Answers
Answer:
[tex]\textsf{i)} \quad \text{T} &=2 \pi r^2 + \dfrac{26}{r}[/tex]
ii) radius = 1.27 cm (3 sf)
height = 2.55 cm (3 sf)
Step-by-step explanation:
[tex]\text{Volume of a cylinder}=\pi r^2 h \quad \text{(where r is radius and h is height)}[/tex]
Given volume = 13 cm³, rewrite the equation making h the subject:
[tex]\implies 13=\pi r^2 h[/tex]
[tex]\implies h=\dfrac{13}{\pi r^2}[/tex]
Substitute found expression for h into the Surface Area equation to find the expression for the total surface area, T:
[tex]\begin{aligned}\text{Surface Area of a cylinder} & =2 \pi r^2 + 2 \pi r h\\\implies \text{Surface Area} & =2 \pi r^2 + 2 \pi r \left(\dfrac{13}{\pi r^2}\right)\\& =2 \pi r^2 + \dfrac{26 \pi r}{\pi r^2}\\ \implies \text{T} &=2 \pi r^2 + \dfrac{26}{r}\end{aligned}[/tex]
To find the radius of the minimum surface area, differentiate T with respect to r:
[tex]\begin{aligned}\text{T}& =2 \pi r^2 +26r^{-1}\\\implies \dfrac{dT}{dr} & =(2)2 \pi r^{(2-1)}+(-1)26r^{(-1-1)}\\ & =4 \pi r-26r^{-2}\\ & =4 \pi r-\dfrac{26}{r^2}\\ & = \dfrac{4 \pi r^3-26}{r^2} \end{aligned}[/tex]
Set it to zero, and solve for r:
[tex]\begin{aligned}\dfrac{dT}{dr} & = 0 \\\implies \dfrac{4 \pi r^3-26}{r^2} & = 0 \\\impliles 4 \pi r^3-26 & = 0 \\4 \pi r^3 & = 26 \\r^3 & = \dfrac{13}{2 \pi} \\r & = \sqrt[3]{\dfrac{13}{2 \pi}} \end{aligned}[/tex]
To find the height, substitute the found value of r into the equation for height (found previously):
[tex]\begin{aligned}h & =\dfrac{13}{\pi r^2} \\\implies h & =\dfrac{13}{\pi \left(\sqrt[3]{\dfrac{13}{2 \pi}}\right)^2} \\& =2.548499134\end{aligned}[/tex]
Therefore,
radius = 1.274249567... = 1.27 cm (3 sf)height = 2.548499134... = 2.55 cm (3 sf)Related Questions
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
the line is going 1/1 so y=1x+2
Step-by-step explanation:
y=mx+b
1 is the slope
2 is the intercept of the graph
Find the nth term
-7,-9, -11, -13,
, ,
Answers
Answer:
you are subtracting 2 so it would be like
-7,-9,-11,-13,-15,-17,-19
A Student was conducting as to determine how many house g apples could be packed in al bay Size at the local farmers. The average gala apples had a Of 3.5 inches. Given the farmer's market wanted to use a box that had the dimensions 16 in x 9in x 9in how many apples should fit based on the information provided by the table. (a) 30 (b) 35 (c)40 (d)
20in × 13in ×12in= 72 apples
12in × 12in × 12in= 40 apples
20in × 10in × 6in= 28 apples
Answers
Answer:
43.1
Step-by-step explanation:
1728/40 = 43.2
3120/72 = 43.3
48 divided by 76.8
I am very confused on the two digits numbers
Answers
How can you find out the similarities and differences in a non-fiction text?
A. look at how the characters speak
B. look at how the subject or events are portrayed
C. look at the genre
Answers
The similarities and differences in a non-fiction text look at how the subject or events are portrayed.
What is a non-fiction text?Comparing non-fiction texts can focus on the similarities between the texts - things they have in common. You can also contrast texts and focus on their differences - things that set the texts apart from each other. You could compare and contrast the following:
Form – What types of text (letter, news report, etc) are they?
Purpose – What job (persuading, informing, advertising) is each text doing?
Audience – Who is the intended reader of the text?
Subject matter – What are the texts about?
Language choices – What kinds of words, images or rhetorical devices are being used?
Structure – How is the text ordered?
Tone – What is the overall tone or mood of the writing?
Non-fiction texts are all around us, and comparing them can help you become more aware of how language is being used in society. Comparing non-fiction texts can often prompt you to notice things that you might not have considered about a text in isolation.
Hence the similarities and differences in a non-fiction text look at how the subject or events are portrayed.
To know more about non-fiction text follow
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What statement is NOT true comparing the two
box and whisker plots?
Answers
Answer:
Its d
Step-by-step explanation:
These are the first four terms of a sequence. 3 -1 -5 -9. Find the nth term.
Answers
Answer:
4n-1
Step-by-step explanation:
Diffrence bweetween each number, 3 and -1, -1 and -5, -5 and -9 is 4
4n
find the closest numbers
4*1=4
4*0=0
4*-1=-4
4*-2=-8
now we figure out how to make these numbers into our terms of this sequence
4n-1
4*1-1=3
4*0-1=-1
4*-1-1=-3
4*-2-1=-9
so the nth term is 4n-1
What are the zeros of the function defined by x +x-12?
A) {-4, -3} B) {-4, 3} C) {-3, 4) D) {3,4}
Answers
Answer:
Step-by-step explanation:
(x + 4)(x - 3)=0
x + 4 = 0
x = -4
x - 3 = 0
x = 3
answer B
A car cover a distance 300 miter in 50 second How much distance a car covers in 1 second
Answers
Divide total distance by total seconds:
300 meters / 50 seconds = 6 meters per second.
Answer: 6 meters
In the figure below, QRT and SRV are complementary,
What is the value of x?
Answers
x = 40
[tex]\bold{SOLUTION:}[/tex]
The pool where Asha swims is rectangular.
It is 2500 cm long and 1250 cm wide.
The four sides of the swimming pool are 150 cm deep.
They are covered with small square tiles of different colours.
Answers
The rectangular pool where Asha swims would need 4.6875 * 10⁸ cm³ of water to make it full.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The pool where Asha swims is rectangular. It is 2500 cm long, 1250 cm wide and 150 cm deep.
Hence:
Volume of the pool = 2500 * 1250 * 150 = 4.6875 * 10⁸ cm³
The rectangular pool where Asha swims would need 4.6875 * 10⁸ cm³ of water to make it full.
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Help. Please and thanks.
Answers
Answer:
(2,6)
Step-by-step explanation:
What is a dilation?
A dilation is a type of transformation that resizes an object.
To apply a dilation ( find the coordinates of a point after a dilation ) you must multiply the x and y values of the coordinates by the scale factor
Applying the dilation rule
We want to find the coordinate of vertex B after a dilation with a scale factor of 2. To do so we multiply the x and y value of vertex b by the scale factor or 2
Current coordinates of the triangle :
A(1,1) B(1,3)C(3,1)Coordinates after dilation
A' = (1,1) ===> (1×2,1×2) ===> (2,2)
B' = (1,3) ===> (1×2,3×2) ===> (2,6)
C' = (3,1) ===> (3×2,1×2) ===> (6,2)
The coordinate of the vertex B after the dilation is (2,6)
what is the approximate length of arc s on the circle ? A) 5.23 in B) 41.87 in C) 52.36 in D) 104.67 in
Answers
Answer:
C
Step-by-step explanation:
a cubic function has the following properties
f'(1)=0
f'(3)=0 = f(3)=0
f(0) =0
f'(2)>0
Draw a rough sketch of f
Answers
find the length of a diagonal of a square whose side is 2 cm
Answers
Answer:
2√2 cm
Step-by-step explanation:
Formula to be understood :
Diagonal of a square = Side length√2Deriving the formula :
Apply Pythagorean Theorem by taking the side lengths as altitudes and the diagonal as a hypotenuseside length² + side length² = hypotenuse²2(side length)² = hypotenuse²hypotenuse = side length√2Solving for the length of the diagonal :
diagonal = 2√2 cmLength of diagonal
side√2a√22√2cmPlease im been stuck on this for ages
Answers
Help me please
Simplify (5x3 + 7x - 8) + (2x3 – 5x2 – X + 3). Choose the standard form of the answer.
A. 7x3 + 6x - 5x2 - 5
B. 7x3 - 5x2 + 6x - 5
C. 7x3 – 5x2 + 6x + 5
D 7x3 – 5x2 + 8x - 5
Answers
Answer:
==7x3−5x2+6x−5
Step-by-step explanation:
=5x3+7x+(-8)+2x3+−5x2+−x+3
Combine Like Terms:
=5x3+7x+−8+2x3+−5x2+−x+3
=(5x3+2x3)+(−5x2)+(7x+−x)+(−8+3)
=7x3−5x2+6x−5
Function g is a transformation of the parent exponential function, . Which graph shows function g?
Answers
Answer:
the answer is b! i got the same question before!
Step-by-step explanation:
.
Jill rolled a regular 6-faced die three times and got 2 each time.
What is the probability that she will roll 2 again on the next roll?
Answers
Answer: 1/6
Step-by-step explanation:
Since there’s only one side on the dice that has two on it out of six sides it has to be 1/6.
PLS HELP ME
Congruent yes or no
Congruent? _______
If so, what property? ________
Congruent yes or no
Congruent? _______
If so, what property? ________
Congruent yes or no
Congruent? _______
If so, what property? ________
Congruent yes or no
Congruent? _______
If so, what property? ________
Answers
Answer:
First picture: SAS and not existent, so not congruent
Second picture: AAA does not exist, so not congruent
Third picture: SAS for both (yes)
Forth picture: AAS for both (yes)
Step-by-step explanation:
Sorry for no long explanation, but if you have any specific questions, feel free to ask in the comments
Hope this helps! If you found my answer helpful, please consider marking me brainliest. Thank you!
What is the domain of the profit function P = 7m + 12n?
O A. Defined for all m> 0 and n_>0
B. Defined for all m _>0 and n > 0
C. Defined for all m> 0 and n > 0
D. Defined for all m _> 0 and n _> 0
Answers
Answer:
D
Step-by-step explanation:
without knowing anything about the background of the function and what it is used for, I give it the max. possible domain (the set or interval of all possible input values).
and so,
Defined for all m >= 0 and n >= 0.
there is no information provided that would eliminate m = 0 or n = 0.
When the core of a reactor overheated, what happened at Chernobyl?
A. Power was cut off to Europe for six months
B. Radiation was released across Europe
C. The power station exploded killing many
D. Though it overheated, no negative impacts occurred
Answers
Answer: D
On April 26, 1986, the Number Four RBMK reactor at the nuclear power plant at Chernobyl, Ukraine, went out of control during a test at low-power, leading to an explosion and fire that demolished the reactor building and released large amounts of radiation into the atmosphere. When the core of a reactor overheated, what happened at Chernoby Though it overheated, no negative impacts occurred
Step-by-step explanation:
I sold a commodity for #16 and made a profit of 20% what percentage will I make if I sell at # 18?
Answers
Answer:
Step-by-step explanation:
since #16 = 20% then #18 will be 18/16 * 20%= 22.5%
The sum of a number and its square is 6. Find the number
Answers
Answer: The sum of a number and its square is 6. Find the number
Step-by-step explanation:
n + n^2 = 6 n^2 + n - 6 = 0 factoring ___ (n + 3)(n - 2) = 0 n + 3 = 0 ___ n = -3 n - 2 = 0 ___ n = 2 two solutions
Answer:
n = -3, 2
Step-by-step explanation:
We're given:
The sum of a number and its square is 6Let the number be n.
The sum of a number and its square is 6⇒ [tex]n+n^2=6[/tex]
[tex]n+n^2=6[/tex]
⇒ Move everything to one side of the equation:
[tex]n+n^2-6=0[/tex]
⇒ Organize in [tex]ax^2+bx+c=0[/tex] form:
[tex]n^2+n-6=0[/tex]
⇒ Factor:
[tex]n^2-2n+3n-6=0\\n(n-2)+3(n-2)=0\\(n+3)(n-2)=0[/tex]
⇒ Use the zero-product property to find n:
[tex]n+3=0\\n=-3[/tex] or [tex]n-2=0\\n=2[/tex]
A ladder leans against a building. The angle of elevation of the ladder is 70°. The top of the ladder is 25 ft from the ground.
To the nearest tenth of a foot, how far from the building is the base of the ladder?
9.1 ft
30.5 ft
32.3 ft
39.5 ft
Answers
Answer:
the answer is C :) hope it helps
Answer:its actually 9.1 ft
Step-by-step explanation: i just took the same test
Find P(x > 120) provided that it is known that
= 95 and o = 14. Assume that the
distribution is approximately normal.
Select one:
а. 1.7936
b. 0.7852
c.0.9633
d. 0.0367
Answers
The probability when x is greater than 120 is 0.0367. Then the correct option is D.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The mean is 95 and the standard deviation is 14. Then the probability when x > 120 will be
The z-score will be
z = (120 - 95)/ 14
z = 1.7857
Then the probability will be
P(x > 120) = P(z > 1.7857)
P(x > 120) = 1 - P(x<120)
P(x > 120) = 1 - 0.96293
P(x > 120) = 0.0367
More about the normal distribution link is given below.
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136 × (8 + (-4) = 136x8+136 × - 4
Answers
Answer:
544
Step-by-step explanation:
Distributive Property: a*(b +c) = (a*b) + (a*c)136 * ( 8 + (-4 ) = 136 * 8 + [ 136 * (-4) ]
= 1088 - 544
= 544
Becky bought a display case with a rectangular lid that is 134 feet long and 56 feet wide.
What is the area of the lid?
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
ft²
Answers
Answer:
1 11/24
Step-by-step explanation:
u multiply both numeators and both denominators for example 1 3/4 5/6 i would first turn 1 3/4 into 7/4 and then multiply
Mrs. Forsyth has 130 pieces of candy. She wants to split it into fifths for each of her classes. How
many pieces of candy will each class get?
Answers
Answer: The answer is 26
I just divided it by 5
Explanation: 130/5 = 26
Please help me ojn this question
Answers
Answer: r = 1.5
Step-by-step explanation:
The geometric sequence formula is in the attached image.
Using the formula, we take number 3, which is 9.
[tex]9 = 4(r)^{2} \\\frac{9}{4} = r^{2} \\\sqrt{\frac{9}{4}} = 1.5[/tex]