The volume of a cone is 180 in3. find a function that models the height h of the cone in terms of its radius r.

Answers

Answer 1

Final answer:

The function modeling the height of the cone in terms of its radius, given the volume of 180 in³, is h(r) = 540 / (πr²).

Explanation:

The volume V of a cone with radius r and height h is given by the formula V = (1/3)πr²h, where π is Pi (approximately 3.14159). Given that the volume of the cone is 180 in³, we can solve for the height h in terms of the radius r.

Starting with the formula:

V = (1/3)πr²h

We plug in the volume:

180 = (1/3)πr²h

To solve for h, we rearrange the equation:

h = 3*180 / (πr²)

h = 540 / (πr²)

So the function modeling the height h of the cone in terms of its radius r is:

h(r) = 540 / (πr²)

Related Questions

Which linear function has the greatest y-intercept?

A) x + 6y = 36

B) y = 15x + 5

C) 3x + 8y = 24

D) y = 4x + 7

Answers

I believe the answer is D).

Answer:

the answer is y=4x+7

Step-by-step explanation:

Find the 200th term, given the first term and the common difference. A1=34 and d=15

Answers

Try this solution:
1. it is arithmetic progression, where a₁=34 and d=15. Formula for aₓ is aₓ=a₁+d(x-1);
2. a₂₀₀=34+15*(200-1)=3019.

answer: 3019.
P.S. if it is possible check the arithmetic part.

A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
A.2.4
B.6.0
C. 9.2
D. 10.8

Answers

c. 9.2 is your answer

Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles?

∠M ≅ ∠A

∠M ≅ ∠D

∠M ≅ ∠C

Answers

Answer:

It is M = C

Step-by-step explanation:

The measure of the angle ∠WMT is congruent to the measure of the angle ∠DCA. Then the correct option is C.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ∆MTW is congruent to the triangle ∆CAD. Then we have

∠MTW ≅ ∠CAD

∠TWM ≅ ∠ADC

∠WMT ≅ ∠DCA

The proportion of the point ∠WMT is harmonious with the proportion of the point ∠DCA. Then, at that point, the right choice is C.

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Can someone please help me with 4?? I’m really struggling.

Answers

4) given is that
m<DAC=y
m<BAC=3x

ABCD is a square so m<DAB = 90° because each angle in a square is a right angle so 3x+y=90° (1) ;
AC is a diagonal in the square so m<DAC=m<BAC so 3x=y (2);

Find x by substituting y to 3x from (2) into (1)
3x+3x=90
6x=90
x=90/6=15°

Answer x=15°

Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .

1. k(x) = 2x + 3x + 2    k(x) = g(x) ∘ h(x)

2. k(x) = 2x - 3x - 2     k(x) = g(x) + h(x)

3. k(x) = (3x)2-x + 2-x + 1   k(x) = h(x) ÷ g(x)

4. k(x) = 23x + 2      k(x) = g(x) - h(x)

5. k(x) = 2x(3x + 2) k(x) = g(x) × h(x)

6. k(x) = 3(2x) + 2 k(x) = h(x) ∘ g(x)

Answers

the correct functions are
h(x) = 3x + 2
g(x) = 2^x

I proceed to calculate the different values of K (x)
case 1) k(x) = g(x) ∘ h(x)
g(x) ∘ h(x)=g(h(x))
k(x) = [2]^[3x + 2]-----------> is the option 4. k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)
k(x) = [2^x]+[3x + 2]=2^x+3x+2--------> is the option 1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)
k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)
is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)
k(x) = [2^x]-[3x + 2]=2^x-3x-2--------> is the option 2.) k(x) = 2^x - 3x - 2

case 5) k(x) = g(x) × h(x)
k(x) = [2^x]*[3x + 2]-----------> is the option 5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)
h(x) ∘ g(x)=h(g(x))
k(x)=3*[2^x]+2---------------> is the option 6. k(x) = 3(2^x) + 2

To simplify the other user's answer (which is correct):

1 = B

2 = D

3 = C

4 = A

5 = E

6 = F

Alternatively, your right boxes should look like:

How do you solve this inequality: 7 ≤ x+11

Answers

solve the inequality like an equation
7 ≤ x + 11
subtract 11 from both sides
-4 ≤ x

From there on, any number greater than or equal to -4 will be a solution to the inequality

Hope this helps

How do you solve this inequality: 7 ≤ x+11

[tex] 7 \leq x+11 \\ \\ 7 -11\leq x \\ \\ -4 \leq x\qquad\to\qquad x\in \left[-4; +\infty) [/tex]

Fiecare dintre cei 25 de elevi ai clasei a |||-a a realizat un jurnal al luni . Stiind ca pentru fiecare zi s-a folosit o pagina si ca luna are 31 de zile,afla cate pagini au jurnalele tuturor elevilor.

Answers

the question in English
Each of the 25 students in the class has made a journal on Monday. Knowing that every day a page was used and that the month is 31 days, find out how many pages the logs of all students.

Let
x--------------> total students
y--------------> total days in a month
z--------------> total page used per one student in 1 day
T--------------> total page used per total students in 1 month

we know that
x=25 students
y=31 pages
z=1 page

T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pages

the answer is 775 pages

the answer in Romanian

lăsa
x--------------> numărul total de elevi
y--------------> total zile într-o lună
z--------------> pagina totală utilizată pentru un student în 1 zi
T--------------> pagina totală utilizată pentru toți elevii în 1 lună
noi stim aia
x=25 elevi
y=31pagini
z=1 pagină

T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pagini

răspunsul este de 775 de pagini

A employer, who started a new business, has promised his employees a minimum starting wage of $3, with an increase of $2 every 4 years. Sketch a graph of wage as a function of time for 16 years. Assume the wages take effect at the beginning of the year where the change is made. (HINT: use a step function to represent the function.)

Answers

This is a step function because it increases in "steps". The wage stays constant for a 4 year period, then jumps by $2 instead of a steady increase.

Final answer:

To sketch the graph, use a step function to represent the wage as a function of time over 16 years. The minimum starting wage is $3, and it increases by $2 every 4 years.

Explanation:

To sketch a graph of wage as a function of time for 16 years, we can use a step function to represent the function.

The minimum starting wage is $3 and it increases by $2 every 4 years. For the first 4 years, the wage will be $3. At the start of the 5th year, the wage will increase to $5. This pattern continues, with the wage increasing by $2 every 4 years.

So, the graph will have flat lines representing each 4-year interval, with a step up at the start of each interval.

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the elevation in denver colorado is 13 times greater than that of waikapu, hawaii. the sum of their elevations is 5600 feet. find the elevation of each city

Answers

h1 = waikapu height
h2 = denver height

A) 13 h1 = h2
B) h1 + h2 = 5,600

B) h1 + 13h1 = 5,600
B) 14h1 = 5,600
h1 = Waikapu height = 400 feet

h2 = 5,600 - h1
h2 = 5,600 -400
h2 = Denver height = 5,200

Question 11 options: you take a ride on a ferris wheel which has a diameter of 300 feet. if you ride for four revolutions, what linear distance did you travel? use 3.14 for pi when completing your calculations. round your answer to the nearest whole number, if necessary. the distance traveled is

Answers

is there a slope/graph here?

Find the exact value of sin ( 2
a. if cos a = 3 /5 . assume a is a quadrant i angle in standard position.

Answers

In a right angled triangle 'efg' cos a = 3/5
From Pythagoras theorem the third side will be 4
cos a =3/5
sin a =4/5
sin 2a =2 x 4/5
sin 2a= 8/5

HELP! ASAP!
What is the measure of ∠A?

What is the measure of ∠B?

Answers

The opposite angles of a parallelogram are equal.
Therefore
m∠A = m∠C, so that
5y - 3 = 3y + 27
Subtract 3y from each side.
5y - 3y - 3 = 3y - 3y + 27
2y - 3 = 27
Add 3 to each side.
2y - 3 + 3 = 27 + 3
2y = 30
y = 30/2 = 15

Therefore
m∠A = 5*15 - 3 = 72°
m∠C = 72°

Let x = m∠B
Then x = , m∠B = m∠C
Because the sum of the angles in the parallelogram is 360°, therefore
x + x + 72 + 72 = 360
2x = 360-144 = 216
x = 216/2 = 108

Answer:
m∠A = 72°
m∠B = 108°

Answer:

What is the measure of ∠A?

72°

What is the measure of ∠B?

108°

Step-by-step explanation:

I literally copied and pasted from edge

Solve the following system of equations using matrices.
4x – 2y = -6
3x – 6y = -18

(40, 90)

(3, 0)

(0, 3)

(-6, 18)

Answers

It is convenient to let a calculator do the math.
.. (x, y) = (0, 3) . . . . . your 3rd selection

_____
I prefer using the RREF function to put the augmented matrix into reduced row-echelon form. If the equations are dependent or inconsistent, using that method tells you so without giving a matrix inversion error.

Select the correct factor from the presentation and calculate how many calories used. (Round to the hundredths.) A person weighing 165 lbs. jogs 1 mile in 8 minutes. How many calories used?
A. 102.30
B. 107.25
C. 253.85
D. 266.13

Answers

Answer:

the answer is 107.25

Step-by-step explanation:

Answer:

B. 107.25

Step-by-step explanation:

Let x be the calories burnt by the man,

Since, when a person runs 1 miles in 8 minutes,

Then,

[tex]\frac{\text{Calories used by him}}{\text{His weight in lb}}=65\%[/tex],

Given,

Weight of the person = 165 lb,

Thus,

[tex]\frac{x}{165}=\frac{65}{100}[/tex],

[tex]x = \frac{165\times 65}{100}[/tex]

[tex]x=\frac{10725}{100}[/tex]

[tex]\implies x=107.25[/tex]

Hence, 107.25 calories will be used.

X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X

Answers

According to ratio theorem;
x = 2/5(Q) + 3/5(P)
= 2/5(12.5,7.5) + 3/5(2,1)
= 2( 2.5, 1.5) + 3( 0.4, 0.2)
= (5,3) + (1.2,0.6)
= (6.2, 3.6)
The Coordinates of X will be;
=(6.2, 3.6)

Answer: (6.2, 3.6)

Step-by-step explanation:

We know that if a point M (x,y) divide a line segment having endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in ratio m:n , then the coordiantes of M is given by :-

[tex]x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}[/tex]

Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).

Then, coordinate of X is given by :-

[tex]x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6[/tex]

Hence, the coordinate of X = (6.2, 3.6)

Marie earns $96 in interest each year on an investment what is the rate of simple interest if her principal was $800

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$96\\ P=\textit{original amount deposited}\to& \$800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &\stackrel{each~year}{1} \end{cases} \\\\\\ 96=800(r)(1)\implies \cfrac{96}{800}=r \\\\\\ 0.12=r\implies r\%=100\cdot 0.12\implies r=\stackrel{\%}{12}[/tex]

The rate of simple interest that Marie earns on her $800 investment is 12% per year, calculated by dividing the annual interest earned ($96) by the principal amount ($800).

To find the rate of simple interest, we can use the formula Interest = Principal * rate * time. Given that Marie earns $96 in interest each year on an investment and her principal was $800, we can rearrange the formula to solve for the rate.

The formula for simple interest is:

Interest = Principal * rate * time

Assuming the interest earned is for one year, we have:

$96 = $800 * rate * 1 year

To find the rate, we divide both sides by $800:

rate = $96 / $800

rate = 0.12

Converting into a percentage, the simple interest rate is 12% per year.

Which graph shows the equation y = x + 2?

Answers

there ya go. your graphs should have this as one of the answers

Which equation has the graph that is a parabola with a vertex at 5,3

Answers

We can solve this using vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
In our case h=5 and k=3, these are coordinates of our vertex point.
There is no way to find a without knowing any other coefficients.
When you start solving some equations to get the parameters you always end up with identity (example 25=25). This means that your equation has an infinite number of solutions. In other words, any a will give you a parabola with vertex at the specified point.
The final answer would:
[tex]y=a(x-5)^2+3[/tex]
Where a is any real number.

Please help me it's homework.

Answers

Left Side
=======
2 faces of 2 * 8 = 32
2 faces of 2 * 7 = 28
2 faces of 7 * 8 = 112
Total = 172

Right Side Prism
=========
2 faces of triangles 1/2 * 7.2 * 4.8 = 34.56
1 bottom face of 7.2 * 10 = 72
2 slanted faces 6 * 10 = 120
Total 34.56 + 72 + 120 = 226.56

I'm in need of Brainlys. If this answer suits you can you award one if it is possible for you to do.

Number of security staff = a over 100 if a audience, is 10500, how many security staff are needed for the event

Answers

Substituting for "a" in the formula, we have
.. Number of security staff = 10500/100 = 105

Find the smallest value of k if 264k is a perfect square

Answers

Try factoring this first.
264k = 132*2k = 11*12*k = 11*3*2*2*k
To get a perfect square, you are going to have to have an even number of prime factors.
You have one 11 and one 3. You are going to have to do something about those two.
k = 11 * 3 <<<<< ======= answer.

Now put that into 264k and you get 11 * 3 * 2 * 2 * 11 * 3 which is a perfect square. 11^2 * 3^2 * 2^2 = 4356

The square root of 4356 = 66
4356 is a perfect square when 33 = k.

Which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x2 – 1) + (2x + 6))

(3x + 4) + (5x2 – 1)

(5x2 – 1) + ((3x + 4) + (2x + 6))

((3x + 4) + (5x2 – 1)) + (2x + 6)

(3x + 4) + (5x2 – 1) + (2x + 6)

Answers

Associative Property of Addition
(3x + 4) + [(5x2 - 1) + (2x + 6)]

As given in the definition below, to make it an associative property, we can change the bracket

[(3x + 4) + (5x2 - 1)] + (2x +6)

Your answer will be the third option :)

It's C.

Trust me, I had trouble figuring out this answer...

this is a physics question that requires a lot of math. Hoping on of you genius could help me.

Q: You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .

How much distance is between you and the deer. I solved this =23m

What is the maximum speed you could have and still not hit the deer?

The answer is 25 m/s. A lot of people had stated to use the quadratic formula. I just don't know where to begin.

Answers

I don't know why you need the quadratic formula.

If it takes 0.5 seconds before stepping on the breaks while going 16 m/s, then you travel 8 meters before anything happens. That means you are 44-8 = 36 meters away from the deer now.
v^2 = v_initial^2 + 2(acceleration)(distance)
0 = (16 m/s)^2 + 2(-10m/s^2)(distance)
256 m^2/s^2 / (2(10 m/s^2) = distance = 12.8 meters (13 meters after significant figures are taken into account).
The maximum speed would be:
0 = v_initial^2 + 2(-10m/s^2)(36m)
v_initial^2 = 720m^2/s^2
v_initial = 27 mph

Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.

Answers

we have that

(v+6)^2 = 324-----> I raise to 1/2 both members----> [(v+6)^2]^(1/2)=(324)^(1/2)[(v+6)]=(324)^(1/2)-------------> v+6=√324
v=√324-6---------> 18-6=12
v=12

the answer is v=12

Answer:

The values of v in increasing order are, -24, 12

Step-by-step explanation:

Given equation is,

[tex](v+6)^2=324[/tex]

[tex]v+6=\pm 18[/tex]

[tex]v=-6\pm 18[/tex]

[tex]\implies v=-6-18\text{ or }v=-6+18[/tex]

[tex]\implies v = -24\text{ or }v=12[/tex]

Since, -24 < 12

Thus, the values of v in increasing order are,

-24, 12

What is the denominator of the fraction 1/9?

Answers

The denominator is the bottom number it will be 9

9

any number below the bar is the denominator, any number above the bar is the numerator

what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π

Answers

All the similar circles have π in common.

Thus, option (c) is correct.

When two circles are similar, it means they have the same shape but possibly different sizes.

However, the ratio of their corresponding lengths, including the circumference, remains constant.

Second, the ratio of the diameter will be constant but not congruent.

Third, the value of π is the universal constant whose value is 22/7 or 3.14.....

which is the same for every similar circle.

Thus, π has a common value.

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Ava bought a rectangular rug for her hallway. The rug is 2\3 yards wide and 2 3\4 yards long. What is the area of the rug as a mixed number in simplest form?

Answers

2/3 * 2 3/4 = 1.83 That translated into fraction form is 1 5/6

Answer:

1 5/6

Step-by-step explanation:

How could the relationship of the data be classified? (1 point)

scatter plot with points loosely scattered going down to the right

Answers

Scatterplots are a useful way of visualizing statistical data and to draw some quick conclusions from the data. Each scatterplot is unique but there are some common trends about association of the 2 variables that can be applied. In a scatterplot with an upward trend, we would say that the variables have a positive association or that they have a positive correlation. When one variable increases, the other increases too (in general). If the plot has a downward trend, we talk of a negative association. Finally, there could also be no association, with plot points scattered all around. Thus, in this case, we have negative correlation. If there is anything else you need regarding this answer, comment.

.can you please help me thank you you will be given brainley

Answers

They aren't marked so that you can't tell. If I had to guess, I'd say it's SSS but it just a guess. Without markings of some kind we can't do much. SSS is based on appearance alone.

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