The volume of the cylinder from the rectangle is the size of the cylinder
The rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
How to determine the rectangleLet the dimension of the rectangle be x and y.
So, the perimeter (P) is:
[tex]P = 2 * (x + y)[/tex]
The perimeter is given as 18.
So, we have:
[tex]2 * (x + y) = 18[/tex]
Divide both sides by 2
[tex]x + y = 9[/tex]
Make y the subject
[tex]y = 9 - x[/tex]
The volume of a cylinder is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V = \pi x^2(9 -x)[/tex]
Expand
[tex]V = \pi(9x^2 -x^3)[/tex]
Differentiate
[tex]V' = \pi(18x -3x^2)[/tex]
Set to 0
[tex]\pi(18x -3x^2) = 0[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]18x -3x^2 = 0[/tex]
Divide both sides by 3x
[tex]6 -x = 0[/tex]
Make x the subject
[tex]x = 6[/tex]
Recall that:
[tex]y = 9 - x[/tex]
So, we have:
[tex]y = 9 - 6[/tex]
[tex]y = 3[/tex]
Hence, the rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
Read more about volumes at:
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Expand. (1-4m)(m^2-3m+8) your answer should be a polynomial in standard form.
Answer:
13m²−35m+8−4m³
Step-by-step explanation:
Expand (1 − 4m)(m² − 3m + 8) by multiplying each term in the first expression by each term in the second expression.
1m² + 1 (−3m) + 1 ⋅ 8 − 4m ⋅ m² − 4m (−3m) − 4m ⋅ 8
Simplify terms.
13m²−35m+8−4m³
What is the trigonometric ratio for cos N?
Enter your answer, as a simplified fraction.
Answer
=12/13
Step-by-step explanation:
I have done it before:)
What is the answer to 4-(-6)+(-4)+3x0
Answer:
9
Step-by-step explanation:
Follow PEMDAS
[tex]4-(-6)+(-4)+3x\\4+6-4+3x\\6+3x\\6+3=9[/tex]
Answer:
6
Step-by-step explanation: [tex]4-\left(-6\right)+\left(-4\right)+3\times0[/tex]
Apply the Inverse Property of Addition
[tex]-\left(-6\right)+3\times0[/tex]
Apply Zero Property of Multiplication
[tex]-\left(-6\right)[/tex]
Determine the sign
[tex]6=YOUR\ ANSWER[/tex]
I hope this helps you
:)
A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form
best describes the total volume of the cylinder? Use the formula V = 3.14r^2h for the volume of a
cylinder
Answer:
The answer is A!
Step-by-step explanation:
area of the base = pi*(4x+2)^2 = pi*(16x^2 +16x +4)
volume of cylinder = pi*r^2 *h
V = pi *(16x^2 +16x +4)(5x+4) = pi*(80x^3 +80x^2 +20x +64x^2 +64x +16) =
= pi*(80x^3 +144x^2 +84x +16)
Answer:
Step-by-step explanation:
The volume of a cylinder can be thought of as the area of a circle, scaled by the height of the cylinder. The formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
Plug in the radius, and the height:
[tex]V=\pi (4x+2)^2(5x+4)[/tex]
Use FOIL to expand the squared binomial:
[tex]V=\pi (16x^2+16x+4)(5x+4)[/tex]
Bring out the binomial to the front of the trinomial:
[tex]V=\pi [(5x+4)(16x^2+16x+4)][/tex]
The process to multiply a trinomial by a binomial involves multiplying the trinomial by each term of the binomial:
[tex]V=\pi [(5x+4)(16x^2+16x+4)]=\pi [5x(16x^2+16x+4)+4(16x^2+16x+4)][/tex]
The rest is just distributing and tedious algebra:
[tex]V=\pi [(80x^3+80x^2+20x)+(64x^2+64x+16)][/tex]
Combine like terms and order the terms from highest exponent to lowest exponent. That is the definition of standard form:
[tex]V=\pi [80x^3+144x^2+84x+16][/tex]
[tex]V=4\pi [20x^3+36x^2+21x+4][/tex]
solve the system substitution y= 4x + 1 and 3x+2y =13
Given :
[tex]{\qquad \sf \dashrightarrow y= 4x + 1 \: –––– \sf \: (i)}[/tex]
[tex]{\qquad \sf \dashrightarrow 3x + 2y = 13 \: –––– \sf \: (ii)}[/tex]
Now, Substituing the value of y in equation (ii) :
[tex]{\qquad \sf \dashrightarrow \: 3x + 2y = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 3x + 2(4x + 1) = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 3x + 8x + 2 = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 11x + 2 = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 11x = 13 - 2 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 11x = 11 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: x = \dfrac{11}{11} }[/tex]
[tex]{\qquad \sf \dashrightarrow \bf \: x = 1 }[/tex]
Now, substituting the value of x in equation (i) :
[tex]{\qquad \sf \dashrightarrow y= 4x + 1}[/tex]
[tex]{\qquad \sf \dashrightarrow y= 4(1) + 1}[/tex]
[tex]{\qquad \sf \dashrightarrow y= 4 + 1}[/tex]
[tex]{\qquad \bf \dashrightarrow y= 5}[/tex]
Do you guys know what 4m - 2m + 3
Answer:
2m + 3 I think.
Step-by-step explanation:
4m - 2m = 2m. So just put that in the equation now and poof. 2m + 3
Slope: Tutorial
у
11
10
9
8
7
6
5
4
3
2
2
3
4
6
7
8
9
10 11
The slope of the line in the graph is
(If your answer is a fraction, write it in simplified terms.)
I’m
Answer:
Step-by-step explanation: just write from 2 to 11 one by one
the following shape has 1 pair of parallel sides. 3, 5, 8, 2, 6
To identify the shape with one pair of parallel sides, we need to consider the given set of numbers: 3, 5, 8, 2, 6.
A shape with one pair of parallel sides is a trapezoid. In a trapezoid, two sides are parallel while the other two sides are non-parallel.
Looking at the given set of numbers, we can form the sides of a trapezoid by pairing the numbers in the following way: 3, 5, 8, 2, 6.
The sides of the trapezoid can be represented as follows:
Parallel sides: 3 and 5 (forming the top and bottom sides)
Non-parallel sides: 8, 2, 6 (forming the slanted sides)
Therefore, the given set of numbers forms a trapezoid with one pair of parallel sides.
For such more question on trapezoid
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Trishia is 4 years older than Caila now. The sum of their ages in 8 years from now will be 38. How old are Caila and Trisha now?
Answer: 13 and 9
Step-by-step explanation:
because since there are two people 38-(8x2)=22
The only numbers that add up to 22 that have a difference of 4 are 13 and 9
Another way:
T=C+4
T+8+C+8=38
C+4+C+8=
How do you know when the Solve box has more than one page of information? A) The page indicator shows 1/4. B) There is an answer box. C) There is a Check Button. D) The words are set apart in a box. Will Mark Brainliest if answered correctly.
Answer:
A) The page indictor shows 1/4
Step-by-step explanation:
Because 1 is out of a multiple 4 pages.
Hope it helps.
Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).
-3x-y - 1
-2x+2y = 10
Add Work
> Next Question
Answer:
2x + 3y = 12 …equation 1
x– y = 1 … equation 2
To solve it by elimination method, let us multiply the second equation by 3
3x — 3y = 3 …equation 3
Now add the first and third equation
5x = 15
x = 3
From equation 2, y = x-1
y = 2
Hence x = 3, y = 2.
(b) 3x + y = 10
Since we have one equation and 2 variables, it cannot be solved by the elimination method.
To solve this, we can go for trial and error
Say y = 1, x = 3 or x = 5, y = —5
(c) x – 3y=1 …eq 1
3x – 2y + 4 = 0 …eq 2
Multiply eq 1 by 3, 3x — 9y = 3 …eq 3
Eq 2 — eq 3,
7y = —7
y = —1, x = —2 Ans
Hope it helps!!!!!!!brainliest pls!!!!!!!!!!!Please show work and thanks
Answer:
2
Step-by-step explanation:
If ABC is equilateral, its angles are all equal to each other and each one measures 60°.
[tex]8x-44 =60\\8x = 16 \rightarrow x = 2[/tex]
the whale swims down 150 more feet more. what is the whales elevation now
Answer:
i think it's 22500 deep down to the ocean
You are buying carpet to cover a room that measures 42 ft by 42 ft. The carpet cost $ 25 per square yard. How much will the carpet cost?
Explanation:
3 feet = 1 yard
14*(3 feet) = 14*(1 yard) .... multiply both sides by 14
42 feet = 14 yards
The carpet is 14 yards by 14 yards.
Its area is 14*14 = 196 square yards.
Since it costs $25 per square yard, this means the total cost is 25*196 = 4900 dollars
Solve for x. Leave your answer in simplest radical form.
Answer:[tex]2\sqrt{3}[/tex]
Step-by-step explanation:
Use pytha. theorem on leftmost triangle and get sqrt(13)
Use it again on the other triangle: 13+b^2=25
First, we find the hypotenuse of the first triangle
(Use the pythagorean theorem) : [tex]3^{2} + 2^{2} = 9 + 4 = 13[/tex]
So, the length of the side = [tex]\sqrt{13}[/tex]
Now, we find x :
x(squared) = [tex]5^{2} -\sqrt{13} ^{2}[/tex] = 25 - 13 = 12
-> x = [tex]\sqrt{12}[/tex] = 2[tex]\sqrt{3}[/tex]
Wendy bought an $80 dress on sale for 40% off. How much did she pay for the dress?
Solution:
We know that:
Discounted price: Original price - (Original price × Discount)Original cost of dress: $80Discount: 40%This means that:
Discounted price of dress: 80 - (80 × 40%)Step-1: Convert "40%" into a fraction.
40% = 40/100Step-2: Find the discounted price.
Discounted price of dress: 80 - (80 × 40/100)Discounted price of dress: 80 - (4 × 40/5)Discounted price of dress: 80 - (4 × 8)Discounted price of dress: 80 - 32Discounted price of dress: $48Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm
Answer:
100
Step-by-step explanation:
Split it into 3 different rectangles, find the area of each, and add them together.
Rectangle 1: length=11 width=4 11×4=44
Rectangle 2: length=11-9=2 width=6 2×6=12
Rectangle 3: length=11 width=4 11×4=44
44+12+44=100
There is a rectangular field in Sheffield Park that is 4 meters long and 2 meters wide.
What is the area, in square meters, of the field?
Answer:
8 m^2
Step-by-step explanation:
4x2=8 and if it needs to be in sq meters it is 8 m^2 (m^2 means meters squared)
A fair die is rolled 3 times what is the probability that is comes up 1 at least Once
Evaluate the following expression for x = 11, y =
3. Enter only the final result.
x + 4
y +2
Answer:
3
Step-by-step explanation:
If x=11 then the top line would equal 11+4, which is 15
If y=3 then the bottom line would equal 3+2, which is 5
So, you end up with 15/5, which equals 3
Beginning with the graph of f(x) = x2, what transformations are needed to form g(x) = -(x - 6)2 + 3?
O The graph of g(x) opens upward and is shifted to the right 6 units and up 3 units.
The graph of g(x) opens upward and is shifted to the left 6 units and up 3 units.
The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
The graph of g(x) opens downward and is shifted to the left 6 units and up 3 units.
The graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units.
How to apply rigid transformations on a given function
Let be [tex]f(x) = x^{2}[/tex], we need to apply the following three rigid transformations on [tex]f(x)[/tex] to obtain [tex]g(x)[/tex]:
Reflection around the x-axis: [tex]f'(x) = -x^{2}[/tex]Translation in the +x semiaxis: [tex]f''(x) = -(x-6) ^{2}[/tex]Translation in the +y semiaxis: [tex]g(x) = -(x-6) ^{2}+3[/tex]Hence, the graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units. [tex]\blacksquare[/tex]
To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538
Answer:
The graph of opens downward and is shifted to the right 6 and up 3 units.
Please help if you know anything about triangles!!
Step-by-step explanation:
125 + 30 + 25 + b is equal to 180 degree 19 + y equal to 180 degree equal to 180 - 190 equal to - -10
The graph below represents the relationship between the number of days a book is overdue and the library fine charged. A graph titled Library Fines. The horizontal axis shows days overdue and the vertical axis shows the fine (dollars). The line shows an increase to $10 at 19 days overdue, then constant. Christen returned an overdue book to the library. Her fine was the same as it would have been if she returned the book the previous day. Which of the answer choices below could be the number of days Christen’s book is overdue? 10 14 18 22
Answer:
(d) 22
Step-by-step explanation:
For numbers of days above 19, the fine is constant. The answer choice that is above 19 is 22. For 22 days overdue, the fine will be the same as for 21 days overdue: $10.
22 could be the number of days
Answer:
D. 22
Step-by-step explanation:
!!!PLEASE HELP!!!
What is one of the solutions to the system of equations graphed here?
(Look at the image for the answer it’s multi choice)
Answer:
B. (-5,-4)
Step-by-step explanation:
The answer must be at the point where the two functions intersect. They meet at the points (-5,-4) and (2,0). Since (2,0) is not an answer choice, (-5,-4) must be the answer.
....pleaseee....helpppppp................
Answer:
16 ounces
Step-by-step explanation:
one pound is sixteen ounces
Teresa has lived one-fourth of her life in England, one-fifth in Ireland, one-third in France and 13 years in
Switzerland. Assuming she lived in no other countries, how many years old is she?
Will give BRAINLIST
Answer:
She is 60 years old
Step-by-step explanation:
The first thing we can do is convert each fraction to have a common denominator. The LCM of 5, 3, and 4 is 60.
[tex]\frac{1}{4} =\frac{15}{60}[/tex]
[tex]\frac{1}{3} =\frac{20}{60}[/tex]
[tex]\frac{1}{5} =\frac{12}{60}[/tex]
Add the numerators:
[tex]15+12+20=47/60[/tex]
Meaning that the time she lived in Switzerland is the remaining 13/60, and since she lived there for 13 years that means she lived for a total of 60 years because the numerator and denominator both equal 60.
#LearnWithBrainly
Answer:
Teresa is 60 years old------------------------------
Let the age of Teresa be x.
Set up equation:
x(1/4 + 1/5 + 1/3) + 13 = xMultiply both sides by 3*4*5 = 60 to clear fraction:
x(60/4 + 60/5 + 60/3) + 13*60 = 60xx(15 + 12 + 20) + 780 = 60x47x + 780 = 60x60x - 47x = 78013x = 780x = 780/13x = 60The expression for thrice of a number m is m +3. true or false
Answer:
False
Step-by-step explanation:
[tex]the \: expression \: is \: 3x[/tex]
Answer:
false
Step-by-step explanation:
thrice a number means 3 times the number
if the number is m then thrice the number is
3 × m = 3m
Find the equation for the line that passes through the points (-4,1) and(2,+3)
How do you solve the picture AND DO NOT TELL ME YOU DO NOT KNOW lol
I don't know use a calculator
Please help!!!!!!!!!!!!!!
Answer:
312.29 square feet
Step-by-step explanation:
[tex]w = \sqrt{ {d}^{2} - {l}^{2} } = \sqrt{ {25}^{2} - {18}^{2} } \\ [/tex]
w = 17.35
A= l × w
= 18 × 17.35
= 312.29 square feet