A cylinder has a height of $10$ and a radius of $3.$ Determine the total surface area, including the two ends, of the cylinder.
Answers
Check the picture below.
[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=10 \end{cases}\implies \begin{array}{llll} SA=2\pi (3)(10+3) \\\\\\ SA=6\pi (13)\implies SA=78\pi \\\\\\ SA\approx 245.04 \end{array}[/tex]
Answer:
[tex]78\, \pi[/tex].
Step-by-step explanation:
A cylinder of height [tex]h[/tex] and radius [tex]r[/tex] could be unrolled into:
two identical circles, one for the top and one for the bottom, andone rectangle, for the side.The radius of each circle is the same as the radius of the cylinder, [tex]r[/tex].
The height of the rectangle is the same as the height of the cylinder, [tex]h[/tex].
The width of this rectangle would be [tex](2\, \pi\, r)[/tex], same as the circumferences of the two circles. The reason is that when this rectangle is rolled to build the cylinder, the top and bottom edges of the rectangle would wrap around the circumference of the two circles.
The area of each circle would be [tex]\pi\, r^{2}[/tex]. Note that there are two such circles, one at the top of the cylinder and one at the bottom.
With a height of [tex]h[/tex] and a width of [tex](2\, \pi\, r)[/tex], the area of the rectangle on the side would be [tex](2\, \pi\, r)\, h[/tex]. Add these areas up to find the total surface area of this cylinder:
[tex]\begin{aligned}& \text{(Surface Area of the Cylinder)} \\ =\; & (\text{Surface area of circle on the top}) \\ & + (\text{Surface area of circle at the bottom}) \\ & + (\text{Surface area of rectangle on the side}) \\ =\; & \pi\, r^{2} + \pi\, r^{2} + (2\, \pi\, r)\, h \\ =\; & 2\, \pi\, r^{2} + (2\, \pi\, r)\, h \end{aligned}[/tex].
For the cylinder in this question, [tex]h = 10[/tex] whereas [tex]r = 3[/tex]. The surface area of this cylinder would be:
[tex]\begin{aligned}& 2\, \pi\, r^{2} + (2\, \pi\, r) \, h \\ =\; & 2 \,\pi \times 3^{2} + (2\, \pi\times 3) \times 10 \\ =\; & 78\, \pi\end{aligned}[/tex].
Related Questions
What is Limit of StartFraction StartRoot x + 4 EndRoot minus 3 Over x minus 5 EndFraction as x approaches 5?
Negative one-sixth
0
One-sixth
DNE
Answers
I assume the limit you're asked to copmute is supposed to be
[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5}[/tex]
Rationalize the numerator by multiplying it by its conjugate:
[tex]\dfrac{\sqrt{x+4}-3}{x-5} \times \dfrac{\sqrt{x+4}+3}{\sqrt{x+4}+3} = \dfrac{\left(\sqrt{x+4}\right)^2-3^2}{(x-5) \left(\sqrt{x+4}+3\right)} = \dfrac{x-5}{(x-5) \left(\sqrt{x+4}+3\right)}[/tex]
Since x is approaching 5, we have x ≠ 5 and can cancel the factors of x - 5 to remove the discontinuity.
Then
[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5} = \lim_{x\to5} \frac1{\sqrt{x+4}+3} = \frac1{\sqrt9+3} = \boxed{\frac16}[/tex]
because the simplified limand is continuous at x = 5.
Answer:
it is C. 1/6th
Step-by-step explanation:
lf Jackie earns $312.00 after working 24 hours what is the hourly rate?
Answers
Answer:
312 divided by 24 = 13.
So the hourly rate is 13/hour
Answer:
$13.00. To find the hourly rate you need to divide the total amount Jackie earned by the amount of hours she worked in total. When you divide 312 by 24 you will get 13, therefore Jackie makes a total of $13.00 per hour.
Which of the following sets of 3 side lengths could form a unique triangle?
O side lengths: 18 feet, 9 feet, 6 feet
O side lengths: 12 feet, 9 feet, 4 feet
O side lengths: 6 feet, 3 feet, 2 feet
O side lengths: 24 feet, 14 feet, 4 feet
Answers
Answer:
side lengths: 12 feet, 9 feet, 4 feet
Step-by-step explanation:
Conditions for unique triangles with 3 sides:
The sum of the two shorter sides must be greater than the third side.9 + 6 = 15
As 15 < 18 this is NOT a unique triangle
9 + 4 = 13
As 13 > 12 this IS a unique triangle
3 + 2 = 5
As 5 < 6 this is NOT a unique triangle
14 + 4 = 18
As 18 < 24 this is NOT a unique triangle
I WILL GIVE YOU 5 STARS ON YOUR PROFILE COMMNET I WILL ALSO GIVE A THANK YOU ON YOUR ACC AND COMMENT!!!!
Answers
Answer:
The answer is C. 2.94
Step-by-step explanation:
All you have to do is take 588 and divide it by 200 which gives you the answer of 2.94.
Sheree purchased a digital camera for $367.99. She received a manufacturer’s $45 mail-in rebate and a $25 rebate from Jack’s Camera Store. What is the final price?
Answers
Answer:
297.99
Step-by-step explanation:
367.99-45-25=297.99
George has 4 sets of socks, and 4 sets of shoes. Each pair has a different color: White, Brown, Black, and Blue. If George selects a pair of socks (same color) and a pair of shoes (same color) at random, what is the theoretical probability that George will choose a white pair of shoes and a pair of socks that are not white
Answers
Using it's concept, it is found that there is a [tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
One out of four pairs of shoes are white.Three out of four pairs of socks are not white.Since the events are independent:
[tex]p = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]
[tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.
More can be learned about probabilities at https://brainly.com/question/14398287
the following are ages in years of members in a group: 8,11,8,19,6,7,3x,11,11. If the mean age is 9, find x
Answers
Mode: 11median: 9
Step-by-step explanations
3x = 3*2 = 6
(6,7,8,8,9,10,11,11,11)/9 = 81/9 = 9
Help!
Square pyramids A and B are similar. In pyramid A, each base edge is 20 cm. In pyramid B, each base edge is 5 cm and the volume is 25 cm.
a. Find the volume of pyramid A.
b. Find the ratio of the surface area of A to the surface area of B.
c. Find the surface area of each pyramid.
Answers
Answer:
Below in bold.
Step-by-step explanation:
a) The volumes will be in the ratio of the cubes of the edges.
So volume of A / volume B = 20^3 / 5^3
Volume A / 25 = 8000/125
Volume a = (25* 8000) / 125
= 8000/ 5
= 1600 cm^3.
b) ratio of the surface area of A to surface area of B
= 20^2 : 5^2
= 400:25
= 16:1.
c. The volume of pyramid B is 25 cm*3 so it' height is 25 / area of its base = 25/5^2
= 1 cm.
Now its slant height = √(1^2 + (2.5)^2)
= √7.25
= 2.6926 cm
So surface area = 25 + 4 * 1/2 * 5 * 2.6926
= 51.926
= 51.93 cm^2 to nearest hundredth.
and the surface area of pyramid B = 51.926 * 16
= 830.82 cm^2 to nearest hundredth.
factorise fully 2ab2+ 8a2b
Answers
[tex]2 {ab}^{2} + {8a}^{2} b[/tex]
solution:[tex]2ab(b + 4a)[/tex]
to factorise first, find the highest common factor of each of the terms in the expression then, write the highest common factor (HCF) in front of any brackets atlast, fill in each term in the brackets by multiplying out.
The value of the expression after factorization will be;
⇒ 2ab (b + 4a)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2ab² + 8a²b
Now,
Factorize the expression as;
⇒ 2ab² + 8a²b
⇒ 2ab × b + 2×2×2a×a×b
⇒ 2ab (b + 4a)
Thus, The value of the expression after factorization will be;
⇒ 2ab (b + 4a)
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HELP PLEASE I WILL GIVE 10 POINTS
Answers
how to I write a one solution function??
Answers
The figures are similar. Find x.
Pls help meee
Answers
pls help thanks!!!!!!
Answers
Answer:
he will have 29 nickles
Step-by-step explanation:
I just solved it on paper, hope it helps and if it's right
Which of the following pairs of numbers are additive inverses of each other? (A) -0.5 and -0.5 (B)-0.5 and 2 (C) 0.5 and -0.5 (D) 0.5 and 2
Answers
Answer: A) -0.5 and -0.5
Step-by-step explanation:
HELP I TOTALLY FORGOT HOW TO DO THISS
Answers
Answer:
13
Step-by-step explanation:
First you would create a ratio.
Convert 3 1/4 gallons in a decimal -> 3.25 gallons
If 1 gallon = 4 quarts, then
[tex]\frac{3.25}{1} =\frac{x}{4}[/tex]
Now, solve for x via cross multiplying
[tex]x=13[/tex]
and sidenote ripp iready i feel your pain
NEED HELP WILL GIVE BRAINLIEST!!! PLEASE ANSWER THE TWO QUESTIONS ABOVE!
Answers
Answer:
1. 9 6/12
2. 4 3/12
Step-by-step explanation:
I did the math on it.
Answer:
3. 9 (6/12)
4. 4 (3/12)
Step-by-step explanation:
Question 3:
6 (2/6) × 1 (1/2)
multiply the whole number by the denominator
6 x 6 = 36 + 2 (numerator) = 38/6
2 x 1 = 2 + 1 = 3/2
(38/6) x (3/2)
multiply (3/2) by 3
3 x 3 = 9
2 x 3 = 6
38/6 x 9/6
38 x 9 = 342
6 x 6 = 36
19/2 = 9 (1/2) or 9 (6/12)
Question 4:
5 (2/3) × (3/4)
15 + 2 = 17
17/3 x 3/4
17 x 4 = 68
3 x 4 = 12
3 x 3 = 9
4 x 3 = 12
(68/12) x (9/12)
68 x 9 = 612
12 x 12 = 144
612/144 = 4 (1/4) or 4 (3/12)
I hope this helps! I'm sorry if this is confusing.
A large food distributor claims that 45% of all individuals who purchase eggs from its grocery stores choose standard white eggs, 25% choose standard brown eggs, 20% choose organic eggs, and 10% choose free-range eggs. To investigate this claim, researchers collected data from a random sample of the distributor's customers in a large city. The results were 274 white, 159 brown, 126 organic, and 41 free-range egg purchases. Are the data from the sample consistent with the distributor's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion.
Answers
The statistical test at the 5% significance level shows that we fail to reject the null hypothesis.
How to compute the statistical test?From the information given, the level of significance is 0.05 and n is 600. The degree of freedom will be:
= 4 - 1 = 3
The test statistic will be:
= ∑(O - E)²/E
= 6.92
The critical value is also given as 7.815 from the table. Since the test statistic is lesser than the critical value, we fail to reject the null hypothesis.
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Using factoring, what is the solution to the equation 2x2 + 3x – 5 = 0
Answers
So start with
2x2+3x-5=0
2x2=4
4+3x-5=0
Subtract 4 from both sides
4+3x-5=0
-4. -4
The 4 cancels out
3x-5= -4
Now add 5 to each side and the 5 will cancel
3x-5=-4
+5. +5
3x=1
Divide 3 from both sides the 3 cancels
3x=1
3/3x= 1/3
So your answer is:
x=1/3
PLEASE HELP!! 90 POINTS!!!
Dianelys owns a small business selling ice-cream. She knows that in the last week 14 customers paid cash, 121 customers used a debit card, and 3 customers used a credit card. If next week, she is expecting 1100 customers, about how many would you expect to pay with cash? Round your answer to the nearest whole number.
Answers
Explanation:
14 is 10.14% of 138
(138 = total of people last week)
10.14 of 1100 is 111.54
111.54 rounded is 112 :)
Answer:
112 customers will pay cash next week
Step-by-step explanation:
1,100/138=7.97= approximately 8
Multiply the amount of customers who paid cash, 14 by 8.
A Premier League footballer is value £30 million and after a bad season his transfer value depreciates by 20%. His next season is a good one and his transfer value appreciates by 20%. how Find the value of the footballer after his good season.
How to work out Sir
Answers
Answer:
£28.8 Milllion
Step-by-step explanation:
£30,000,000 × 0.8 = £24,000,000 (Depreciates by 20%)
£24,000,000 × 1.2 = £28,800,000 (Appreciates by 20%)
While on a business trip to Millersburg, Camilla treated her co-workers to a meal that cost $300. Camilla knew that when the bill came, she would need to pay Millersburg sales tax of 8% and would want to leave a 15% tip on the original $300. Including tax and tip, how much did Camilla's meal cost?
Answers
When the bill came, she would need to pay Millersburg sales tax of 8% and would want to leave a 15% tip on the original $300. Including tax and tip, Camilla's meal cost $369.
Given that,
Original Meal Cost: $300
Sales Tax: 8% of the original meal cost
Tip: 15% of the original meal cost
Total Cost: Sum of the original meal cost, sales tax, and tip
Original Meal Cost = $300
Sales Tax = 8% of $300 = 0.08 * $300 = $24
Tip = 15% of $300 = 0.15 * $300 = $45
Total Cost = Original Meal Cost + Sales Tax + Tip
Total Cost = $300 + $24 + $45 = $369
Including tax and tip, Camilla's meal cost $369.
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a packaging designer wants to find how much fabric is needed to cover the jewelry box shown the box is 12cm shown 4 cm wide and 5m high find the surface area of the box
Answers
Step-by-step explanation:
I guess you mean it is
12 cm long, 4cm wide and 5 cm high.
and the fabric goes outside on the box ? strange, but ok.
a box (like a die) has 6 sides in the form of 3 pairs of equal rectangles :
top-bottom, left-right, front-back
the surface area is the sum of all 6 rectangles.
top-bottom :
2 × 12×4 = 2 × 48 = 96 cm²
left-right :
2 × 4×5 = 2 × 20 = 40 cm²
front-back :
2 × 12×5 = 2 × 60 = 120 cm²
in total
120 + 40 + 96 = 256 cm²
462,453,444 find 30th term
Answers
Answer:
a₃₀ = 201
Step-by-step explanation:
there is a common difference between consecutive terms , that is
453 - 462 = 444 - 453 = - 9
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 462 and d = - 9 , then
a₃₀ = 462 + (29 × - 9 ) = 462 - 261 = 201
If a circle has a circumference of 94.2cm, determine the area
Answers
Explanation:
To find the area of a circle we can use the formula pi times the radius squared.
Since we don’t know the radius that is what we must find. To find the radius of a circle from the circumference you divide the circumference by pi. So 94.2 divided by 3.14 gives use 30. Then we take 30 and divide by 2.
30/2 = 15
So the radius of our circle is 15cm
To find the area we take our radius and square it 15^2 which is just another way of saying 15 x 15
Which equals 225. Then we take 225 and multiply it by pi.
225 x 3.14 = 706.5
So the area of the circle is 706.5cm^3
The square of a non-zero number is equal to 70% of the original number. What
is the original number?
Answers
Answer:
0.7.
Step-by-step explanation:
x^2 = 0.7x
x^2 - 0.7x = 0
x(x - 0.7) = 0
x = 0, 0.7.
After solving the quadratic equation x² = 0.7x , we get that the original number is 0.7
What is a quadratic equation?
Quadratic equation is an equation which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the standard quadratic equation in x is given by
ax²+bx+c =0, where a, b, c are constants and a≠0
We can solve this equation by factorizing ax²+bx+c and putting those factors equal to zero to solve for x.
Let a non zero number be x, x≠0 and given that the square of a non zero number is equal to the 70% of the original number.
As 70 % of the original number = 70/100(x) = 0.7 x
⇒ x² = 0.7 x
⇒x²-0.7 x = 0
⇒ x(x -0.7)= 0
⇒ x =0 and x - 0.7 = 0
⇒ x = 0.7, as we have given that x is a non zero number
Therefore, the original number is 0.7
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Is it possible for a sixth degree polynomial function with integer coefficients to have no real zeroes? Choose all that apply: Yes No
Answers
Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, [tex]\pm i, \pm 2i, \pm 3i[/tex], a sixth degree function with no real zeros is formed, so the answer is Yes.
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RSM find all 2-digit natural numbers that have exactly 3 factors
Answers
Answer:
25 and 49
Step-by-step explanation:
25 = 1, 5, 25
49 = 1, 7, 49
Hope this helps!
please help me!!!!!!!
Answers
The distance between you and train 1 at time t is
20.6 km + (0.2 km/h) t
and the distance between you and train 2 at time t is
59.7 km - (2.1 km/h) t
The trains are an equal distance away from you when
20.6 km + (0.2 km/h) t = 59.7 km - (2.1 km/h) t
Solve for t :
(2.3 km/h) t = 39.1 km
t = 17 h
at which point they are
20.6 km + (0.2 km/h) (17 h) = 24 km
away from you.
The volume of a number cube is 27 cm^3. What is the length of each side of a cube?
Answers
Lets see
Volume of a cube=side³ATQ
side³=27side=³√27side=3cmAnswer:
a = 3 cm
Step-by-step explanation:
The length of each side of a cube is 3 cm.
(Refer to the attachment)
if a rectangle has a perimeter of 18 cm, and a height of 4 cm, what is the area?
Answers
Answer:
20 cm²
Step-by-step explanation:
Look at the diagram attached.
If the height is 4cm, we will have two sides that are 4cm for our rectangle.
We can label the other sides as x.
They are both x since opposite sides of a rectangle are equal in length.
We can make an equation with our perimeter:
[tex]2(4) + 2(x) = 18\\8 + 2x = 18\\2x = 10\\x = 5[/tex]
Now that we know the length & height, we can calculate the area:
4 × 5 = 20 cm²