The volume of the cylinder is the amount of fruit juice it can contain.
The relationship between the volume and the surface area is:
[tex]\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}[/tex]
The given parameter is:
[tex]\mathbf{V = 0.946}[/tex]
The volume of a cylinder is calculated as:
[tex]\mathbf{V = \pi r^2 h}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{V}{ \pi r^2}}[/tex]
The surface area (A) of a cylinder is:
[tex]\mathbf{A = \pi r^2 + \pi rh}[/tex]
Substitute [tex]\mathbf{h = \frac{V}{ \pi r^2}}[/tex]
[tex]\mathbf{A = \pi r^2 + \pi r \times \frac{V}{\pi r^2}}[/tex]
[tex]\mathbf{A = \pi r^2 + \frac{V}{r}}[/tex]
Differentiate
[tex]\mathbf{A' = 2\pi r - Vr^{-2}}[/tex]
Set to 0
[tex]\mathbf{2\pi r - Vr^{-2} = 0}[/tex]
Rewrite as:
[tex]\mathbf{ 2\pi r = Vr^{-2}}[/tex]
Multiply through by r^2
[tex]\mathbf{ 2\pi r^3 = V}[/tex]
Solve for r
[tex]\mathbf{r = \sqrt[3]{\frac{V}{2\pi}}}[/tex]
[tex]\mathbf{A = \pi r^2 + \frac{0.946}{r}}[/tex]
So, we have:
[tex]\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}[/tex]
Hence, the relationship between the volume and the surface area is:
[tex]\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}[/tex]
Read more about surface areas and volumes at:
https://brainly.com/question/3628550
HELP, VERY EASY MATHS QUESTION
Answer:
z=7
Step-by-step explanation:
area = ½ × (a + b) × h.
260 = 37 + 4z × 8 ×0.5
260/0.5 = 520
520/8=65
37 + 4z = 65
65-37 = 28
28/4=7
z=7
Answer:
7
Step-by-step explanation:
1/2 (37 + 4a) 8 = 260 260/8 = 32.5 32.5 * 2 = 65 65-37=28 28/4 = 7 a = 7
May I please receive help?
George walked 6 miles in 2 hours
What was his average walking rate in miles per hour?
2 miles per hour
3 miles per hour
4 miles per hour
I don't know.
Answer:
b) 3 miles per hour
Step-by-step explanation:
If George walked 6 miles is 2 hours, his average walking rate would be 3 miles per hour.
6 ÷ 2 = 3.
2. Solve x2 + 2x + 7 = 0 using the Quadratic Formula
Answer:
-1 ± i√7Step-by-step explanation:
x² + 2x + 7 = 0D = 2² - 4*7 = 4 - 56 = -52x = (-2 ± √-28)/2 = (-2 ± 2√-7)/2 = -1 ± i√7Is -3 the same as 0.3
No they are not same .
Hope it helps
Answer:
Nope! They are not the same. This is because -3 is a negative whole number. On the other hand, 0.3 converts to 3/10 which is a positive decimal number. Hope this helps. I have attached below a number line showing the two different points (with the given number on each end).
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
What is the solution and answer of this question:
3 log 10 + 9 log 10
Answer:
12
Step-by-step explanation:
the answer is 12 ndndbdbdndnfnnfnfnfnfnfnfnfnfn
What is the fraction form of the following decimal expansion?
Answer: B
Step-by-step explanation:
x-2y=-8 slope intercept form
need it asap plz
Answer:
y = 1/2x + 4
Step-by-step explanation:
hope this helps
16% of 95 is what number?
Please answer this fast I'll mark you as brainliest. Thank You.
Answer:
16% of 95 is 15.2
Step-by-step explanation:
0.16×95= 15.2
A mechanic charges a flat fee of $30 plus $25 an hour for labor. Which equation can be used to determine how many hours, 1, the mechanic spends working on a
particular job if the total amount earned is T dollars?
Question 1 (2 points)
What is the common difference d of the sequence?
-15, -4, 7, 18, 29, ...
• 11
•-11
•12
•-12
How many solutions does the nonlinear system of equations graphed below have?
A. One
B. Four
C. Two
D. Three
Answer:
There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.
Step-by-step explanation:
Activity Give the exponential model for the following situation
Answer:
Suppose that a couple invested $50,000 in an account when their child was born, to prepare for the child's college education. If the average interest rate is 4.4% compounded annually, ( A ) Give an exponential model for the situation, and ( B ) Will the money be doubled by the time the child turns 18 years old?
( A ) First picture signifies the growth of money per year.
( B ) Yes, the money will be doubled as it's maturity would be $108,537.29.
a = p(1 + \frac{r}{n} ) {}^{nt}a=p(1+
n
r
)
nt
a = 50.000.00(1 + \frac{0.044}{1} ) {}^{(1)(18)}a=50.000.00(1+
1
0.044
)
(1)(18)
a = 50.000.00(1 + 0.044) {}^{(1)(18)}a=50.000.00(1+0.044)
(1)(18)
a = 50.000.00(1.044) {}^{(18)}a=50.000.00(1.044)
(18)
50,000.00 ( 2.17074583287910578440507440 it did not round off as the exact decimal is needed.
a = 108.537.29a=108.537.29
Step-by-step explanation:
Hope This Help you!!
If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?
[tex]\large\underline{\sf{Solution-}}[/tex]
Given:
[tex] \rm \longmapsto x = a \sin \alpha \cos \beta [/tex]
[tex] \rm \longmapsto y = b \sin \alpha \sin \beta [/tex]
[tex] \rm \longmapsto z = c\cos \alpha[/tex]
Therefore:
[tex] \rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta [/tex]
[tex] \rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta [/tex]
[tex] \rm \longmapsto \dfrac{z}{c} = \cos \alpha[/tex]
Now:
[tex] \rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } [/tex]
[tex] \rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha [/tex]
[tex] \rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha [/tex]
[tex] \rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha [/tex]
[tex] \rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha [/tex]
[tex] \rm = 1[/tex]
Therefore:
[tex] \rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1[/tex]
Does anyone know this answer for 5 and 6??
Armando wants to raise funds at his school fair. He plans to charge 10 cents to pick marshmallows from his bag without looking. He will give: • 20 cents to anyone who picks a Blue marshmallow. • 50 cents to anyone who picks a Yellow marshmallow. • $1 to anyone who picks a White marshmallow. • Anyone picking a Red or Green marshmallow will lose their money There are as equal number of marshmallows of each color. 3a. Show work and explain why Armando will lose money with this game. Justify using mathematics.
Since the expected value for this game is negative, Armando will lose money.
The expected value is given by the sum of all outcomes multiplied by it's respective probability.In this problem:
There are blue, yellow, white, red and green marshmallows, each with a [tex]\frac{1}{5}[/tex] probability of being picked.If red or green marshmallows are picked, Armando get the charge of $0.1.If someone picks a blue marshmallow, he loses $0.1.If someone picks a yellow marshmallow, he loses $0.4.If someone picks a white marshmallow, he loses $0.9.Thus, the expected value is:
[tex]E = 0.1\frac{2}{5} - 0.1\frac{1}{5} - 0.4\frac{1}{5} - 0.9\frac{1}{5} = \frac{0.2 - 0.1 - 0.4 - 0.9}{5} = -0.24[/tex]
Since the expected value for this game is negative, Armando will lose money.
A similar problem is given at https://brainly.com/question/24855677
Show that the expression 1.50(10-r) is equivalent to 15-1.50r
Answer:
third answer
Step-by-step explanation:
Whats This Questions Answer Answer It Cuz I Have math Exam After 3Days
Answer:
bde=30 degrees
Step-by-step explanation:
angle abc = 50 degrees
50+100=150
180-150=30degrees
what is the value of x for 10x+1=3(4x+2)-3?
Answer:
x= 7
Step-by-step explanation:
Answer:-1
Step-by-step explanation:
10x+1=3(4x+2)-3
10x+1=12x+6-3
10x+1=12x+3
1=2x+3
-2=2x
1=x
Direction: the indicated operation reduce the answer to lowest terms whenever possible.
1. 11/12 - 5/12 = ?
2. 6 ½ - 1 9/10 =?
3. 5 ¾ + 9 1/6 =?
4. 7 2/8 - 4 5/6 = ?
5. 5 1/3 - 1 4/5 = ?
6. 7 ¾ - 5 ½ = ?
7. 5/8 - 3/8 = ?
8. 7/15 + 8/15 + 2/15 = ?
9. ¾ + ½ + 2/8 = ?
10. 9/10 - 2/5 = ?
PLEASE HELP NOW
MATHEMATICS
Answer:
1/24 3/5 14 11/122 5/ 123 8/ 152 1/ 41/ 41 2/ 151 1/ 21/ 2A hardware dealer has 168kg of nails, if one nail weighs 0.25kg, how many nails he have?
Answer:
He has 672 nails
Step-by-step explanation:
168/.25
Answer:
He has 672 nails.
Step-by-step explanation:
Weight of all nails=168
Weight of a nail=0 .25
Then,
Number of nails=168/0.25
=672
(b) It takes 37 pounds of seed to completely plant a 4-acre field. How many pounds of seed are needed per acre?
Answer:
9.25 lbs
Step-by-step explanation:
37 is the amount for 4 acres or 4a:
37 = 4a
Isolate and find a by dividing both sides by 4:
4a = 37
4a ÷ 4 = [tex]\frac{37}{4}[/tex]
a = [tex]\frac{37}{4}[/tex] or 9.25 lbs
Hope this helps!
PLS HELP ASAP ILL GIVE BRAINLIEST TYSM
Answer:
3x+2=16
Step-by-step explanation:
Answer:
the answer is most likely to be rather the first or second choice, but i choose B
Step-by-step explanation:
*Hope this helps*
based on what i understood, 3 green rectangles (or whaever that shape is), the 2 red squares, and the 16 small yellow squares. and the answer choices have
3x - 2 = 16
3x +2 = 16
3x + 4 = 20
3x = 24
and i dont think its 3x + 4 = 20 or 3x = 24 because there isn't any shapes to represent the 4, 20, and 24.
I might be wrong but i hope its right...
Can someone tell me the answer to this please?
Answer:
B
Step-by-step explanation:
On a blueprint, the scale says that 2 cm represents 3 m. What is the actual length of a wall if it's measurement on the blueprint is 7 cm?
Answer:
7!!
Step-by-step explanation:
guys help please what is this
Answer:
A & C
Step-by-step explanation:
You're looking for rational numbers that are also integers, but because (as the figure shows) ALL integers are already rational, you only have to worry about the integer part. An integer is a whole number, positive or negative. So, you need to simplify each element of each set (the numbers inside the curly braces) to see if they're whole.
A - The square root of 100 is just 10 or -10, divided by -2 is -5 or 5. 4, -2, 5, and -5 are all integers.
B - Wrong because 4/3 is not a whole number
C - 16/4 is just 4, and the square root of 49 is 7 or -7. 4, -6, 2, 7, & -7 are all integers.
D - Wrong because 27/2 is not a whole number
E - Wrong because 0.2 is not a whole number
Let me know if you need a more thorough explanation! (:
Which equation in slope-intercept form has a graph with an x-intercept at 3 and a y-intercept at -2?
Answer:
a
Step-by-step explanation:
A is the answer, since when you graph it, you are able to visualize y crossing -2 and x crossing 3.
find x if m<2=6x-12
a)12
b)9
c)6
d)-7
Answer:
12 ,,............,.,...,,,.
The value of x is 12 (Option a) if m∠2 = 6x - 12.
The given figure is an equilateral triangle, it means all three angles are equal. Therefore, we can assume that m∠2 is one of the angles of the equilateral triangle.
From the given information, we have:
m∠2 = 6x - 12
Since all angles of an equilateral triangle are equal, we can set up the equation:
m∠2 = m∠1 = m∠3
Let's assume m∠1 = m∠2 = m∠3 = y (where y represents the measure of each angle in the equilateral triangle).
We can equate the measures of the angles:
y = 6x - 12
Now, let's solve this equation to find the value of x:
6x - 12 = y
Since y represents the measure of each angle in the equilateral triangle, we can substitute y with 60° (since the sum of the angles in an equilateral triangle is 180°, and each angle is 60°).
6x - 12 = 60
Adding 12 to both sides:
6x = 72
Dividing both sides by 6:
x = 12
Therefore, the value of x is 12.
So, the correct option is: (a) 12
To know more about value, refer here:
https://brainly.com/question/22572776
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Brandon enters bike races 8 1/2 miles every 1/2 hour.
what does x equel if there are 9 people 2 run away and the remaining number is x
Answer:
x=7 people
Step-by-step explanation:
x=9-2