A company makes storage tanks in the shape of a cylinder of height H and radius R. The standard model the company sells has a height of 20 cm in the radius of 20 cm. Customers may also request tanks that have a smaller radius. For each centimeter a tank’s radius decreases, however it’s height must increase by 5 cm.

The volume of a cylinder Jeckel storage tank is represented by the formula V= 3.14 (radius)^2 (height). X represent the number of centimeters by which the radius is decreased due to a customer’s request. Write a function V(x) to represent the volume of a tank a customer a request as a function of X.

Answers

Answer 1

We are given the formula for volume V:

V = 3.14 r^2 h

where r is radius and h is height

The standard height and radius is both 20 cm each, therefore we can write it as:

V = 3.14 (20)^2 (20)

It is stated that the radius can be modified, for every 1 cm change in tanks radius, the height must increase by 5 cm, therefore:

V = 3.14 (20 – x)^2 (20 + 5x)

or in general form:

V = 3.14 (r – x)^2 (h + 5x)

Related Questions

How to solve it using the system of substitution

Answers

Find x, y,and z. Once ypu find that you should be able to find your answer

In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance? In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance?

Answers

no because it is taking the mean if the whole group and not each individual

Answer:

The weight loss program is statistically significant.

Step-by-step explanation:

We can define a statistically significant difference or result as a result which is not attributed to chance. In other words we can say that a statistical significance shows if the difference observed between groups is real or if it has occurred simply due to chance.

Here, given is that 40 subjects lost a mean of 3.0 lb after 12 months.

So, here the weight loss program is statistically significant as the results are unlikely to occur by chance.

Please help me with this!!

Answers

Answer: Choice C) 115 degrees

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

Explanation:

The three angles are 42, 73 and 65 degrees. Let's call them x,y, and z respectively
x = 42
y = 73
z = 65

To find an exterior angle for x, we subtract the given angle x from 180
180-x = 180-42 = 138
The exterior angle adjacent to angle x is 138 degrees. This isn't listed so we move on

Do the same for y
180-y = 180-73 = 107
This isn't listed either. So we move on

Repeat for angle z
180-z = 180-65 = 115
This is listed as choice C. That's why choice C is the answer

What is 2(6+5•2)=5(4-2•5)

Answers

32=-30
..................................

Answer: Not true

Step-by-step explanation: 2(16)=5(-6)

32=-30

This is not true

find an angle measure that is supplementary to this angle 126 degrees

Answers

Answer:

Step-by-step explanation:

Answer:

54°

Step-by-step explanation:

The sum of the measures of two supplementary angles is 180°.

180° - 126° = 54°

Answer: 54°

How many solutions are there?

Answers

the answer should be two

Lets find F^(-1) if
y=-2x+1
I’m not sure if the F^(-1)=1+x/2

Answers

close enough, let's do the switcharoo of the variables and solve for "y".

[tex]\bf y=-2x+1\qquad \boxed{x}=-2\boxed{y}+1\implies x-1=-2y \\\\\\ \cfrac{x-1}{-2}=y\implies \cfrac{1-x}{2}=\stackrel{f^{-1}}{y}[/tex]

So, again, we have our rules for mapping [tex]y[/tex] to [tex]x[/tex]:

[tex]y=-2x+1[/tex]

To find [tex]f^{-1}[/tex], we solve for [tex]x[/tex].

[tex]y-1=(-2x+1)-1[/tex] (subtract 1 from both sides)
[tex](y-1)/(-2)=(-2x)/(-2)[/tex] (divide both sides by -2)

That gives us

[tex]x= \frac{y-1}{-2} [/tex]

Now that we have a way of mapping [tex]y[/tex] back to [tex]x[/tex], all we do is swap the domain and range, and we have

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

Else's math class has 11 female students and 10 male students.Write the ratio of female students to the total number of students in two different ways.

Answers

The detailed answer explains how to write the ratio of female students to the total number of students in two different ways.

The ratio of female students to the total number of students:

11 female students to 21 total students: 11/21

Alternatively, you can simplify the ratio to 1 female student to 2 total students: 1/2

Please do not make into a fraction because I can’t use a fraction as an answer. Rewrite using a negative exponent.
1/(xy)^1

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ \cfrac{1}{(xy)^{+1}}\implies (xy)^{-1}[/tex]

The graph of a line goes up and to the right when

Answers

it has a positive slope.

Answer: When the coefficient of X is positive!

Y -2 > -11 what is the answer to this

Answers

-9 because you add positive 2 to counter act -2 which gives you -9

14???????????????????????

What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?

Enter your answer in the box.

Answers

Answer:

the slope is 3/4

Step-by-step explanation:

the slope is 3/4 because 3 is the y line and 4 is the x line giving you 3/4 as your slope.

The slope of the line that is perpendicular to a line whose equation is 3y=−4x+2 is 3/4

The given line equation is:

3y = -4x + 2

Express the equation in the point-slope form of a line equation

The point-slope form of the equation of a line is y = mx + c

where m represents the slope

and c represents the y-intercept

3y = -4x + 2

[tex]y = \frac{-4}{3}x +\frac{2}{3}[/tex]

Comparing the equation [tex]y = \frac{-4}{3}x +\frac{2}{3}[/tex] with y = mx + c:

The slope, m = -4/3

The slope of the line perpendicular to [tex]y = \frac{-4}{3}x +\frac{2}{3}[/tex] will be:

[tex]m_2= \frac{-1}{m} \\\\m_2= \frac{-1}{\frac{-4}{3} }\\\\m_2 = \frac{3}{4}[/tex]

The slope of the line that is perpendicular to a line whose equation is 3y=−4x+2 is 3/4

Learn more here: https://brainly.com/question/1417258

Dani is working a sample booth at the national soda and beverage convention. She is paid $1.50 for each of the first ten tastings $2.50 for each of the next twenty tastings and $4.00 for each tasting beyond thirty she conducts each day. Today Dani conducted 36 tastings. How much total pay did Dani earn today?

Answers

She conducted 36 tastings.

10 tastings are in the category of the first 10 tastings.
10 * $1.50 = $15.00

36 - 10 = 26
Out of the remaining 26 tastings, 20 are int eh category of "the next 20 tastings."
20 * $2.50 = $50.00
This accounts for 10 + 20 = 30 tastings.

36 - 30 = 6
She did 6 tastings beyond the 30 tastings, so for the last 6 tastings, she gets paid
6 * $4.00 = $24.00

The total pay is:
$15.00 + $50.00 + $24.00 = $89.00

5. A piece of plywood has a length that is 5 more than twice its width. Write the expression that represents the area of the plywood.

Answers

5w^2 = A

You would multiply the width (w) by 5 because it's 5 times more than twice it's width. Then w (Width) would be to the power of 2 because it's 5 times more than twice its width. And this will all equal the Area (a)

for the function:

f(x) = -3x^4

complete the table of values using at least 5 points.

x -2 -1 0 1 2

f(x)

Answers

To find the value of f(x) at the 5 provided values of x, we substitute that particular value for x in [tex]-3x^4[/tex].

Doing so, we get:

[tex]f(-2)=-3(-2)^4=-3(16)=-48\\ f(-1)=-3(-1)^4=-3(1)=-3\\ f(0)=-3(0)^4=0\\ f(1)=-3(1)^4=-3(1)=-3\\ f(2)=3(2)^4=-3(16)=-48[/tex]

A set of positive and negative rational numbers are shown. 715 , –215 , 1115 , 415 , –815 What is the difference between the largest and the smallest numbers in the list?

Answers

the largest is 1115
The smallest -815

to get the range, subtract smallest from largest

1115 - (-815) = x

x = 1930

The difference is 1930

hope this helps

The difference between these numbers is 1930

An ion has a charge of +7. How far is it from being neutral?

A. -0.07
B. -7
C. 7
D. 70
E. 0.7

Answers

wsedrftghjiuytrewsdfghjhgres

Your answer is E. Sorry if wrong hope this helped

(Might be wrong!)

Answer:

B. -7

Step-by-step explanation:

An atom has a neutral charge with equal numbers of positive and negative particles,

That is, an atom with no chargen or 0 charge is called neutral.

Given,

The ion has a charge of +7,

Also, + 7 - 7 = 0,

Thus, for being neutral the ion needs -7 charge,

Hence, option 'B' is correct.

What type of angles are 6 and 8?

Answers

These angles are called vertical angles. They will always be equivalent with each other.

These angles are called vertical angles.They will always be equivalent with each other and yes that’s the right answer smart cookie

willie wants to save for a new racing bike. if he deposits $250 in a saving account at 4% simple annual interest, what willis balance be after 3 years?
A.15
B.30
C.265
D.280

Answers

To find how much he gets a year, we multiply 250 by 0.04. He gets 10 dollars the first year. for year 2, we multiply 260 by 0.04 to get 10.4. Do the same to 270.4 to get 281.22. I'd only have to assume you don't get interest off of interest, so it'd round down to 280.

The formula is
A=p (1+rt)
A future value?
P present value 250
R interest rate 0.04
T time 3years
A=250×(1+0.04×3)
A=280

Hope it helps!

The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?

Which three expressions could be used to represent the numbers?

n; n - 4; 4n
n; 4 - n; n + 4
n; n/4; n + 4

Answers

Let's translate these sentences to math one-by-one.

"The sum of three numbers is 62..." translates to the expression:

? + ? + ? = 62

We aren't given any modifications to the first number, so let's just pick a variable n to represent it.

n + ? + ? = 62

The second number is "equal to the first number diminished by 4. We can interpret "diminished by 4" as meaning "subtracted by 4," so we now have:

n + (n - 4) + ? = 62

And finally, we have that the third number is "four times the first," which evidently implies multiplication of the first number by 4. Which gives us:

n + (n - 4) + (4n) = 62

At this point, we don't even need to solve for n, since we already have our three expressions, and those are n, n - 4, and 4n.

David bought a used car for $3,000 and later sold it for $1,000. What was the approximate percent decrease in the price of the car?

Answers

The approximate decrease is around 66 percent.

The approximate percent decrease in the price of the car, would be 66%. Hope this helps.

Write 3 ½% as a fraction

Answers

Answer:

7/200

Step-by-step explanation:

3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200

_____

The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.

Factor this expression: ab + 4 + a + 4b

Answers

Grouping method works best on this one:

ab+a+4+4b=a(b+1)+4(b+1)
=(a+4)(b+1)

Answer:

Grouping method works best on this one:

ab+a+4+4b=a(b+1)+4(b+1)

=(a+4)(b+1)

Step-by-step explanation:

A card is drawn from a standard deck of 52 playing cards. find the probability that the card is an ace or a black card.

Answers

answer:28/52 chance aka 54% chance

Work:
Prob(ace or black card)= Prob(ace) + Prob(black card) - P(ace and black card)

=4/52 + 26/52 -2/52
=28/52

The probability that the card is an ace or a black card is 7/13

Probability is the likelihood or chance that an event will occur.

A standard card contains 52 cards. Hence the total outcome is 52.

Since there are 4 aces, the expected outcome is 4The total number of black cards is 26The total card that is ace and black is 2

Get the required probability;

Prob(ace or black card) = Prob(ace) + Prob(black card) - P(ace and black card)

Prob(ace or black card) = 4/52 + 26/52 -2/52

Prob(ace or black card) = 28/52

Hence the probability that the card is an ace or a black card is 7/13

Learn more on probability here: https://brainly.com/question/14192140

The coefficients of the expression 5x^4-4x^2+3 are??

Answers

The coefficients of the expression are 5 and 4 because they have a variable next to them. Hope this helps.

Which is the quadratic variation equation for the relationship y varies directly with x^2 and y=72 when x=3

Answers

y =72

x = 3

X^2 = 3^2 = 9

k = y/x = 72/9 =8

so you should have an option of:

y =8x^2

the answerto your question is =8x^2

bh+hr=25
solve for h and r

Answers

Take h common:

h(B + r) = 25

Divide b+r
h = 25/ b + r

Subtract bh:

hr = -bh + 25

Divide h:

r = -bh/h + 25/h

Simplify:

r = -b + 25/h

Hope this helps!

Final answer:

To solve for h and r in the equation bh + hr = 25, isolate one variable, solve for h using division, and solve for r by expanding the equation. There is no unique solution for h and r in terms of each other.

Explanation:

To solve for h and r in the equation bh + hr = 25, we need to isolate one variable on one side of the equation. Let's solve for h first:

bh + hr = 25

Factor out h from the left side of the equation:

h(b + r) = 25

Divide both sides by (b + r) to solve for h:

h = 25 / (b + r)

Now, let's solve for r. Replacing h in the original equation:

bh + hr = 25

b(25 / (b + r)) + r(25 / (b + r)) = 25

Multiply both sides by (b + r) to get rid of the denominators:

25b + 25r = 25(b + r)

Expand the equation:

25b + 25r = 25b + 25r

As we can see, the equation is an identity, meaning any value of r will satisfy it. Therefore, there is no unique solution for r in terms of h, and vice versa.

Learn more about Solving equations here:

https://brainly.com/question/14410653

#SPJ3

What is an equation of the line in slope-intercept form? m = 2 and the y-intercept is (0, 3)

Answers

set up as y=mx+b
y=2x+3

Straight line equation is given in the form

y = mx + c

m represents the gradient and c represent where the line intercept y-axis

The y-intercept happens when the value of x-coordinate is 0, so the coordinate is (0, c)

We have, m = 2 and c = 3
The equation of the line is: y = 2x + 3

(y3 - 4y2 + 7y - 6) ÷ (y - 2)

Answers

(3y-8y+7y-6)/(y-2)
(2y-6)/(y-2)
2(y-3)/2(y/2-2)
(y-3)/(y/2-2)

The blade of a circular saw rotates at a rate of \2500 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a 7 and one fourth7 1 4 inch diameter blade?

Answers

The answer to this question is 0.276miles for hour

Final answer:

The linear velocity of a point on the tip of the outer edge of the circular saw blade is 0.429 miles per hour.

Explanation:

To find the linear velocity of a point on the tip of the outer edge of the circular saw blade, we can use the formula:

Linear velocity = 2 * π * radius * angular velocity

Where the radius is half of the diameter. Given that the diameter is 7 1/4 inches, the radius is 7 1/4 / 2 = 3 5/8 inches or 3.625 inches. Converting this to feet, we get 3.625 / 12 = 0.302 feet. To convert the angular velocity from revolutions per minute to radians per second, we multiply by 2 * π / 60. Substituting these values into the formula, we get:

Linear velocity = 2 * π * 0.302 * (2500 * 2 * π / 60) = 37.699 feet per minute.

To convert this to miles per hour, we divide by 5280 (since there are 5280 feet in a mile) and multiply by 60 (since there are 60 minutes in an hour):

Linear velocity = (37.699 / 5280) * 60 = 0.429 miles per hour.

Other Questions