Answers
Answer:
Formulas
[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac{1}{2}\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
[tex]\textsf{Radius of a circle}=\sf \dfrac{1}{2}d\quad\textsf{(where d is the diameter)}[/tex]
[tex]\textsf{Perimeter of a semicircle}=r(\pi +2) \quad \textsf{(where r is the radius)}[/tex]
Use the above formulas to calculate the various measurements, remembering to calculate the radius first when given the diameter.
Question 9a) Radius = 2.7 cm
[tex]\implies \textsf{Area}=\sf \pi (2.7)^2=22.9\:\:cm^2\:(1\:d.p.)[/tex]
[tex]\implies \textsf{Circumference}=\sf 2 \pi (2.7)=17.0\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
b) Diameter = 45 mm
[tex]\sf \implies Radius =\dfrac{45}{2}=22.5\:\:mm[/tex]
[tex]\implies \sf Area= \pi (22.5)^2=1590.4\:\:mm^2\:(1\:d.p.)[/tex]
[tex]\implies \sf Circumference= 2 \pi (22.5)=141.4\:\:mm\:(1\:d.p.)[/tex]
Question 10a) Radius = 8.5 cm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=8.5(\pi +2)=43.7\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
b) Radius = 24 mm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (24)^2=904.8\:\:mm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=24( \pi +2)=123.4\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
c) Diameter = 32 cm
[tex]\sf \implies Radius =\dfrac{32}{2}=16\:\:cm[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (16)^2=402.1\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=16( \pi +2)=82.3\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
d) Diameter = 15 m
[tex]\sf \implies Radius =\dfrac{15}{2}=7.5\:\:m[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=7.5( \pi +2)=38.6\:\:m\:(1\:d.p.)[/tex]
Related Questions
Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like.
y=1/27((9x^2)+(6))^3/2 ,from x=3 to x=6
Answers
The length of the curve [tex]y = \frac{1}{27}(9x^2 + 6)^\frac 32[/tex] from x = 3 to x = 6 is 192 units
How to determine the length of the curve?The curve is given as:
[tex]y = \frac{1}{27}(9x^2 + 6)^\frac 32[/tex] from x = 3 to x = 6
Start by differentiating the curve function
[tex]y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x[/tex]
Evaluate
[tex]y' = x(9x^2 + 6)^\frac 12[/tex]
The length of the curve is calculated using:
[tex]L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx[/tex]
This gives
[tex]L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx[/tex]
Expand
[tex]L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx[/tex]
This gives
[tex]L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx[/tex]
Express as a perfect square
[tex]L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx[/tex]
Evaluate the exponent
[tex]L =\int\limits^6_3 {3x^2 + 1} \ dx[/tex]
Differentiate
[tex]L = x^3 + x|\limits^6_3[/tex]
Expand
L = (6³ + 6) - (3³ + 3)
Evaluate
L = 192
Hence, the length of the curve is 192 units
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which situation representd 24÷6
Answers
Answer:
= 4
Step-by-step explanation:
24÷6
= 4
What is 2/3 by 4/5 in fraction
Answers
Answer: If you mean to multiply, the answer is 8/15.
Step-by-step explanation:
Multiply numerator by numerator and denominator by denominator.
2 x 4 = 8
3 x 5 = 15
ANSWER: 8/15
What is 6 months to 5 years expressed as a ratio
Answers
Answer:
6:5
Step-by-step explanation:
the To represents :
this makes 6:5
David has 30 sweets. He gives Sarah of his sweets and Joe 20% of his
sweets. How many sweets does David have left?
Answers
Answer:
24
Step-by-step explanation:
20 percent of 30 is 6
30-6=24
therefore david has 24 sweets left
How would you apply the fundamental counting principle to a bike lock combination with 5 numbers?
1. 10+ 10+ 10+ 10+10
2. 10x5
3. 10x10x10x10x10
4.none of these
Answers
Answer:
3
Step-by-step explanation:
Which equation is quadratic in form?
Answers
A quadratic equation is written in the form [tex]ax^{2} + bx + c = 0[/tex]
Looking at the second, third, and fourth options, we see that the highest powers are greater than two, which automatically disqualifies them from being quadratics (since the highest power in a quadratic is 2).
This makes the first option the correct choice since the expansion of the equation gives [tex]2x^{2} + 28x + 61[/tex]
Answer:
a
Step-by-step explanation:
Kevin works at a restaurant. He stacks glasses as shown. Let x be the number of glasses and f(x) be the height of the stack. If 5.5 inch glasses with 1.2 inch lips are stacked vertically, which table correctly models this situation?
Answers
The table that correctly models the linear equation is table A.
Which table correctly models this situation?
The first glass added will have a height of 5.5 inches, and then for each glass that we add, we are adding a height of 1.2 inches.
This means that the first value on the table must be 5.5 in.The second value must be 5.5 in + 1.2in = 6.7 in.The third value must be: 6.7in + 1.2in = 7.9 inAnd so on, so we have the linear relation:
y = 5.5in + x*1.2in
Where x is the number of glasses in the tower.
Then the table that correctly models this situation is table A.
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Answer:
the one with 5.5, 6.7 etc
Step-by-step explanation:
no
Choose the words to finish the sentence. Euler’s Formula states that the of the number of faces and the number of in a polyhedron is equivalent to two more than the number of its .
Answers
Answer:
see explanation
Step-by-step explanation:
Euler's formula states that the sum of the number of faces (F) and the number of vertices (V) of a polyhedra is equivalent to two more than the number of its edges (E) , that is
F + V = E + 2
Connor leaves Omaha heading directly east at a rate of 32 miles per hour.
One hour later, Jason leaves from Omaha heading in the same direction at a rate of 50 miles per hour.
How long, in hours, after Jason leaves does Jason catch up with Connor?
Round your answer to the nearest hundredths place if necessary.
Answers
Answer:
1.02 miles
Step-by-step explanation:
A regular hexagonal prism has a height of 7 cm and base edge length of 4 cm. Identify its lateral area and surface area.
Answers
Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.
What is lateral and surface area of the regular hexagonal prism?For a regular hexagonal prism, the Lateral surface area and the surface area is expressed as follows:
Lateral Area = 6a × h
Surface Area = 6ah + 3√3a²
Where a is base edge and h is height.
Given that;
Base edge length a = 4cmHeight h = 7cmThe Lateral Area of the regular hexagonal prism will be;
Lateral Area = 6a × h
Lateral Area = 6( 4cm ) × 7cm
Lateral Area = 24cm × 7cm
Lateral Area = 168cm²
The Surface Area of the regular hexagonal prism will be;
Surface Area = 6ah + 3(√3)a²
Surface Area = 6(4cm × 7cm) + 3(√3)(4cm)²
Surface Area = 168cm² + 3(√3)16cm²
Surface Area = 168cm² + 83.138cm²
Surface Area = 251.138cm²
Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.
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Which of the following values are solutions to the inequality -5 -6x > -8?
I. - 4
II. - 3
III. - 5
Answers
Answer:
I. - 4
II. - 3
III. - 5
Step-by-step explanation:
All values are the solution to the inequality
twice a number added to 13 is equal to 27 what is the number
Answers
The number is 7. Let's represent the number as "x." According to the given information, "Twice a number added to 13 is equal to 27," which can be expressed as an equation.
2x + 13 = 27
Now, solve the equation for "x":
Subtract 13 from both sides:
2x = 27 - 13
2x = 14
Divide both sides by 2:
x = 14 / 2
x = 7
Therefore, the number is 7.
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HELP QUICK!!!! NOW!!!!
Answers
Answer: B. 2,448π units³
Step-by-step explanation:
We will use the formula for the volume of a cylinder to solve.
(The formula, put simplify, finds the area of the base circle and multiples by the height.)
V = πr²h
V = π(12)²(17)
V = (144)(17)π
V = 2,448π
The volume is 2,448π units³ which is option B for your problem.
Solution :
We have been provided with the height and radius and we need to calculate the volume of cylinder. So we would be using it's formula :
V = πr²hHere,
r is radius h is heightWe have :
height (h) = 17 radius (r) = 12Substituting the value :
>> V = π (12)² (17)
>> V = π (12 × 12) (17)
>> V = π × 144 × 17
>> V = π × 2448
>> V = 2448 π
Therefore :
Option B is correct.
Admission to a baseball game is $3.00 for general admission and $5.50 for reserved seats. The receipts were $3277.50 for 845 paid admissions. How many of each ticket were sold?
Answers
Answer:
548, 297
Step-by-step explanation:
We can set this up as a system of equations. The first equation is for how many tickets were sold, which is x+y=845. The second equation is for the cost of the tickets, which is 3x+5.5y=3277.50. The best method for this problem (other than graphing) is elimination. First, we need to multiply one equation to get the opposite of one of the variables. The easiest one to do for this problem is x. The opposite of 3 is -3, so we have to multiply ALL of the first equation by -3. If you do this, then you get -3x-3y=-2535. Now, combine the equations:
3x + 5.5y = 3277.50
-3x -3y = -2535
________________
0x+2.5y=742.5
Now, isolate y by dividing both sides by 2.5. If you do this, you get y=297. Now, plug this in for the y in the first equation. Isolate x.
x+297=845
-297 -297
__________
0 548
x=548
Hope this helps!
a web adminitrator is interested in the average number of visitors per day that her website receives. Match the vocab word with its corresponding example'
Answers
The correct matching of the vocabulary words and the examples given of the web administrator's process are:
Population - All the days that the website has been in existence.Statistic - The average number of visitors per day for the 42 days that the administrator tracked.Sample - The 42 randomly selected days that the administrator tracked.Variable - The number of visitors that the website receives on a given day.Data - The list of visitor counts for the 42 days that were tracked. Parameter - The average number of visitors per day that have come to the website since it was created.What metrics are used by the website administrator?The entire population being looked at would best be all the days that the website has existed and the sample will be some selected days that have been tracked.
Parameters can be created such as the average number of visitors per say and then data would be derived on this. A statistic would simple show certain information such as the average visits in the days tracked.
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Which quadratic function in vertex form has a vertex at (3, 4) and passes through the point (7,-4)
Answers
Answer:
First option
Step-by-step explanation:
Given the following question:
We are being asked to find the quadratic function that has a vertex of (3, 4) and passes through the point (7, -4). Remember that the vertex of any parabola is the point on the top of the parabola, directly in the middle of the top of the function.
First option:
[tex]y=-\frac{1}{2} (x-3)^2+4[/tex]
(see photo below)
As you can see the function has a vertex of (3, 4) which means the point on the top of the parabola is (3, 4) or the vertex. It also passes through the point (7, -4) meaning the first option is your answer.
Hope this helps.
find the radius of a circle whose arc length is 55 m and its central angle measure if 5 radians
Answers
Answer:
Step-by-step explanation:
To solve this question, we can use the formula [tex]S=\theta r[/tex], where [tex]S[/tex] is the arc length, [tex]\theta[/tex] is the central angle of the sector in radians, and [tex]r[/tex] is the radius.
In this situation, we know that [tex]S=55[/tex] and [tex]\theta=5[/tex]
This means that [tex]55=5r \longrightarrow \boxed{r=11}[/tex]
Chords AC and DB intersect at point E. Select all pairs of angles that must be congruent.
Answers
∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.
What are congruent angles?Congruent angles are said to be angles that have equal measure.
From the figure, we can see that;
∠ADE and ∠ACB are congruent because they are corresponding angles, corresponding angles are equal.
∠DEA and ∠CEB are congruent because they are corresponding angles
∠CAD and ∠CBD are also congruent because they are corresponding angles
Therefore, ∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.
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Carol buys a house for £234 900
She pays a 10% deposit.
Work out the amount of deposit paid by Carol.
Answers
Answer:
211410
Step-by-step explanation:
234900x.10
23490
234900-23490
211410
2a - (a + 3) I need Answers
Answers
Answer:
a-3
Step-by-step explanation:
[tex]2a-(a+3)\\= 2a - a - 3\\= a - 3[/tex]
Answer:
a-3
Step-by-step explanation:
2a - (a+3)
removing bracket
2a -a-3
a-3
final answer
a-3Stephanie read 45 pages from a book of 120 pages. Which of the following equations shows the number of pages (n) Stephanie still needs to read?
Answers
The equation of the number of pages Stephanie still needs to read will be n + 45 = 120. Then the correct option is A.
The missing options are given below.
A. n + 45 = 120
B. n - 45 = 120
C. 45ⁿ = 120
D. n/45 = 120
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Stephanie read 45 pages from a book of 120 pages.
Let n be the number of remaining pages.
Then the equation, we have
n + 45 = 120
Then the correct option is A.
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What are the domain and range of the function f(x)=x²-2x² -4?
Answers
Answer:
The domain is -∞, ∞
The range is -∞, -4
Step-by-step explanation:
The domain is the data in a set representing the possible real numbers for a function.
The range is the range that this function's result is likely to be in.
Polygons: Mastery lest
?
What is the distance between C(4, 5) and
D(4,-5)?
5 units
08 units
O 10 units
Answers
Answer:
10 [units].
Step-by-step explanation:
1) the x-coordinates have the same value, then
2) the required distance can be calculated as distance between '-5' and '5':
5--5=10 [units].
a) The scale of a map is 1:20 000. What distance in metres does 4cm on the map represent?
Answers
Answer:
80 000
Step-by-step explanation:
1 cm : 20 000 (The question does not state the unit of the other half)
So
4 cm : 4×20 000
4 cm : 80 000
I'm not sure about units but hope this helped and brainliest please
Answer:
80 000 meters
Step-by-step explanation:
In the map:
1 cm = 20000 m
4 cm = 4(20000) = 80 000 meters
4 cm on the map represents 80 km in reality.
Hope this helps
a)1 year into second
Answers
Answer:
31536000 seconds in a year
Step-by-step explanation:
there are 365 days in a year, 24 hours in a day, 60 minutes in an hour, and 60 seconds in each minute. you have to multiply all of them
The graph shows China’s workforce from 2000 to 2019. A graph titled Percentage of Workers in Economic Sectors in China from 2000 to 2010 has year on the x-axis and percentage of workers on the y-axis, from 0 to 60 in increments of 10. Agriculture starts at 50 percent in 2000 and then decreases gradually to 37 percent in 2010. Industry starts at 23 percent and then slowly increases to 30 percent. Services starts at 29 percent and then slowly increases to 35 percent. Based on this graph, globalization has affected China’s workforce by creating a shift toward specialization in agriculture and away from services. services and away from agriculture. industry and away from services. agriculture, services, and industry.
Answers
Based on the graph, globalization affected China's workforce by creating a shift toward specialization in: B. services and away from agriculture.
What is globalization?Globalization is a strategic process that involves the integration of various markets across the world, in order to enhance and foster the continuous buying and selling of different goods and services between them.
This ultimately implies that, globalization helps in the creation of new forms of the following systems:
TransportationCommunicationTechnologyAgricultureBased on the given graph, we can logically deduce that globalization affected China's workforce by creating a shift toward specialization in services (increased from 29% to 35%) and away from agriculture (decreased from 50% to 37%).
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Answer:
B. services away from agriculture
Step-by-step explanation:
Hi i have exams coming up soon within 4 months time what can i don't to focus more and not be easily distracted?
Answers
i would recommend setting a schedule for each day. a to do list can also help. this can help you stay on track make a list of things you need to do and have set goals for every week or month. if you're studying something you dont like, i would recommend doing pomodoros. you can find videos to follow along to.
i hope this was helpful!
find the product of
2a(a+b)
3xy(2x-3y)
Answers
Answer:
2a² + 2ab , 6x²y - 9xy²
Step-by-step explanation:
using the distributive property
a(b + c) = ab + ac
given
2a(a + b) ← multiply each term in the parenthesis by 2a
= 2a² + 2ab
given
3xy(2x - 3y) ← multiply each term in the parenthesis by 3xy
= 6x²y - 9xy²
Answer:
6x2-9x2
Step-by-step explanation:
because I don't know the explanation
1.
In AXYZ, |XZ| = 13 cm, XY = 12 cm and
ZXYZ = 90°. Find YZ if the area of the
triangle is 30 cm².
Answers
Step-by-step explanation:
I think you mean triangle XYZ. and angle XYZ.
so, the angle at Y is 90°.
that makes XZ the Hypotenuse (baseline opposite of the 90° angle) of the right-angled triangle.
so, we can actually use Pythagoras (we don't need the area of the triangle to solve) :
13² = 12² + YZ²
169 = 144 + YZ²
25 = YZ²
YZ = 5 cm
just to check - the area of this triangle is (remember, it is a right-angled triangle, so XY and YZ serve also as baseline and height) :
area = 12 × 5 / 2 = 60/2 = 30 cm²
correct, it fits.