A right circular cone has a radius of x+4 and a height 5 units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is V=13πr2h for radius r and height h. Enter π as pi.

A Right Circular Cone Has A Radius Of X+4 And A Height 5 Units Less Than Its Radius. Express The Volume

Answers

Answer 1

The equation of the volume function is V(x) = 1/3(x + 4)²(x - 1)

How to determine the volume function?

The given parameters are

Radius, r = x + 4

Height, h = 5 units less than the radius

This means that

h = r - 5

So, we have

h = x + 4 - 5

Evaluate

h = x - 1

The volume of a cone is calculated as

V = 1/3πr²h

Substitute the known values in the above equation

V = 1/3 * (x + 4)² * (x - 1)

This gives

V = 1/3(x + 4)²(x - 1)

Express as a function

V(x) = 1/3(x + 4)²(x - 1)

Hence, the function is V(x) = 1/3(x + 4)²(x - 1)

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Related Questions

can you please help me with my homework and I have a picture of it. 2 raised to the power 3

Answers

The power 3 means "multiplying 3 copies" of (in our case) 2 ;

[tex]2^3=2\times2\times2[/tex]

which is equal to 8.

Answer:

8

Step-by-step explanation:

Kinsley is thinking of a secret number, she tells her brother the number she's thinking of is divisible by 3, then tells her friends it's divisible by 17, if Kinsley is telling the truth to both of them, what could be the number she is thinking of?​

Answers

I’d say 51. 51 divided by 3 is 17 and 51 divided by 17 is 3

Answer:

51

Step-by-step explanation:

17 x 3 = 51. To check this answer, you can do

51 ÷ 17 = 3

51 ÷ 3 = 17

Eva is making smoothies. Each smoothie uses scup of yogurt. How many
cups of yogurt does she need to make 4 smoothies? Express your answer in
simplest form.

Answers

Cups of yogurt she needs to make 4 smoothies is 20 cups

What is Fraction?

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

Given,

5cups of yogurt is used to make 1 smoothie

We have to find out that how cups of yogurt will it take to make 4 smoothies

1 smoothie = 1 x 5cups

4smoothies = 4 x 5cups

                    = 20 cups

Hence, 20 cups of yogurt is needed to make 4 smoothies

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The prime factor trees for 14 and 15 are
shown.
a) Write down the lowest common
multiple (LCM) of 14 and 15 as the
product of its prime factors.
b) Hence, work out the lowest common
multiple (LCM) of 14 and 15.
2
14
7
3
15
5

Answers

Answer:

14 = 2 * 7

15 = 3 * 5

LCM = 2 * 3 * 5 * 7 = 210

Which point is a solution to this system of inequalities?
y < 1/2x - 3y + 2x > 6
A. (7-8)
B. (2-3)
C. (5,-2)
D. (4,1)

Answers

Option C is correct. The (5,-2) point solves the given system of inequalities y < 1/2x - 3 and y + 2x > 6.

What exactly is an inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

The given system of inequalities is as follows:

y < 1/2x - 3, y + 2x > 6

Substituting (7,-8) in these inequalities,

y < 1/2x - 3

y < 0.5

-8 < 0.5 is true

y + 2x > 6

-8 + 14 > 6

6 > 6 is false

So this is incorrect option.

Similarly, substituting (2,-3) in these inequalities,

y < 1/2x - 3

y < -3

-3 < -2 is true

y + 2x > 6

1 > 6 is false

So this is incorrect option.

Substituting (5,-2) in these inequalities,

y < 1/2x - 3

-2 < -0.5 is true

y + 2x > 6

8 > 6 is true

So, this is correct option.

Therefore, (5,-2) point is a solution to the given system of inequalities y < 1/2x - 3 and  y + 2x > 6. So, Option C is correct.

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Pic below!! Find the surface area of a cube with side length of three meters.

Answers

A 3x3 Rubik's cube has a total surface area of 54 cm2.

HELP please

Giving brainlyest

Answers

The equation of the line that contains (-4, 6) and (7, -5) in point slope form is y + 5 = - 1(x - 7).

How to represent equation in point slope form?

The point slope form can be represented as follows:

y - y₁ = m(x - x₁)

where

m = slopex₁ and y₁ are the coordinates.

Therefore, the equation of the line that contains (-4, 6) and (7, -5) can be found in point slope form as follows:

Hence,

m = -5 - 6 / 7 + 4

m = - 11 / 11

m = -1

Therefore, using (7, -5)

y + 5 = - 1(x - 7)

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1. Kylie mowed Mr. Johnson's lawn for
4 weeks. Every week Mr. Johnson
paid Kylie $15.43. How much money
did Kylie earn after the four weeks?
$71.62
c. $60.72
b. $61.72
d. $70.62

Answers

Answer:

The answer is b. $61.72

Step-by-step explanation:

Since she mowed the lawn for 4 weeks, and each week Kylie earned $15.43, then 4 x 15.43 = $61.72 after 4 weeks.

The answer to this question would be
B. $61.72

Which binomial is a factor of
x² + 2x - 15?

O A. (x+15)
O B.(x-3)
O c.(x - 1)
O D. (x - 5)

Answers

 Binomial is a factor of ( x² + 2x - 15) is (x − 3) .

Why does a binomial qualify as a factor?

Despite the fact that many distinct expression types can be categorized as binomials, not all of them can be factored. A binomial must have one of the following in order to be factorable: a difference of two squares, a difference of cubes, a sum of cubes, or a greatest common factor.

In math, what is a binomial?

Having two terms makes a polynomial a binomial. Binomials include, for instance, x 2 x -2 x2 and x 6 x -6 x6. This article will go over multiplying these binomials.

Separate the expression into groups using (x^2+3x)+ (5x-15)

Factor x from (x^2-3x)

x(x-3)

Subtract 5 from 5x-15.

5(x-3)

=> x(x-3)+5(x-3)

Remove the common term (x-3) (x-3)(x+5) since (x-3) and (x+5) are binomials of (x2+2x-15).

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Parking for 4 hours costs $10. Parking for 5 hours costs $12. Is this a proportional relationship, and if so, what is the constant of the proportionality

Answers

No, this is not a proportional relationship.

Proportional relationships are relationships between two variables where their ratios are equivalent.

In this scenario the ratio between 4 hours and $10 parking cost comes out to be 10/4=2.5

But in the second case the ratio between 5 hours and $12 paring cost comes out to be 12/5=2.6

Since the ratios don't come out to be equal therefore this is not a proportional relationship .

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Which table has a constant of proportionality between y and c of 3/4?

Answers

Answer:

answer Is A.............

Express your answer as a polynomial in standard form.
f(x) = 2x² + 3x + 12
g(x) = 5x - 6
Find: (gof)(x)

Answers

The  answer as a polynomial in standard form is 50x² - 45x +66.

What are polynomials?

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of a single indeterminate x polynomial. Sums of terms with the pattern k x n—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

g(x) = 5x - 6

So,

f(x) = 2(5x - 6)² +  3(5x - 6) + 12

= 2( 25x² + 36 - 60x ) + 15x - 18 + 12

= 50x²  + 66 - 45x

= 50x² - 45x +66

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Solve the problem. Express your answer to the correct number of significant figures.

6.221 × 7.11 − 13.7 =

Answers

We need to know about significant figures to solve this question. The value of the expression is 30.53131

Significant figures are the number of digits in a value that contribute to the degree of accuracy of the value. In the given expression we have three decimal numbers that have different significant figures, we need to solve the expression to get the answer with the right number of significant numbers. When a number starts with zero, the zeros are not significant, when a decimal number ends with zero, the zeroes are not significant.

6.221x7.11-13.7=44.23131-13.7=30.53131

Therefore the solution of the expression is 30.53131

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5.
Amelia buys 6 cans of beans for $1.50 each. She also buys a
pineapple. The total cost of the items is $12.30, What is the cost of
the pineapple?

Answers

The answer is $3.30. Each can is $1.50 so 6x1.5=9. Then you have to subtract the 9 from 12.30 to get the cost of the pineapple. 12.30-9=$3.30

2. Big TV prices Here are prices and screen sizes (in inches, measured diagonally) for 7 different sizes of one brand of LED HD television.47 Use technology to calculate the equation of the least- squares regression line relating y = price to x = screen size. Screen size Price 60 1000 55 800 50 700 47 600 42 430 39 400 32 300

Answers

The general formula for the least-squares regression is:

[tex]y=a+bx_i[/tex]

Where

a represents the y-intercept

b represents the slope

To estimate the y-intercept and the slope of the regression line you have to apply the following formulas:

[tex]b=\frac{\Sigma xy-\frac{\Sigma x\Sigma y}{n}}{\lbrack\Sigma x^2-\frac{(\Sigma x)^2}{n}\rbrack}[/tex][tex]a=\bar{y}-b\bar{x}[/tex]

First, calculate the sums and the means for both variables.

X= screen size

Y= price

n=7

[tex]\begin{gathered} \Sigma x=60+55+50+47+42+39+32 \\ \Sigma x=325 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2=60^2+55^2+50^2+47^2+42^2+39^2+32^2 \\ \Sigma x^2=15643 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{\Sigma x}{n} \\ \bar{x}=\frac{325}{7} \\ \bar{x}=46.43 \end{gathered}[/tex][tex]\begin{gathered} \Sigma y=1000+800+700+600+430+400+300 \\ \Sigma y=4230 \end{gathered}[/tex][tex]\begin{gathered} \bar{y}=\frac{\Sigma y}{n} \\ \bar{y}=\frac{4230}{7} \\ \bar{y}=604.29 \end{gathered}[/tex][tex]\begin{gathered} \Sigma xy=60\cdot1000+55\cdot800+50\cdot700+47\cdot600+42\cdot430+39\cdot400+32\cdot300 \\ \Sigma xy=210460 \end{gathered}[/tex]

Calculate the slope of the line:

[tex]\begin{gathered} b=\frac{\Sigma xy-\frac{\Sigma x\Sigma y}{n}}{\Sigma x^2-\frac{(\Sigma x)^2}{n}} \\ b=\frac{210460-\frac{325\cdot4230}{7}}{15643-\frac{325^2}{7}} \\ b=\frac{210460-196392.85}{15643-15089.29} \\ b=\frac{14067.75}{553.71} \\ b=25.41 \end{gathered}[/tex]

Once you have calculated the slope, you can calculate the y-intercept:

[tex]\begin{gathered} a=\bar{y}-b\bar{x} \\ a=604.29-25.41\cdot46.43 \\ a=604.29-1179.7863 \\ a=-575.23 \end{gathered}[/tex]

The regression line for the price with respect to the screen size is:

[tex]y=-575.23+25.41x[/tex]

The residents of a village want to paint a sign that shows the
The residents of a village want to paint a sign that shows the elevation of their village relative to the sea. Their altimeter shows +2,100 feet. What should their signboard read?

A.
2,100 feet above sea level
B.
2,100 feet below sea level
C.
-2,100 feet above sea level
D.
+2,100 feet below sea level

Answers

The residents of a village want to paint a sign that shows the elevation of their village relative to the sea. Their altimeter shows +2,100 feet. What should their signboard read?

A. 2,100 feet above sea level

B. 2,100 feet below sea level

C. -2,100 feet above sea level

D. +2,100 feet below sea level

EXPLANATION

Depth above water levels refers to a location's peak just above ocean.

If indeed the height is positive (+) then the depth might well just above water level and if negative (-) therefore the depth will be lower than the water level.

It would be answer A , 2100 feet above sea level

what is the answer to -3(4-5b+7)

Answers

Answer:

-33+15n

Step-by-step explanation:

You will have to first distribute the -3.

-3*4 is equal to -12

-3*-5b is equal to 15b     Note: -*-=+

-3*7 is equal to -21

Once you get those numbers you will have a equation like this

-12+15b-21

Combine like terms and you will get -33+15n as you answer

for a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as a. small as that provided by the sample. b. large as that provided by the sample. c. small as that provided by the population. d. large as that provided by the population.

Answers

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic is at least as small as that provided by the sample.

Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Probabilistic analysis of events is called statistics.

The lower-tailed test is a one-tailed test in which the critical region of the distribution is one-sided (leftmost) and tests whether a sample is less than a specified value.

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-9y+2(5y-2)
Preciso da resposta o Mais rápido possível

Answers

Answer:

y-4

Step-by-step explanation:

Which equation is perpendicular to
5-10y=6
and passes through (2.1)

Answers

Answer: x=2

Step-by-step explanation: Because there is only one variable in this equation, it makes a straight line. so to get a line, just do x= blank, but you need a point to go through (2,1), so x-2 is your equation.

If the odds against an event are 4:7, then the probability that the event will fail to occur is

Answers

The odds against an event is 4:7

Unfavourable elements for the event = 4

Favourable elements for the event = 7

Total = 4 + 7 = 11

Hence the probability that the event will fail = 4/11.

Please help mee,
It’s what I’m doing in technology class

Answers

Area of square with side = 4cm is : 16cm²

Area of rectangle with height = 2cm and width = 3cm is : 6cm²

Explanation :

To find the area of square:

A square is a two-dimensional figure with equal-sized sides. Because all of the sides are equal, the area is length times width, which equals side side. As a result, the area of a square is side square.

                   Area = a×a

                            = a²

To find the area of rectangle :

In the rectangle opposite sides are equal .The area of a rectangle is calculated once the length and width are known. A rectangle's area can be calculated by multiplying its length and width.

                    Area = l x b

Given sides of square a = 4cm .

                   Area = a²

                   Area = 4²

                            = 16 cm²

Given sides of rectangle ,

                 l = 3cm

                b = 2cm

              Area = l × b

                      = 3 × 2

                      = 6 cm²

Area of square  is 16 cm²

Area of rectangle is 6 cm²

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What is the monthly payment for a $4,000 two-year loan with an APR of 4%?

Answers

     A loan calculator is an automated instrument that enables you to comprehend what your potential monthly loan payments and total loan cost might be. Online, you can find a variety of loan calculators, such as those for mortgages or other kinds of specialized loans.

What is the cost of a $4000 loan every month?

The amount due each month is $4000.

Detailed explanation:

Given: $4168.79 in total interest has been paid for a loan with a two-year term at 4% interest compounded monthly.

Identify: What is the loan's monthly payment?

Answer: $4168.79 in total interest for a two-year loan compounded monthly.

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I need help please!!

Answers

The most appropriate choice for slope will be given by -

1) Initially, as x increases, y also increases

2) Slope of the graph between x = 3 and x = 5  is 2

3) Slope of the graph between x = 5 and x = 9  is -1

4) Greatest value of y is y = 4 and it occurs when x = 5

What is slope of a line?

Slope of a line is equal to the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, slope = tan [tex]\theta[/tex]

Suppose  [tex](x_1, y_1)[/tex]  and [tex](x_2, y_2)[/tex]be two points on a line then the slope of the line is calculated by the formula

slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here,

1) Initially, as x increases, y also increases

2) Slope of the graph between x = 3 and x = 5 = [tex]\frac{4 - 0}{5 - 3}[/tex]

                                                                             = [tex]\frac{4}{2}[/tex]

                                                                             = 2

3) Slope of the graph between x = 5 and x = 9 =

                                                                                 [tex]\frac{4 - 0}{5 - 9}\\-\frac{4}{4}\\-1[/tex]

4) Greatest value of y is y = 4 and it occurs when x = 5

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PLEASE HELP!! These two shapes are similar. True or False?
(Be sure to use the two rules of similarity to make your choice)

A- True, because the corresponding side lengths are proportional and the corresponding angles are congruent.
B- False, because the corresponding side lengths are congruent but the angles are not proportional.
C- False, because the corresponding side lengths are congruent but the angles are not proportional.
D- True, because the corresponding side lengths and corresponding angles are the same size.

Answers

Answer:

True, because the corresponding side lengths are proportional and the corresponding angles are congruent.

Step-by-step explanation:

The statement (A) True, because the corresponding side lengths are proportional and the corresponding angles are congruent is correct.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that:

The two triangles are shown in the picture.

As we know from the definition of a similar triangle, two triangles have the same shape, but it is not compulsory to have the same size.

The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

As we can see in the picture,  the relevant angles are congruent and the corresponding side lengths are proportionate.

The triangles are similar.

Thus, the statement (A) True, because the corresponding side lengths are proportional and the corresponding angles are congruent is correct.

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Please help me solve this

Answers

On solving the expression 1/2 - 1/10 we get 2/5

What is fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example -  5/9. Here, (5) is called numerator and (9) is called denominator.

Given is the following expression -

1/2 - 1/10

We have -

1/2 - 1/10

Multiplying the denominator and numerator in 1/2 by 5, we get -

5/10

Now, the expression becomes -

5/10 - 1/10

(5 - 1)/10

4/10

2/5

Therefore, on solving the expression 1/2 - 1/10 we get 2/5.

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Angelica's bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the
bouquet is pink roses? There are 12 roses in a dozen.
O
O
O
5
12
12
517
775

Answers

Answer: 7/12

Step-by-step explanation:12/12-5/12=7/12

Find the unknown value please helppp​

Answers

Answer:

30

Step-by-step explanation:

To get from 15 to 5, you multiply 15 times 1/3, so do the reciprocal to get from x to 10. So, 10 times 3 is 30.

the unknown value is 30.
as you can see 5 times 3 equals to 15 therefore times 10 with 3 makes 30.

help me a=1/7(b+c-d-d)

Answers

The simplified equation of the equation given as a=1/7(b+c-d-d) is a = b/7 + c/7 - 2/7d

How to simplify the equation?

From the question, the equation is given as

a=1/7(b+c-d-d)

Rewrite the above equation properly

So, we have the following representation

a = 1/7(b + c - d - d)

Evaluate the like terms in the above equation

So, we have the following equation

a = 1/7(b + c - 2d)

Open the brackets in the above equation

So, we have the following equation

a = 1/7 * b + 1/7 * c - 1/7 * 2d

Evaluate the products in the above equation

So, we have the following equation

a = b/7 + c/7 - 2/7d

The above equation cannot be further simplified

So, we leave it like that

Hence, the simplified equation of a=1/7(b+c-d-d) is a = b/7 + c/7 - 2/7d

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Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?

Answers

Answer:

  $53

Step-by-step explanation:

You want to know Elijah's initial deposit if his deposits were ...

first week: 2x+3second week: addition = double the first weekthird week: addition = double the total so far; total is $477

Backward

If x2 is the amount in the bank after the deposit of week 2, the amount deposited in week 3 is 2(x2). The total after that deposit is 477, so we have ...

  x2 +2(x2) = 477

  x2 = 477/3 = 159

Working back another week, we figure ...

If x1 is the amount in the bank after the initial deposit, the amount deposited the following week was 2(x1). Then the total amount in the bank after that deposit is ...

  x1 +2(x1) = 159

  x1 = 159/3 = 53

Elijah put $53 in the bank the first week.

__

Additional comment

We're not asked for the value of x, so the expression 2x+3 doesn't come into play in this problem. (We can see that 2x+3 = 53  ⇒  x = 25.)

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