Answers
Step-by-step explanation:
the whole 120° sector of the circle is the sum of the white isoceles triangle (120° top angle, 2 equal sides of 4) and the shaded segment.
so, to get the area of the shaded segment, we need to calculate the area of the sector and subtract the area of the triangle.
as the area of the full circle (360°) is
pi × r²,
the area of a sector with angle theta is
theta/360 × pi×r²
simply the theta/360 part of the whole circle.
so, in our case that means
120/360 × pi×4² = 1/3 × 16pi = 16pi/3
the area of the white triangle is a bit trickier.
in general it is
baseline × height / 2
for a right-angled triangle that means
leg1 × leg2 / 2
now, if we draw the height in the main triangle, this splits the main triangle into 2 equal right-angled triangles. theta gets split in half as well (120/2 = 60°).
and the area of one of them is then
(half of main baseline) × height / 2
and we get 2 of them, so the area the main triangle is
(half of main baseline) × height
how long are the height and half of the main baseline ?
we know from trigonometry that such a right-angled triangle with theta/2 as angle at the center of the circle makes
half of main baseline = sin(theta/2)×r
height = cos(theta/2)×r
remember, in any circle larger than r = 1 we need to multiply the trigonometric functions sine and cosine by the radius to get the actual lengths.
so, the area of the main triangle is
sin(theta/2)×r × cos(theta/2)×r =
= sin(theta/2)×cos(theta/2)×r² =
= sin(60)×cos(60)×4²
and therefore, the area of the shaded segment is
16pi/3 - sin(60)×cos(60)×4² =
= 16pi/3 - sin(60)×1/2 × 16 =
= 16pi/3 - sin(60)×8 = 9.826957589... ≈ 9.8 units²
Related Questions
Juan tiene 15 años más que Antonio. Dentro 10 años, la edad de Juan será el doble que la de Antonio¿ Cuantos años tienen los dos?
Answers
Plzzz solve for x
X/3=5/4
Answers
Answer: x=3.75 or 15/4
Step-by-step explanation:
Multiply both sides by 3
3(x) / 3 = 5x3/4
x= 15/4 or 3.75
Answer:
exact form:15/4
Step-by-step explanation:
decimal form:3.75
mixed number: 3 3/4
just in case you need any different forms :)
x*4/4=3*5/4 divide both sides of equation by 4
cancel 4 with 4=x
multiply 3 and 5 =15/4
On sports day at Lakewood middle school, gold, silver, and bronze medals were awarded to the top three finishers in each event Miniature replicas of the medals were sold as souvenirs in booths around the field. For $26, attendees could purchase a package containing 5 gold, 4 silver, and 2 bronze replicas, or one containing 4 gold, 4 silver, and 4 bronze replicas, or one that had 3 gold, 4 silver, and 6 bronze replicas. Which system of equations may be used to find the price, in dollars, of each type of replica?
Answers
Answer:
[tex]5G + 4S + 2B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
[tex]3G + 4S + 6B = 26[/tex]
Step-by-step explanation:
Given
Represent Gold with G, Silver with S and Bronze with B
Required
Determine the system of equations
The packages are represented as:
The first: 5G + 4S + 2B
The second: 4G + 4S + 4B
The third: 3G + 4S + 6B
Each of the package costs $26.
So, we have:
[tex]5G + 4S + 2B = 26[/tex] -- (1)
[tex]4G + 4S + 4B = 26[/tex] -- (2)
[tex]3G + 4S + 6B = 26[/tex] -- (3)
Divide both sides of (2) by 2
[tex]4G + 4S + 4B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
So, the system of equations are:
[tex]5G + 4S + 2B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
[tex]3G + 4S + 6B = 26[/tex]
Uh Expanded form pls? 4.02 x 10^5
Answers
Answer:
4.02 x 10 x 10 x 10 x 10 x 10
Step-by-step explanation:
The part that needs expanding is the exponent. Since it is to the power of 5 there needs to be 5 written out 10's, all multiplied.
4.02 x 10 x 10 x 10 x 10 x 10
Answer:
the answer in expanded form is 402000
the problem in expanded form is 4.02 x 10 x 10 x 10 x 10 = above
Step-by-step explanation:
pls leave a thank you trynna rank up
if 20(mod 9) is equivalent to y(mod 6) find y
Answers
Answer:
First, reduce 20(mod 9) to its simplest form in mod 9; 9 x 2 + 2 = 2(mod 9)
If 2(mod 9) y(mod 6), then y = 2 by comparism
Hope it helped!!!
The ratio of petunias to geraniums in the green house was 15 to 2. The combined number of of petunias and geraniums was 1020. How many geraniums were in the green house
Answers
Answer:
136
Step-by-step explanation:
divide 1020 by 15 = 68. 68 x 2 is 136
Answer the question provided in the picture below.
Answers
Answer: see the explanation
Step-by-step explanation:The perimeter is the distance around the outside of a shape. Perimeter is measured in units (e.g., cm). The area is the amount of space the inside of the shape takes up. Area is measured in square units (e.g., cm2).
Find the value of 5(a +c) when a = 4 and c = 9.
answer quick
Answers
Answer:
Your answer is 65
Want more answer then follow me, like and MARK MY ANSWER AS BRAINLIST ANSWER.
I need that urgently.
How is this equation wrong?? I’m giving brainlest
Answers
Answer:
It isn't?
Step-by-step explanation:
Step 1:
x + 8y = 21
x + 8y - 8y = 21 - 8y
x = -8y + 21
Step 2:
(-8y + 21) + 8y = 21
-8y + 21 + 8y = 21
21 = 21
MATH HOMEWORK! 20 points
Answers
Answer:
×=-1 or x=2/3
Step-by-step explanation:
yeah yeah yeah
Answer:
x=-1 , x=2/3
Step-by-step explanation:
x=-b+/- sqr root b^2-4ac/2a
x=-1+/ sqr root 1^2-4(3)(-2)/2(3)
x=-1+/- sqr root 25/6
Split into two outcomes
x=-1+5/6
x=2/3
x=-1-5/6
x=-1
Portland, OR is 180 miles away from Seattle, WA. If it takes a driver 3 hours to drive from Portland to Seattle, what is the driver's average rate of speed? ill mark brainliest please help this is my final grade
Answers
Answer:
60km/h
Step-by-step explanation:
4 times the sum of 3 and x can the answer be 4x plus 3 ?
Answers
Answer:
4x + 3
Step-by-step explanation:
Since you can't add variables and numbers, just switch up the operations for each number.
Basically,
4(3+x)
4 times x = 4x
4x + 3
Answer:
The answer would be 4(3x).
Step-by-step explanation:
4 times: 4(_)
The sum of 3 and x: 3x
4(_)+3x = 4(3x).
Determine if the expression 10b^2 + b^3/6+ b^5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answers
Yes it is a polynomial, Degree: 5, Type: Trinomial
Hope this helps!
Answer:poly of 5
Step-by-step explanation:
mono
if i get the right answer i will give brainlist
Which point on the scatter plot is an outlier?
Point A
Point B
Point C
Point D
Answers
Answer:
Point D
Step-by-step explanation:
PLS give me brainliest
Answer:
D, I would love to be given brainliest look i have an explanation
Step-by-step explanation:
An outlier is a number that seems for the data. The outlier is usually to far fro the data.
Find the missing angle.
20°
80°
Answers
Answer:
40
Step-by-step explanation:
20, 40,80 is a 2 xdregre angle
8/9i+12=2/9i+34 (solve for a)
Answers
Answer: I=33, O and when you said solve for a I don’t see a, I see i and that all...if you know what I mean
Step-by-step explanation: hope this help
I NEED THIS DONE ASAP PLS-
ok so i completely forgot how to do long division, and my hand writing sucks ik, sooo i need help pls! q-q
I SWEAR I WILL GIVE THE BRAINLY CROWN THINGY!! (and 20 points)
Answers
Answer:
you wrote that wrong cause ur answer is 0.01225490196
Step-by-step explanation:
Answer:
The answer is 321.6
Step-by-step explanation:
We have to go step by step when we are solving this.
Lets think of it like this
Does 25 go into 8? No! So lets put a 0 on the top (I see you already did that so good start)
Does 25 go into 80? Yes! How many times though? 3 times; So lets put a 3 on the top (Our top should look like 03) Since 25 goes into 80 3 times we need to multiply 25 and 3.
25x3= 75 -> Subtract that 75 from 80
Now we have a remainder of 5. We are going to bring down the 4 so it can be a complete number, and now it would be 54.
Does 25 go into 54? Yes! How many times? 2 times; So lets put a 2 on the top (Our top should look like 032) Since 25 goes into 54 2 times we have to multiply 25 and 2.
25x2=50 -> subtract that 50 from 54 -> 54-50=4
Now we have a remainder of 4. Bring down the last number, 0 and now we should be with 40.
Does 25 go into 40? Yes! How many times? 1 time; therefore we will just be subtracting 25 from 40. (our top should look like 0321)
40-25= 15 -> we have a remainder of 15. 25 can't go into 15 because 15 is too small. Therefore we are going to have to make a decimal. So on the top add a decimal after 1 and bring down an invisible 0. (Our top looks like this 0321.)
Does 25 go into 150? Yes! How many times? 6 times; so lets multiply 25 and 6 and then subtract that from our 150 that is down there.
25*6= 150
150-150= 0
THAT MEANSSSSS..... our answer is 321.6! P.S yes drop that 0!
Hopefully this helped
Solve the following proportions 6.5/40.3=m/12.4
Answers
Answer:
m = 2
Step-by-step explanation:
cross multiply to get:
40.3m = 6.5(12.4)
40.3m = 80.6
m = 80.6/40.3
m = 2
Select the pair of terms that are NOT like terms. a) 3x2 , 3x3 b) -7xy, -9yx c) 8b, -0.5b d) -p2q2 , (pq)2
Answers
Answer:
b), c), d)
Step-by-step explanation:
Like terms are terms that have same variables with same powers.
a)
[tex]3x^2,3x^3[/tex] have same variable [tex]x[/tex] with different powers.
So, [tex]3x^2,3x^3[/tex] are not like terms.
b) [tex]-7xy,-9yx[/tex]
Power of [tex]x[/tex] in each of the terms = 1
Power of [tex]y[/tex] in each of the terms = 1
[tex]-7xy,-9yx[/tex] are terms that have same variables [tex]\{x,y\}[/tex] with same powers.
So, [tex]-7xy,-9yx[/tex] are like terms.
c) [tex]8b,-0.5b[/tex]
Power of [tex]b[/tex] in each of the terms = 1
[tex]8b,-0.5b[/tex] are terms that have same variable [tex]b[/tex] with same power.
So, [tex]8b,-0.5b[/tex] are like terms.
d) [tex]-p^2q^2,(pq)^2=p^2q^2[/tex]
Power of [tex]p[/tex] in each of the terms = 1
Power of [tex]q[/tex] in each of the terms = 1
[tex]-p^2q^2,(pq)^2[/tex] are terms that have same variables [tex]\{p,q\}[/tex]with same powers.
So, [tex]-p^2q^2,(pq)^2[/tex] are like terms
Jesse made a list of chores he needed to complete before his father came home from work and he showed the time it would take him to complete each chore.
If Jesse's father is expected home at 6:10 p.m., what is the latest time Jesse could begin his chores?
A. 3;45 p.m.
B. 3:55 p.m.
C. 4:05 p.m.
D. 4:15 p.m.
Answers
Answer:
3:55 pm
Step-by-step explanation:
Lets add all the time duration of each chore to know the overall time taken to complete all the chores .
Total time taken to finish the chores :-
5 + 25 + 30 + 60 + 15 = 135 mins or 2hr 15 min
If Jesse's father is expected to come at 6:10 pm , the exact time he should begin his chores is :-
6:10 - 2:15 = 3:55 pm
It takes a landscaper 75 minutes to plant a tree. He spent a total of 450 minutes planting trees
one day. Using t to represent the number of trees he planted, which equation can be used to
represent this situation? How many trees did the landscaper plant that day
Answers
Answer:
450 divided by 75 = t
he plated 6 trees
Step-by-step explanation:
Answer: 75t = 450 ; 6 trees
Step-by-step explanation:
To get t by itself, we have to divide 75t by 75. 75t ÷ 75 = t
You also divide the other side by 75 to keep the sides equal. 450 ÷ 75 = 6 trees
I am not a professional, simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
find the value of X
Answers
please help i’ll give brainliest if you give a correct answer and show your work!
Answers
Answer:
as the cycle continues, you will always get 50 as the answer, since you are dividing both the numerator and the denominator with 10 in each expression. In other words, the 10:00 you divide the numerator which cancels out with the 10 you divide the denominator with. So the answer will always be 50 in each next expression.
Step-by-step explanation:
(I) 45÷90= 4500/90 = 50
(ii) 450÷9= 450/9 =50
(iii) 45÷0.9 = 45/0.9=50
(iv) 4.5 ÷ 0.09 = 45/0.09
starting with (I) 4500÷90 = 4500/90 =50
you divide the numerator and the denominator by 10 to get ; (ii) 450÷9 = 450/9 = 50
as the cycle continues you will always get 50 as the answer since you are dividing both the numerator and the denominator with 10 in each expression. In other words, the 10:00 you divide the numerator with cancels out with the 10 you divide the denominator with. So the answer will always be 50.
15 POINTS!!
answer the question in the picture
Answers
Answer:
10, 0, 2.
Step-by-step explanation:
It means that the number is greater than -3.
So, 10, 0, 2, are all greater than -3, and all the other numbers are smaller. So 10, 0, 2 are the numbers that are part of the solution for x>-3.
Answer:
10(a), 0(c), 2(d)
There is a sale on Blu-rays in a local shop – 20% off selected items. Your favorite Blu-ray before the sale cost $18. How much will you save? How much will you pay?
Answers
Answer:
save $3.6, pay $14.4
Step-by-step explanation:
A cd costs $18
If there is a 20% discount, you only have to pay 80% of the original price.
This means you only have to pay (0.80 x $18=) $14.4 dollars, which means you saved ($18 - $14.4=) $3.6.
Or you could just do $18 x 0.20 = $3.6
1×2×3×4×5×6×7×8×9×10=
Answers
Answer:
just use a calc
Step-by-step explanation:
1. Which of the points below
is a solution to the system:
y = 3x + 2 and y = 5x - 6?
A. (3, 11)
B. (4, 14)
C. (2, 4)
D. (18, 60)
Answers
Answer:
B
Step-by-step explanation:
I found this out my pluging in the points from B into the two each equation
[tex]14 = 3(4) + 2[/tex]
[tex]14 = 5(4) - 6[/tex]
Hope this helped
Uri has 22 same-sized circles that are divided into different numbers of equal-sized parts. He shades 1/5 of the first circle. The second circle has three times as many parts as the first circle. Uri shades an equivalent fraction of the second circle. What fraction of the second circle does Uri shade?
Answers
Answer:
The fraction of the second circle does Uri shade = [tex]\frac{1}{15}[/tex]
Step-by-step explanation:
As given,
Total number of same sized circle = 22
In first circle :
He shades [tex]\frac{1}{5}[/tex] of the first circle.
⇒ He divide the first circle in 5 parts and shaded 1 part.
Now,
The second circle has three times as many parts as the first circle.
⇒Total parts of second circle = 3 × 5 = 15
Now,
Given that Uri shades an equivalent fraction of the second circle.
⇒Uri shade second circle = [tex]\frac{1}{15}[/tex]
∴ we get
The fraction of the second circle does Uri shade = [tex]\frac{1}{15}[/tex]
Please help I need it ASAP!!
Answers
Answer:
5+z=190....././......
What should you write as the answer to a
question that has no solution?
Answers
Answer:
If you are talking about a equation and if the equation has no solution suppose the variable is x and the answer is x=2x that has no solution then you just write x = no solution or x has no solution.