Answers
Answer:
The surface area of the cylinder is 251.2cm²
Step-by-step explanation:
To solve this problem we have to calculate the circle area and the lateral area
radius = half of diameter
r = 10/2 = 5cm
To calculate the area of the circle we use the following formula
a = area
r = radius = 5cm
π = 3.14
a = π * r²
we replace with the known values
a = 3.14 * (5cm)²
a = 3.14 * 25cm²
a = 78.5cm²
The area of the circle is 78.5cm²
To calculate the lateral area of the cylinder we use the following formula
a = area =
h = heighti = 3cm
r = radius = 5cm
π = 3.14
a = 2 * π * r * h
we replace with the known values
a = 2 * 3.14 * 5cm * 3cm
a = 6.28 * 15cm²
a = 94.2cm²
The lateral area of the cylinder is 94.2cm²
Now we add the lateral area of the cylinder with 2 times the area of the circle and obtain the area of the cylinder
94.2cm² + (2 * 78.5cm²) = 251.2cm²
The surface area of the cylinder is 251.2cm²
Related Questions
Find the volume of a cylinder 10mi and 22mi
Answers
Answer:
If the radius is 10mi, height is 22mi, the answer is V≈6911.5
If the radius is 22mi, height is 10mi, the answer is V≈15205.31
oac is a sector of a circle of radius 8cm, centre O ba and bc are tangents to the circle angle aoc = 120 degrees calculate the area of the shaded region give your answer to 3 significant figures
Answers
Answer:
The area of the shaded region is [tex]49.5 cm^{2}[/tex] to 3. significant figures
Step-by-step explanation:
Step one: find the two diagonals of the kite.
The Horizontal diagonal can be obtained using the cosine rule:
[tex]AC^{2}=OA^{2}-OC^{2}- 2\times (OA)\times (OC)cos (\theta)[/tex]
[tex]AC^{2}=8^{2}+8^{2}- 2\times 8 \times 8 \times cos (120)= 212\\AC =\sqrt{212}=14.56cm[/tex]
The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:
Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.
This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.
[tex]cos 60 = \frac{8}{OB}\\OB=\frac{8}{cos 60}= 16cm[/tex]
Step two: Use the dimensions of the two diagonals of the Kite to find the area:
The area of a Kite is obtained using this formula:
[tex]Area = \frac{pq}{2}[/tex], where p and q are the two diagonals.
hence,
[tex]Area = \frac{14.56 \times 16}{2}= 116.48cm^{2}[/tex]
Step three: Calculate the area of the sector of the circle.
Area of the sector is obtained using this formula
[tex]Area = \frac{\theta}{360}\times \pi\times r^{2}\\Area = \frac{120}{360} \times \pi \times 8^{2}=67.03cm^{2}[/tex]
Step Four: Subtract the area of the sector from the area of the kite:
Area of the shaded region will be [tex]116.48cm^{2} -67.03cm^{2} = 49.45cm^{2}[/tex]
This will be[tex]49.5 cm^{2}[/tex] to 3. significant figures
Answer:
43.8 cm²
Step-by-step explanation:
1. Split the kite in two and find the length of OB
When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.
Then, use the sine rule we can find out the length of OB. It goes like this:
[tex]\frac{OB}{sin90} = \frac{8}{sin30}\\ \\{OB} = \frac{8sin90}{sin30}\\\\ {OB} = 16cm[/tex]
2. Calculate the area of the kite
Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of [tex]area of triangle=\frac{1}{2}absinc[/tex].
[tex]\frac{1}{2}[/tex]×8×16×sin60 = [tex]32\sqrt{3}[/tex]
But as there are two triangles, we duplicate the answer.
2×[tex]32\sqrt{2}[/tex] = [tex]64\sqrt{3}[/tex]
2. Calculate the area of the sector
area of sector =[tex]\frac{angle of sector}{360} \\[/tex]×πr²
[tex]\frac{120}{360}[/tex]×8²π = [tex]\frac{64}{3}[/tex]π
3. Subtract the area of the sector from the area of the kite
[tex]64\sqrt{3}[/tex] - [tex]\frac{64}{3}[/tex]π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)
HOPE THIS WILL HELP YOU :)
Find the diameter, area and circumference.
11
0
Answers
Answer:
diameter = two times the radius
2r
the area = πr²
the circumference= 2πr
hope it helps
Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x + 4 6x + 3y = -12 -4 4 12
Answers
Answer:
Option (4)
Step-by-step explanation:
The given system of equations is,
y = -2x + 4 ------ (1)
6x + 3y = a --------(2)
We have to find the value of a for which the system of equations will have infinitely many solutions.
Option (1). If a = -12
6x + 3y = -12
2x + y = -4
y = -2x - 4
Both the equations have same slope, therefore, they are parallel and will have no solutions.
Option (2). If a = -4
6x + 3y = -4
3y = -6x - 4
[tex]y=-2x-\frac{4}{3}[/tex]
Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.
Option (3). If a = 4
6x + 3y = 4
3y = -6x + 4
y = -2x + [tex]\frac{4}{3}[/tex]
Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.
Option (4). If a = 12
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
Therefore, both the equations (1) and (2) are same for a = 12 and they will have infinitely many solutions.
This question is based on system of linear equation .Thus, for a=12 will have infinitely many solution.
Given:
y = -2x + 4 ------ (a)
6x + 3y = a ------(b)
We need to determined the value of a for which the system gives infinitely many solution.
Now check all the options as given below:
Option(1) a = -12 and put it in (b) we get,
6x + 3y = -12
2x + y = -4
y = -2x - 4
Both the equations have same slope, therefore, they are parallel to each other and have no solutions.
Option(2) a= -4 and put it in (b) we get,
6x + 3y = -4
3y = -6x - 4
[tex]y=-2x-\dfrac{4}{3}[/tex]
Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.
Option(3) a= 4
6x + 3y = 4
3y = -6x + 4
[tex]y=-2x+\dfrac{4}{3}[/tex]
Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.
Option(4) a= 12
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
Both the equation are same for a= 12.
Thus, for a=12 will have infinitely many solution.
For further details, please prefer this link:
https://brainly.com/question/13712241
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
x5
Step-by-step explanation:
Answer:
(x - 1) (x + 4)
Step-by-step explanation:
Need some help with number word problems, tysm if you do :)
Answers
Answer:
Read below
Step-by-step explanation:
x is always the smaller number
y is always the larger number
underlined means it's the question
bolded means it's the answer
1.
One number is 6 times as large as another. Their sum is 42. Find the numbers.
The numbers need to fit the criteria:
6x=yx+y=42A. 6+36=42 (correct)
B. 7+42=49 (incorrect)
C. 7+35=42 (incorrect because it doesn't follow the 1st rule)
D. 6+42=48 (incorrect)
Only A. 6, 36 fits the criteria.
2.
One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.
The numbers need to fit the criteria:
x+3=y4x-4=3yA.
4+3=7
12-6≠21 (incorrect)
B.
7+3=10
28-3≠30 (incorrect)
C.
13+3=16
52-4=48 (correct)
D.
9+3≠13 (incorrect)
Only C. 13, 16 fits the criteria.
3.
One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.
The numbers need to fit the criteria:
x+4=y5x+3=4yA.
13+4=17
65+3=68 (correct)
B.
-23+4= -19
-115+3≠ -76 (incorrect)
C.
17+4=21
85+3≠84 (incorrect)
D.
-11+4+ -7
-35+3≠ -33 (incorrect)
Only A. 13, 17 fits the criteria.
4.
The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.
The numbers need to fit the criteria:
x+y=23y-3x=3A.
5+18=23
18-15=3 (correct)
B.
8+15=23
15-24≠3 (incorrect)
C.
-13+36=23
36+39≠3 (incorrect)
D.
-5+28=23
28+15≠3 (incorrect)
Only A. 5, 18 fits the criteria.
5.
The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.
The numbers need to fit the criteria:
x+y=26y-2x=2A.
8+18=26
18-16=2 (correct)
B.
9+17=26
17-18≠2 (incorrect)
C.
7+19=26
19-14≠2 (incorrect)
D.
6+20=26
20-12≠2 (incorrect)
Only A. 8, 18 fits the criteria.
What is the x-intercept of the line whose equation is x/3 + y/2 = 1
Answers
Answer:
y- intercept = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
[tex]\frac{x}{3}[/tex] + [tex]\frac{y}{2}[/tex] = 1
Multiply through by 6 to clear the fractions
2x + 3y = 6 ( subtract 2x from both sides )
3y = - 2x + 6 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope- intercept form
with y- intercept c = 2
i need help with this and how you got it please! 10 points
Answers
Answer:
B, x=40 is the right answer
Step-by-step explanation:
DAC is one half of the right angle and CAB is another half. So, you know that since a right angle is 90 degrees, DAC + CAB must equal 90.
They have given you equations for both angles, so now its just a matter of rearranging and solving for x.
DAC = x
CAB = 2x - 30
DAC + CAB = 90
Using the equations above, we can come up with this final equation:
x + 2x - 30 = 90
If we add the x together:
3x - 30 = 90
If we move the 30 to the other side by adding it to 90
3x = 90 + 30
3x = 120
If we divide 120 by 3:
x= 40
Therefore, the answer is B
Hope this helped : )
I NEED HELP ITS ON FUNCTIONS! HELPPPPPPPPPPP
Explanation needed
Answers
Answer:
D
Step-by-step explanation:
A function of x means that there can only be one value of y per x value. Therefore, D does not match this because there are 4 values of y per x value (3).
Answer:
D
Step-by-step explanation:
Each x value can have only ONE y value
this means that there cannot be more than one of the same x value:
think of the x values as an input, each input has one output right?
ex:
input: 7
output:8
input:3
output:2
how is it possible that the same input has different outputs?
input: 5
output: 6,7
this does not make any sense, one input should only have one output hence, one value of x(input) should have only one value of y(output)
Hope this helps!
yo help me with this pllease
Answers
Answer:
a) 6
b) 37.5
c) 6th term
Step-by-step explanation:
a) plug in 2 for n
3(2)^2/2
6
b) plug in 5 for n
3(5)^2/2
37.5
c) since 5 is 37.5, I am going to check 6
3(6)^2/2
54
The 6th term will be the first to have a value higher than 50
Joy made a deposit of $1600 into an account with a rate of 5%. How long should she leave the money into the account if she wants to earn $240 in interest
Answers
Answer: 3 years
Step-by-step explanation:
The following can be gotten from the question:
Principal = $1600
Rate = 5%
Simple interest = $240
Time = Unknown
Interest = Principal × Rate × Time /100
240 = (1600 × 5 × Time)/100
240 = (8000 × Time)/100
240 × 100 = 8000 × Time
24000 = 8000 × Time
Time = 24000/8000
Time = 3 years
givenvl that 3×6=12 and 2×5=9 then a×b maybe defined as?
Answers
PLEASE ANSWER How do you think industries vary according to the wealth of a country? Justify your answer.
Answers
Answer:
They very according to the wealth of a country because the wealth of the country also reflects on how much supply there is, and if for example, there is a shampoo factory they will use less quality items because they don't have enough money or supplies to make good quality shampoo. The wealth of the country also affects how many sales are made from those lower quality items. Since the country is so poor, they don't have enough money to buy expensive products from overseas so they will buy the lower quality items, even if they know that they aren't the best quality. This might result to diseases in some serious cases, like in food industries of poor countries.
Step-by-step explanation:
it vary because if the country in which the company is being operated is a wealthy country it means that the company or industry will gain more customers than a country that is poor. Because if the country is wealthy people will come to that country because of it's rich economy but it also differs if the country in which the company is operating and does not offer quality service that industry will not be successful
A car has a full tank of gas, holding
15 gallons
. It drives
300 miles
, and then stops for gas. After
10 gallons
of gas are added, the tank is full again. What is the gas mileage of the car?
Answers
Answer:
The mileage of the car is 30 miles per gallon
Step-by-step explanation:
Here, we are interested in calculating the gas mileage of the car.
The gas mileage refers to the number of kilometers the car can travel on a particular amount of fuel.
The full capacity of the car tank is 15 gallon
Now after traveling 300 miles, it stops for gas and 10 gallons of fuel are added to make the car full again.
What this means is that the car used up a total of 10 gallons of fuel for the 300 miles
Thus, the gas mileage of the car is that it used 10 gallons to travel a total of 300 miles
Expressing this as a ratio, we have 300 miles/10 gallons = 30 miles/ gallon
This means that on a gallon of fuel, the car can travel 30 miles
16 points!
What is the length of line AB?
√17
√35
6
4
Answers
Answer:
i think its 6
Step-by-step explanation:
The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The dimension of the rectangular prism will be 3 units long, 5 units wide, and 1 unit high. Then the diagonal of the prism is given as,
D² = 3² + 5² + 1²
Simplify the equation, then we have
D² = 3² + 5² + 1²
D² = 9 + 25 + 1
D² = 35
D = √35 units
The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.
More about the rectangular prism link is given below.
https://brainly.com/question/12649592
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What is (7x − 9) + (3x + 14)?
Answers
Answer:
[tex](7x - 9) + (3x + 14) = 10x + 5[/tex]
Step-by-step explanation:
[tex]\left(7x-9\right)+\left(3x+14\right)[/tex]
Remove parentheses: [tex]\left(a\right)=a[/tex]
[tex]=7x-9+3x+14[/tex]
Group like terms:
[tex]=7x+3x-9+14[/tex]
Add similar elements: [tex]7x+3x=10x[/tex]
[tex]=10x-9+14[/tex]
Add/Subtract the numbers: [tex]-9+14=5[/tex]
[tex]=10x+5[/tex]
Hope I helped. If so, may I get brainliest and a thanks?
Thank you. Have a good day! =)
Answer:
pls refer to the pic
Step-by-step explanation:
PLS MARK ME AS BRAINLIAST PLS MARK ME AS BRAINLIAST AND DON'T FORGET TO FOLLOW AND THANKS MY ANSWER PLS MARK ME AS BRAINLIAST AND DON'T FORGET TO FOLLOW AND THANKS MY ANSWER HOPE IT HELPS.....Explain how to find the value of x. Be sure to include the postulates, definitions and theorems that justify your answer.
Answers
Answer:
It's 180 degrees? I'm not so sure.
Step-by-step explanation:
Juan has 36 red pencils and 42 blue pencils, Juan wants to make equal groups of pencils of the same color. How many groups of red and blue pencils can he make with each group having the same number of pencils
Answers
Answer:
Juan can make 6 groups having the same number of pencil
Step-by-step explanation:
42/7=6
36/6=6
42+36=78
78/6=13
Each group will get 13 pencils
Graph f(x) = -1/2x click on the graph till f(x) =-1/2x appears
Answers
Answer:
Step-by-step explanation:
Order the situations from the account that yields the greatest amount to one that yields the least amount.
Situation A: You invest $500 in an account at a 12% interest rate, compounded monthly, for 12 years.
Situation B: You invest $500 in an account at a 10% interest rate, compounded quarterly, for 15 years.
Situation C: You invest $500 in an account at a 15% interest rate, compounded annually, for 10 years.
Answers
Answer:
Order from the greatest yield to the least as follows
1. Situation B=$2,119.8949
2. Situation A=$2,095.3078
3. Situation C=$2,022.7789
Step-by-step explanation:
Situation A
A=P(1+r/n)^nt
=500(1+0.12/12)^12*12
=500(1+0.01)^144
=500(1.01)^144
=500(4.1906155936008)
=$2,095.3078
Situation B
A=P(1+r/n)^nt
=500(1+0.1/4)^4*15
=500(1+0.025)^60
=500(1.025)^60
=500(4.3997897488150)
=$2119.8949
Situation C
A=P(1+r)^t
=500(1+0.15)^10
=500(1.15)^10
=500(4.0455577357079)
=$2022.7789
Order from the greatest yield to the least as follows
1. Situation B=$2,119.8949
2. Situation A=$2,095.3078
3. Situation C=$2,022.7789
Please answer correctly !!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
49
Step-by-step explanation:
y = 7^2
= 49
Mr. Márquez had 123 eggs in a refrigerator in his restaurant. He put 32 more cartons of eggs in the
refrigerator. Each carton contained 18 eggs. Which of these is the best estimate of the number of eggs Mr.
Márquez now has in his refrigerator?
A. 600
OB. 400
OC. 700
D. 900
Answers
Answer:
700 eggs
Step-by-step explanation:
First take the cartons and determine the number of eggs
32 cartons * 18 eggs per carton
576 eggs
Add the eggs not in cartons
576+123 =699
Which inequality represents the values of x that ensure triangle ABC exists? a triangle with side lengths of 6.5 units, 3.5 units, and 2.5 + x units A. 0.5 < x < 7.5 B. 3.0 < x < 7.5 C. -0.5 < x < 7.5 D. -3.0 < x < 7.5
Answers
Answer:
1 < x < 7.5
Step-by-step explanation:
This problem can be solved using given below property of triangle.
Sum of two sides is always greater than third side of triangle.
Difference of two sides is always lesser than third side of triangle.
_______________________________________________
Given
sides length
6.5 units
3.5 units
Third side is 2.5 + x
using the property, Sum of two sides is always greater than third side of triangle.
6.5 + 3.5 > 2.5 +x
=>10 >2.5 + x
=>2.5 + x< 10
=> x< 10 -2.5
=> x < 7.5
using the property, Difference of two sides is always lesser than third side of triangle.
6.5 - 3.5 > 2.5 +x
=>3.5 > 2.5 +x
=> 2.5 +x > 3.5
=> x > 3.5 - 2.5
=> x > 1
combining both we have
1 < x < 7.5
out of the given option none is 1 < x < 7.5
hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.
The inequality that represents the values of x that ensure triangle ABC exists is A. 0.5 < x < 7.5
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given that the side lengths of a triangle are as; 6.5 units, 3.5 units, and 2.5 + x units
By using the property, the Sum of two sides is always greater than third side of triangle, then;
6.5 + 3.5 > 2.5 +x
=>10 >2.5 + x
=>2.5 + x< 10
=> x< 10 -2.5
=> x < 7.5
Also, by using the property, Difference of two sides is always lesser than third side of triangle then we get;
6.5 - 3.5 > 2.5 +x
=>3.0 > 2.5 +x
=> 2.5 +x > 3.0
=> x > 0.5
Now combining both we have;
. 0.5 < x < 7.5
Learn more about inequality ;
brainly.com/question/14164153
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I need help with shifting functions
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
g(x) = h(x - 7) + 5
The plus 5 on the outside of the brackets represents the graph moving up by 5 units
The minus 7 on the inside of the brackets represents the graph moving right by 7 units.
Note: When it is on the inside of the brackets, you would do the opposite of what it suggests.
Normally, minus 7 would mean the graph shifts to the left, however, it means the opposite in this case.
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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What is 6:12 in simpiest form?
Answers
Answer:
6:12=1:2
Step-by-step explanation:
as we will cut 6:12 by 6 . please mark me as brainliest and follow me
Answer:
1:2
Step-by-step explanation:
6 and 12 are divisible by 6
6 ÷ 6 = 1
12 ÷ 6 = 2
What is the solution to the equation
1/2x+3 = 2/3+1?
Answers
Answer:
x = -8/3
Step-by-step explanation:
1/2x+3 = 2/3+1
Combine like terms
1/2x+3 = 2/3 + 3/3
1/2x + 3 = 5/3
Subtract 3 from each side
1/2x + 3-3 = 5/3 - 3
1/2x = 5/3 - 9/3
1/2x = -4/3
Multiply each side by 2
1/2x *2 = -4/3*2
x = -8/3
What is the measure of A?
Answers
ΔABC is an equilateral triangle.
All 3 angles must be equal in an equilateral triangle.
[tex]180/3[/tex]
[tex]=60[/tex] °
Fred is planning a fundraiser where he will collect $4.50 fir every mile he runs.
Answers
If y = 1 and y = cos x , list the values of x where 0 degrees <= x <= 360 degrees to make these statements true.
Answers
Answer:
90°
Step-by-step explanation:
cosx = y=1
Therefore cosx =1
For cosx= 1
x= 90°, 450°, 810° ... etc.
Now 0° ≤ x ≤ 360°
The only value that satisfies both relations is 90°
Therefore, x= 90°
someone help me pls.
I will give you branliest question
Answers
Answer:
C = 25.1 cm
Step-by-step explanation:
C = 2(3.142r)
C = 2(3.142*4)
C = 2(12.568)
C = 25.136
Round to the nearest hundredth
C = 25.1