ≤ 0 and

The last one because it applies when x ≥ 3 and 4 is greater than 3.  The answer is the last expression.

since 4 lies between 0 and greater than

f(4) = 2 - 3(4)

f(4) = -10

Hence, the requested value of f(4) is -10.

To learn more about the expressions from the given link

https://brainly.com/question/4344214

#SPJ1

The term which are not constant are;

⇒ 32pq², - 4p²q, 12 pq

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

⇒ 32pq² - 4p²q + 12pq - 7

Now,

We know that;

In the algebraic expression the constant term has no variables.

Thus, The term which are not constant are;

⇒ 32pq², - 4p²q, 12 pq

Therefore, The term which are not constant are;

⇒ 32pq², - 4p²q, 12 pq

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer: 2

Step-by-step explanation:

By using the concept of function, it can be calculated that-

(g.f)(x) = 8x - 5

(g - f)(x) = -2x - 5

(g + f)(3) = 13

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

a) The given functions are

   f(x) = 4x

  g(x)= 2x - 5

  (g.f)(x) = g(f(x)) = 2(4x) - 5 = 8x - 5

   (g - f)(x) = g(x) - f(x) = 2x - 5 - 4x = -2x - 5

    (g + f)(x) = g(x) + f(x) = 2x - 5 + 4x = 6x - 5

     (g + f)(3) =  6 [tex]\times[/tex] 3 - 5 = 13

To learn more about function, refer to the link -

https://brainly.com/question/22340031

#SPJ4

Answer:

1= 50

2=1,16

Step-by-step explanation:

because it not have graph

Answer:

B

Step-by-step explanation:

Assuming these 4 are the only possibilities:

A: This cannot be correct because if 181 were divisible by 9, it would not be prime, as the problem suggests.

C: This cannot be correct because 181/9 is 21.11, which is not a whole number

D: This cannot be correct because 181/3 is 60.333, which is not a whole number

Thus, the answer is B.

FUN FACT:

When seeing whether a number is divisible by 3, add up its digits, and if they are divisible by 3, so is the number. Example: 36 is divisible by 3 because   3 + 6 = 9, and 9 is divisible by 3. 181 is not, however, because 1+8+1=10, and 10 is not divisible by 3.

Same with 9! 459 is divisible by 9 because 4+5+9 = 18, which is divisible by 9. 181 is not, however, because 1+8+1 = 10, which is not divisible by 9.

I hope this helps!

Answer:

B. 181 is prime because its only factors are 1 and itself.

Step-by-step explanation:

Prime number

A whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).  

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.

Composite number

A number that is divisible by a number other than 1 and itself (so it has more than 2 factors).  

An example of a composite number is 6 as its factors are 1, 2, 3 and 6.

The factors of 181 are 1 and 181.

Therefore, it is prime because its only factors are 1 and itself.

Answer:

I believe it is positive although I am not 100% sure.

Step-by-step explanation:

The arrows tend to go upwards even though it does have a curve at the bottom. It is still going upwards.

The diagonal of a rectangle with a width of 12 units and a length of 16 units is 20 units

From the question, we are to determine the length of the diagonal of the rectangle

From the given information,

The width of the rectangle is 12 units

and

The length of the rectangle is 16 units,

The diagonal, D, of a rectangle is given by

D = √(l² + w²)

Where l is the length of the rectangle

and w is the width of the rectangle

l = 16

w = 12

Thus,

The diagonal of the rectangle is

D = √(16² + 12²)

D = √(256 + 144)

D = √400

D = 20

Hence, the diagonal is 20 units

Learn more on Calculating the diagonal of a rectangle here: https://brainly.com/question/15728315

#SPJ1

Answer: 2 or 1?

Step-by-step explanation:

3^1 = 3 then 3 - 1 = 2

or 3^(1 - 1) then 3^0 = 1

The required intersection of the two sets A and B is given as A∩B = [8, 5, 0].

Given that,
Let A={9,8,3,0,5} and B={8,4,7,5,0}. The intersection of A and B is to be determined.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

here,
P[PUB] = {9,8,3,4,0,5,7} = 7
P[A∩B] = P[A] + p[B] - P[AUB]
P[A∩B] = 5 + 5 - 10
            = 3
From accumulating the common elements between the sets,
A∩B = [8, 5, 0]

Thus, the required intersection of the two sets A and B is given as A∩B = [8, 5, 0].

Learn more about sets here:
https://brainly.com/question/8053622
#SPJ1

Some answers are correct, but not all.  These are ones that need fixing.

2a.  

[tex]\lim_{x\rightarrow-2^-}f(x) = 0[/tex] because as you come towards x = –2 from the left, your y-values are getting closer to 0.

2b.

[tex]\lim_{x\rightarrow-2^+}f(x) = 1[/tex] because as you come towards x = –2 from the right, your y-values are getting closer to 1.

2e.

[tex]\lim_{x\rightarrow5}f(x) = -1[/tex] because as you come towards x = 5 from both sides, your y-values are getting closer to -1.

3a.

[tex]\lim_{x\rightarrow3^-}f(x) = -1[/tex] because as you come towards x = 3 from the left, your y-values are -1.

[tex]\lim_{x\rightarrow3^+}f(x) = 1[/tex] because as you come towards x = 3 from the right, your y-values are 1.

[tex]\lim_{x\rightarrow3}f(x)[/tex] does not exist, since those two one-sided limits aren't don't agree.

3b.

[tex]\lim_{x\rightarrow0^-}f(x) = -\infty[/tex] because as you come towards x = 0 from the left, your y-values are getting huge in a negative way.

[tex]\lim_{x\rightarrow0^+}f(x) = \infty[/tex] because as you come towards x = 0 from the right, your y-values are getting huge in a positive way.

Answer:

Below

Step-by-step explanation:

$ 5   for the first one   <=== a fixed constant ....admission charge

.25  per minute   <===== charges dependent on the number of minutes

Answer:

pls rate brainliest

Step-by-step explanation:

the entrance fee to the skating rink=$5

each minute the skater uses the rink costs=$0.25

HOPE IT HELPED YOU

The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.

It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,

C(x) = 270 ln(x+1) + 1900

The average intake of calories consumed per day is given by C(x) = 2200

Here x is the number of acres of land. Then, the required number of acres of land is

C(x) = 270 ln(x+1) + 1900

⇒ 2200 = 270 ln(x+1) + 1900

⇒ 270 ln(x+1) = 2200 - 1900

⇒ 270 ln(x+1) = 300

⇒ ln(x+1) = 300/270 = 10/9

Applying base 'e' on both sides, we get

⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]

⇒ x+1 = 3.0377

⇒ x = 3.0377 - 1 = 2.0377

When rounding the final answer to the nearest tenths, we get x = 2 acres.

When rounding the final answer to the nearest thousand, we get x = 2.038 acres.

Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.

Learn more about algebraic expressions at the following link:

https://brainly.com/question/24875240

#SPJ1

Answer: 1/2

Step-by-step explanation:

slope is rise over run (up and down over left to right)

Answer:

Step-by-step explanation:

Its A

Answer:A

Step-by-step explanation:A cylinder with 8 units.

Answer:

5 i think

Step-by-step explanation: