Answer:
[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]
[tex]Cost = \$1.05[/tex]
Step-by-step explanation:
Given
[tex]Volume = 100in^3[/tex]
[tex]Cost =\$0.014[/tex] -- Top and Bottom
[tex]Cost =\$0.007[/tex] --- Sides
Required
What dimension of the cylinder minimizes the cost
The volume (V) of a cylinder is:
[tex]V = \pi r^2h[/tex]
Substitute 100 for V
[tex]100 = \pi r^2h[/tex]
Make h the subject
[tex]h = \frac{100 }{\pi r^2}[/tex]
The surface area (A) of a cylinder is:
[tex]A = 2\pi r^2 + 2\pi rh[/tex]
Where
[tex]Top\ and\ bottom = 2\pi r^2[/tex]
[tex]Sides = 2\pi rh[/tex]
So, the cost of the surface area is:
[tex]C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007[/tex]
[tex]C = 2\pi r(r * 0.014+ h * 0.007)[/tex]
[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]
Substitute [tex]h = \frac{100 }{\pi r^2}[/tex]
[tex]C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})[/tex]
[tex]C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})[/tex]
[tex]C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})[/tex]
[tex]C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})[/tex]
Open bracket
[tex]C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{2 *0.7}{r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{1.4}{r}[/tex]
[tex]C = 0.028\pi r^2+ \frac{1.4}{r}[/tex]
To minimize, we differentiate C w.r.t r and set the result to 0
[tex]C' = 0.056\pi r - \frac{1.4}{r^2}[/tex]
Set to 0
[tex]0 = 0.056\pi r - \frac{1.4}{r^2}[/tex]
Collect Like Terms
[tex]0.056\pi r = \frac{1.4}{r^2}[/tex]
Cross Multiply
[tex]0.056\pi r *r^2= 1.4[/tex]
[tex]0.056\pi r^3= 1.4[/tex]
Make [tex]r^3[/tex] the subject
[tex]r^3= \frac{1.4}{0.056\pi }[/tex]
[tex]r^3= \frac{1.4}{0.056 * 3.14}[/tex]
[tex]r^3= \frac{1.4}{0.17584}[/tex]
[tex]r^3= 7.96178343949[/tex]
Take cube roots of both sides
[tex]r= \sqrt[3]{7.96178343949}[/tex]
[tex]r= 1.997[/tex]
Recall that:
[tex]h = \frac{100 }{\pi r^2}[/tex]
[tex]h = \frac{100 }{3.14 * 1.997^2}[/tex]
[tex]h = \frac{100 }{12.52}[/tex]
[tex]h = 7.987[/tex]
Hence, the dimensions that minimizes the cost are:
[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]
To calculate the cost, we have:
[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]
[tex]C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)[/tex]
[tex]Cost = \$1.05[/tex]
Answer pls quick I don’t have enough time
hey there ..
plz show the graph also ..
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Which term best describes the savings account that Isabel has set up, given its purpose?
Select the correct answer.
es
Comments
O emergency fund
O mutual fund
Orainy-day fund
sinking fund
Answer:
Emergency Fund
Step-by-step explanation:
Isabel has setup fund for her emergency needs. She has started saving with named as emergency fund so that she can use her savings when she is in severe needs. Isabel has saved money and then she is now saving her money in saving accounts in the bank.
Lesson 3.4 different forms of liner
Equation
How do you solve it?
Y=2+3(×-1)
-3x - 4y = 4
-5.2 +y = 2
Is (2, 10) a solution of the system?
Answer:
No
Step-by-step explanation:
when checking to see if a point satisfies a system of equations
plug in x and y values from your point into the system
(2, 10)
x y
-3(2) - 4(10) = 4. and. -5.2 + 10 = 2
-6-40 = 4. 4.8. = 2
-46 = 4.
invalid statement. invalid statement
therefore the point (2, 10) does not satisfy this system of equations.
Tony bought x cans of tennis balls for $3 each. He bought the same number of water bottles for $5. He also
bought a tennis racket for $42
Ayana received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded 20 songs and 3 movies, which cost a total of $73. Using another, she purchased 5 songs and 17 movies, which cost a total of $197. How much does each download cost?
20s + 3m = 73
5s + 17m = 197
Eliminate s terms: Multiply second equation by -4, then add to first equation:
-20s - 68m = -788
20s + 3m = 73
—————————-
-65m = -715
m = (-715)/(-65) = 11
20s + 3(11) = 73
20s = 40
s = 2
A movie download costs $11. A song download costs $2
pls help asap!!!!!!!!!!!
Answer:
I can not see it well
Step-by-step explanation:
i don't see what your asking but thanxs for the points
i'll give you free point about 40 just look asap because people may snag it
How do you get from 4 to 4/3
Answer:
- 8/3
Step-by-step explanation:
Simply subtract 4 from 4/3
4/3 - 4 = 4/3-12/3=-8/3
Lets check of our answer is correct:
4 - 8/3 = 12/3 - 8/3 = 4/3. So our answer is correct.
in each bouquet of flowers there are four roses and 6 white carnations complete the table to find how many roses and carnations you still are in four bouquets of flowers
Answer:
so i hope im understanding this. for every 1 bouqet there is 4 roses 6 white carnations so the amount of roses in total you will need for the 4 bouques is 16 and the amount of carnations is 24
Step-by-step explanation:
1 b= 4r an 6c r= roses c=carnations
sooo 4+4+4+4=16 6+6+6+6= 24
1b= 4r 6c
1b= 4r 6c
1b= 4r 6c
1b= 4r 6c
a garden contains 135 flowers, each of which is either red or yellow. there are 3 beds of yellow flowers and 3 beds of red flowers. there are 30 yellow flowers in each yellow flower bed.
Part A: if r represents the number of flowers in each red flower bed, what equation could you use to represent the number of red and yellow flowers.
Answer:
135 = 3y + 3r
y = 30; r = 15
Step-by-step explanation:
y = 3y + 3r
Where,
y = total number of flowers in the garden = 135
y = number of flowers in each yellow flower bed = 30
r = number of flowers in each red flower bed
135 = 3(30) + 3r
135 = 90 + 3r
135 - 90 = 3r
45 = 3r
r = 45/3
r = 15 flowers
number of flowers in each red flower bed = 15
Exercise 1.6.3: Translating mathematical statements in English into logical expressions. info About Consider the following statements in English. Write a logical expression with the same meaning. The domain is the set of all real numbers. (a) There is a number whose cube is equal to 2. (b) The square of every number is at least 0. (c) There is a number that is equal to its square. (d) Every number is less than or equal to its square..
Answer:
a) Эx ∈ R ⊇ x³ = 2
b) ∀x ∈ R, x² ≥ 0
c) Эx ∈ R ⊇ x³ = x
d) ∀x ∈ R, x ≤ x²
Step-by-step explanation:
Given the data in the question;
let us first go through some symbols and their possible meanings;
Э ⇒ there exists
∀ ⇒ for all
∈ ⇒ belongs to or set membership or element of the set
⊇ ⇒ such that
now;
a) There is a number whose cube is equal to 2
let x represent the number; so
Эx ∈ R ⊇ x³ = 2
b) The square of every number is at least 0
x² ≥ 0, ∀x ∈ R
∀x ∈ R, x² ≥ 0
c) There is a number that is equal to its square
Эx ∈ R ⊇ x³ = x
d) Every number is less than or equal to its square.
x ≤ x², ∀x ∈ R
∀x ∈ R, x ≤ x²
A shoe store uses a 50
%
markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $59
?
Answer:
88.50
Step-by-step explanation:
59 divided by 2 (50%) = 29.50
59+29.50=88.50
Natasha rolls a fair dice 66 times.
How many times would Natasha expect to roll a number greater than 5?
Find 110.9% of 419.Round to the nearest hundredth.
Answer:
400
Step-by-step explanation:
When you are rounding to the nearest hundred you
You round the number up to the nearest hundred if the last two digits in the number are 50 or above.
Then, round the number down to the nearest hundred if the last two digits in the number are 49 or below and if the last two digits are 00, then you don't have to do any rounding, because it is already to the hundred.
Which pair of triangles can be proven congruent by SAS?
Answer:
SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.
*20 POINTS*
i swear to GOD PLEASEEE HELP MEEEEEBEJEBKE I’LL GIVE BRAINLEST TO WHOEVER ANSWERS CORRECTLY FIRST
The function below has at least one rational zero. Use this fact to find ALL zeros of the function.
g(x)=5x^3+x^2-20^x-4
If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.
Answer:
If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.
P: ±1, ±2, ±3, ±6 (all prime factors of constant term)
Q: ±1, ±7 (all prime factors of the leading coefficient)
P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7 (all possible values of P/Q)
Now, start testing your values of P/Q in your polynomial:
f(x)=7x4-9x3-41x2+13x+6
You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):
f(2)=7(16)-9(8)-41(4)+13(2)+6
112-72-164+26+6 ≠ 0
f(-2)=7(16)-9(-8)-41(4)+13(-2)+6
112+72-164-26+6 = 0 OK!! There is a zero at x=-2
This means (x+2) is a factor of the polynomial.
Now, do synthetic division to find the polynomial that results from
(7x4-9x3-41x2+13x+6)÷(x+2):
-2⊥ 7 -9 -41 13 6
-14 46 -10 -6
7 -23 5 3 0 The remainder is 0, as expected
The quotient is a polynomial of degree 3:
7x3-23x2+5x+3
Now, continue testing the P/Q values with this new polynomial. Try f(3):
f(3)=7(27)-23(9)+5(3)+3
189-207+15+3 = 0 OK!! we found another zero at x=3
Now, another synthetic division:
3⊥ 7 -23 5 3
21 -6 -3_
7 -2 -1 0
The quotient is a quadratic polynomial:
7x2-2x-1 This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:
x= (1±2√2)÷7
The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7
Step-by-step explanation:
simplify the expression by using distributive property and combine like terms. 4(3x - 1) -2(6+ 2x)
Answer:
8x-16
Step-by-step explanation:
multiple the 4 and the -2 by everything in the parentheses beside them then add them together to simplify
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a
viable solution if x represents the number of days that a library book is late and y represents the total fee?
O (-3,-0.90)
O(-2.5, -0.75)
O(4.5, 1.35)
O (8, 2.40)
I need the answer mate
Answer:
d
Step-by-step explanation:
The only viable solutions for the given condition are (4.5, 1.35) and (8, 2.40).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Since the fee is charged at a rate of $0.30 per day, if a book is x days late, the total fee charged would be y = 0.30x.
We can check each ordered pair given to see if it satisfies this equation:
For (-3,-0.90), y = 0.30x = 0.30(-3) = -0.90.
This satisfies the equation, but the fee cannot be negative, so this is not a viable solution.
For (-2.5, -0.75), y = 0.30x = 0.30(-2.5) = -0.75.
Again, this satisfies the equation but the fee cannot be negative, so this is also not a viable solution.
For (4.5, 1.35), y = 0.30x = 0.30(4.5) = 1.35.
This satisfies the equation and the fee is positive, so this is a viable solution.
For (8, 2.40), y = 0.30x = 0.30(8) = 2.40.
This satisfies the equation and the fee is positive, so this is also a viable solution.
Therefore, the viable solutions are (4.5, 1.35) and (8, 2.40).
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ7
Another virus starts spreading on July 1st, 2020. No one
was infected prior so there is no constant. But it does spread at a rate of 11
people per day
Write an equation to solve for the number of days it would take to reach 1,000 cases
How many days will it take to reach 1000 cases?
On what date will Gotham City reach 1000 cases?
THE PICTURE SHOWS ABOUT THE FIRST VIRUS
Answer:
1000÷11=90.9
So,29th September
Please help! Will make brainliest !!
Answer:
5: 40.6
6: 26.57
7: 22.21
8: 66.35
Step-by-step explanation:
I am going to assume that you know
SOH CAH TOA (if you don't just ask)
For 5: we have the adjacent and opposite side, we need the angle
I think here it's easiest to use TOA
so we have
tanx=60/70
take the arctan or tan^-1 and get
arctan(60/70)=x x= 40.6
For number 6 it's just the same deal
tanx=10/20
arctan(10/20) =x =26.57
For number 7 we have the adjacent side and we need to find the oppsoite side
for this I will once again use TOA
tan(48)=x/20
20tan(48)=x=22.21
For number 8 it's the same deal as 7
tan53=x/50
50tan53=x=66.35
pythagorean theorem. and I need to calculate the missing sides. If possible I would like an explanation but an answer is also fine.
Answer:
Step-by-step explanation:
To calculate the missing sides square the side length of the legs of the triangles( the lines that form a 90 degree angle) then add them together, then take the sqr root of that to find the hypotunse( the slanted side). In simplier terms, here how it look.
[tex]a^{2}+b^{2} =c^{2}[/tex]
where a and b are the legs, and c is the hypotunese. For example, Ill do 3. The bases are 22, and 11 so plug them in the equations.
[tex]a^{2}+b^{2} =c^{2}[/tex]
11^2+22^2=c^2
121+484=c^2
605=c^2
c=about 24.6
Dario borrows $12,000 to buy a car. He borrows the money at a yearly, or annual, simple interest rate of 4.2%. How much more interest will Dario owe if he borrows the money for 5 years instead of 1 year?
ITS URGENT HURRY!!!!!
Answer:
$2016 moreStep-by-step explanation:
Borrowed amount = $12000Interest rate = 4.2% per year simpleInterest in 1 year:
$12000*4.2/100 = $504Interest in 5 years:
$12000*4.2*5/100 = $2520The difference between 1-year interest and 5-year interest:
$2520 - $504 = $2016solve the equation
PLZ I need a good grade
answer:
p = 6
1. pull out like factors
7p - 42 = 7 • (p - 6)
2. solve it
7=0
this equation can't be solved, therefore has no solution.
What is the standard algorithm
Kelly has 7 days to read 60 pages of a book for school. She plans to read 8 pages a night for 6 nights.What percent of the assigned pages will she have left to read on the last night?
Answer:
20 percent left
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
Your grandfather tells you that he has four coins in his pocket. He has no pennies, and no coin is worth more than a quarter. Calculate all the possible amounts. If Grandpa offers to give you the coins if you are able to guess the amount within ten cents, what is your guess ? Include all combinations in your answer, but include each combination only once be sure to indicate what your guess is.
Answer:
20 cents
Step-by-step explanation:
Possible coins in grandfather's pocket include : nickel, dime, quarter
A nickel = 5 cents
A dime = 10 cents
A quarter = 25 cents
First combination= nickel+dime+quarter+quarter
Second combination=nickel+quarter+quarter+quarter=
Third combination= dime+quarter+quarter+quarter
Third combination=quarter+quarter+quarter+quarter
4th combination = nickel + nickel+dime+quarter
5th combination= nickel +nickel+nickel+dime
6th combination =nickel+nickel+nickel+quarter
7th combination= nickel + nickel + nickel +nickel
8th combination = dime + dime +quarter +nickel
9th combination = dime +dime+dime+quarter
10th combination =dime+dime+dime+nickel
11th combination=dime+dime+dime+dime
If Grandpa offers to give you the coins if you are able to guess the amount within ten cents, then all coins are below ten cents and all coins are nickels = 4 nickels ×5 = 20 cents
I NEED HELP ASAPPPPPPPPPPPPPPPPPPP
How many times does 3 4 go into 6 ?
Answer:
8
Step-by-step explanation:
Answer:
8 is the correct answer.
Students running a food drive have collected their goal amount of canned goods. Over the weekend, volunteers collect an additional 18% of the goal. Write an expression to represent the total percentage of their goal collected in two different ways.
Answer:
[tex]Expression = x + 18x\%[/tex]
[tex]Expression = 1.18x[/tex]
Step-by-step explanation:
Given
Represent their goal with x
Additional = 18%
Required
Write two expressions to describe the total percentage
The expression is derived using:
[tex]Expression = Goal + Additional[/tex]
This gives:
[tex]Expression = x + 18\% * x[/tex]
[tex]Expression = x + 18x\%[/tex]
Solving further (Express percentage as decimal)
[tex]Expression = x + 0.18x[/tex]
[tex]Expression = 1.18x[/tex]
In gym class, the sixth graders walk 3 laps for every 2 laps they run. If the students run 6 laps, how many laps will they walk?
(p.s whoever types it fast and correct i will friend you. i like to do these brain stretches for people to have fun :D
Answer:
They walk 9 laps
Step-by-step explanation:
If the run for 6 laps you need to multiply how many times they walked when they ran for 2 laps by 3 (3*3) which should give you 9
Answer:
5
Step-by-step explanation: