Please help me with this problem, 35 points!
The four small circles are identical. The total area of the small circles is 16 pi square inches. What is area of the larger circle? Write your answer in terms of pi .
Answers
Answer:
64[tex]\pi[/tex] in²
Step-by-step explanation:
I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.
Remember,
A = [tex]\pi r^2[/tex]
And if we have 4 circles that means the area of one circle is 1/4th the total
So,
[tex]A = \frac{\pi r^2}{4}[/tex]
Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.
[tex]A = \frac{16\pi}{4} = \frac{4\pi}{1}= 4\pi[/tex]
Now lets get it back to [tex]r^2[/tex] by square rooting the 4
[tex]A = \sqrt{4}\pi = 2\pi[/tex]
The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.
This gives us a final radius of the bigger circle of 8
Therefore, the area of the bigger circle is 8²[tex]\pi[/tex] which simplifies to 64[tex]\pi[/tex]
And a final answer of
64[tex]\pi[/tex] in²
Hope this helps :)
The area of the larger circle is 64π in²
What is a circle?A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
Given that, there are 4 identical circles inside a big circle, the total area of the small circles is 16π in²
We know that,
Area = π × radius²
16π = 4π × radius²
Therefore, the radius of each circle = 2 in
Now, according to the arrangement we can say that the adding the diameter of two small circles will give the radius of the big circle,
Therefore, the radius of the big circle = 4 + 4 = 8 in
Therefore, the area of the big circle = π × 8² = 64π
Hence, the area of the larger circle is 64π in²
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Related Questions
A bakery sells 3642 pastries in 2010. The bakery sells 8422 pastries in 2015. Write a linear model that represents the number y of pastries that the bakery sells x years after 2010
Answers
Answer:
y = 936x + 3742
Step-by-step explanation:
If it is a linear model, then we should have a slope and y-intercept with the equation representing the model as;
y = mx + c
where m is the slope and c is the y-intercept
Thus, we have for the slope;
(8422-3742)/(2015-21010) = 4680/5 = 936
So the equation will be;
y = 936x + c
To get c , we can use the years after 2010 which is 2015 in this case
8422 = 936(5) + c
c = 8422- 4680
c = 3742
So the linear model is;
y = 936x + 3742
The back to back stem plot below shows the heights (in centimeters) of the players on the University of
Maryland women's basketball and field hockey teams.
Basketball
team
Field hockey
team
15
7 7 7 7 7
5
16
0 0 3 3 3 3 3 3 5 5 5 8 8 8 8
5 2 0
17
0 0 2 2 8
8 8 3
18
3 3 1 1
19
3
20
Key : 178 = 178 cm
Answers
Answer:
Im bored wanna talk?
Step-by-step explanation:
Determine if the figures below are congruent? Explain why or why not. I need it for a test please answer fast!
Answers
Answer:
Yes they should be congruent ones just at a different angle.
Step-by-step explanation:
is 10.6 greater than 10.600
Answers
Answer:
no its the same value
Step-by-step explanation:
A right triangle has leg lengths of 3.4 cm and 6.7 cm. Which answer below shows the length of the triangle’s hypotenuse rounded to the nearest tenth?
A. 8.5 cm
B. 7.5 cm
C. 5.5 cm
D. none of the above
Answers
Answer:
D
Step-by-step explanation:
The hypotenuse squared is equal to the sum of the legs squared in a right triangle.
∴ c² = a² + b² (Pythagorean’s Theorem)
c² = 3.4² + 6.7² (substitute the given values for a & b)
c² = 11.56 + 44.89 (square both right hand terms)
c² = 56.45 (add the right hand side values)
c = √56.45 (square root of both sides)
c ≈ 7.5 to the nearest tenth QED
Need help ASAP!!!Thanks
Answers
Answer:1144.2 for question 5
Step-by-step explanation:
What method of characterization does the following character description use?
Oh! But he was a tight-fisted hand at the grindstone, Scrooge! a squeezing, wrenching, grasping, scraping, clutching, covetous, old sinner! Hard and sharp as flint, from which no steel had ever struck out generous fire; secret, and self-contained, and solitary as an oyster. The cold within him froze his old features, nipped his pointed nose, shrivelled his cheek, stiffened his gait; made his eyes red, his thin lips blue; and spoke out shrewdly in his grating voice. A frosty rime was on his head, and on his eyebrows, and his wiry chin. He carried his own low temperature always about with him; he iced his office in the dog-days; and didn’t thaw it one degree at Christmas. from:
Answers
Answer:
The author is intending the character to be mean, old, and snobby. He also hates Christmas
Step-by-step explanation:
He does this by comparing the character to other objects.
20 POINTS NO CAP PLEASE HELP ME NEED RIGHT ANSWER
Answers
Answer:
3x-10+25+x+15=180
4x+30=180
4x=180-30
4x=150
x=37.5
Answer:
37.5555
Step-by-step explanation:
Find m and b in the following equations.
What do m and b represent?
a.
y= 2x +1
b. y=zx-4
Answers
Answer:
Step-
by-step explanation:
Is this correct or wrong?
Answers
Answer:
It is correct :)
Step-by-step explanation:
Sketch a 9 red counters and 4 yellow counters.How many zero pairs can you make?How many counters do you have after you remove the zero pairs? What do they represent
Answers
Answer:
36.75 and 1/6 ( 6 accounts equally distributed )
Step-by-step explanation:
Number of Red counters to be sketched = 9
Number of Yellow counters = 4
The number of Zero pairs that can be made = 36.75
When you remove the Zero pairs the number of counters you would have = 6 accounts ie. 1/6
y=6(x-7)(x+2) standard form
Answers
Answer:
y=6x^2-30x-84
Step-by-step explanation:
The momentum of an object, p, is determined by its mass, m, and its velocity, v. The formula for this relationship is shown.
P=mv
Which equation shows the formula correctly solved for v?
A. V=m/p
B. V=p/ m
C. V= p-m
D. V=pm
Answers
Answer:
b
Step-by-step explanation:
a research lab is to begin experiments with a bacteria that doubles every 4 hours. the lab starts with 200 bacteria. a. how many bacteria will be present at the end of 12th hour? b. how many bacteria will be present at the end of one day? please answer this
Answers
Answer:
A) 1600 bacteria
B) 12800 bacteria
Step-by-step explanation:
We are told that the bacteria doubles every 4 hours.
Now, if the amount of bacteria is X, it means that for 4 hours, it becomes 2X and after 8 hours it becomes 2(2X)
For 12 hours, it becomes; 2 × (2(2X))
This means that for 12 hours, it becomes 2 × (2(2X)) = 8X
A) Since the lab starts with 200 bacteria, after 12 hours, it has;
N_12 = 8 × 200.
N_12 = 1600 bacteria
B) From above, we have seen that after t hours, where t is a multiple of 4, the number of bacteria is;
N_t = [2^(¼t - 1)] × (2X)
Where X is initial amount of bacteria.
Thus, after a day which is 24 hours, we have;
N_24 = 2^(¼(24) - 1) × 2X
N_24 = 2^(5) × 2X
Where X is 200, N_24 = 32 × 2(200) = 12800 bacteria
HELP ME ASAP PLZ !!!!!!!
Answers
Answer:
0.5 × 10^7
Step-by-step explanation:
1.6 divided by 3.2 =0.5
10 to the power or 14 minus 10 to the power of 7 = 10 to the power of 7
in division you must subtract the power number
Answer: C. 5.0 * 10^6
Step-by-step explanation:
1.6(10^14)
3.2(10^7)
=
(1.6)(100000000000000)
3.2(10^7)
=
160000000000000
3.2(10^7)
=
160000000000000
(3.2)(10000000)
=
160000000000000
32000000
=5000000 =
5*10^6
are these two photos the same? or is there a difference?
Answers
Answer:
Yes on one picture it says -40 and on the other one it says -4 so there is a differemce.
Step-by-step explanation:
A local fun park charges an admission fee plus a fee for each Go-Kart ride. Admission plus five
go-kart rides is $16.25. Admission plus three rides is $12.25. What is the charge for each Go-
Kart ride?
HELPPPPPPP PLEASE
Answers
The admission price is $6 and the rides are $2 each.
⚠️ IM DESPERATE ⚠️⚠️ please help me
Answers
Answer:
B (0, 1)
Step-by-step explanation:
(I’m not 100% sure about this)
Answer:
B. (0,1)Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y = m x + b , where m is the slope and b is the y-intercept.
y = m x + b
Find the values of m and b using the form y = m x + b .
m = 1
b = 1
The slope of the line is the value of m , and the y-intercept is the value of b .
Slope: 1
y-intercept: 1
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f ( 0 ) = ( 0 ) + 1
Simplify the result.
Add 0 and 1 .
f ( 0 ) = 1 The final answer is 1 . 1
The y value at x = 0 is 1 .
y = 1
Choose 1 to substitute in for x to find the ordered pair.
Replace the variable x with 1 in the expression.
f ( 1 ) = ( 1 ) + 1
Simplify the result.
Add 1 and 1 .
f ( 1 ) = 2
The final answer is 2 . 2
The y value at x = 1 is 2 .
y = 2
Create a table of the x and y values.
x : 0,1
y: 1 ,2
Graph the line using the slope and the y-intercept, or the points.
Slope: 1
y-intercept: 1
x : 0,1
y : 1 ,2
Alex chose a pair of jeans that sells for $19.50, but today all jeans are on sale for 10% off. How much will Alex save. Explain your answer.
Answers
Answer:
He saves $1.95. Instead of paying $19.50, He pays $17.55
Step-by-step explanation:
$19.50 ×10/100 = $1.95
That is the discount of the jeans. Taking
$19.50 - $1.95 = $17.55
Neil's bank offered him a 4.95% interest rate for his mortgage. If he
purchases 3 points, what will his new rate be?
O A. 0.375%
O B. 4.575%
C. 1.75%
O D. 4.375%
Answers
Neil's new interest rate after purchasing 3 points would be 7. 95%. The closest option is B. 4.575%.
How to calculate the interest rate?To calculate the new interest rate after purchasing points, we need to know the cost of one point and the number of points purchased.
One point typically costs 1% of the mortgage amount, so three points would cost 3% of the mortgage amount. The cost of the points is usually paid upfront at closing.
Assuming Neil's mortgage amount is $100,000, the cost of 3 points would be:
3% x $100,000 = $3,000
To calculate the new interest rate, we need to add the cost of the points to the original interest rate and then recalculate it as a percentage:
New rate = Original rate + (Cost of points / Mortgage amount)
New rate = 4.95% + ($3,000 / $100,000)
New rate = 4.95% + 3%
New rate = 7.95%
So, Neil's new interest rate after purchasing 3 points would be 7. 95%. The closest option is B. 4.575%.
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what do racecar drivers like to do
Answers
They like to flip over and set their car on fire
In general, racecar drivers like to engage in activities related to speed, adrenaline, and competition both on and off the race track.
Racecar drivers have a passion for speed and competition, which extends beyond their time on the track. When not racing, many of them enjoy activities that provide an adrenaline rush, such as go-karting, motocross, or other extreme sports. Staying physically fit is crucial for their performance, so they often participate in rigorous training, including cardio workouts, strength training, and reflex drills.
Additionally, they may spend time honing their racing skills through simulators or practice sessions on race circuits. Away from the track, some drivers may have interests in classic cars, car collecting, or automobile engineering. Their lifestyle revolves around the excitement of racing and everything associated with it, both professionally and recreationally.
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------------The given question is incomplete, the complete question is:
"What do race car drivers like to do in general?"-----------------
If the vertex form of a
quadratic equation is y = (x -
7)^2-4, what are the zeros and
the coordinate of the y-
intercept? *
Answers
Answer: x = {5, 9} ; (0,45)
I need help on this one
Answers
Answer:13.7
Step-by-step explanation:
The question is asking us to build an algebraic model of this question, to do this, we need to use the slope intercept form.
Let's first identify the known data. We know that a pizza with two toppings is 9.95. In addition, we know that a topping itself is 1.25. We need to find the y intercept first in order to solve this equation, therefore we need to find how much a pizza his without the two toppings. So, we do 1.25(2)=2.5 and subtract it from 9.95. 9.95-2.5= 7.45. Now, this is our y intercept, because this will always stay the same and this is where we always start off. The slope itself however will be 1.25x, because x is the amount of toppings. So, as of now, we have constructed our equation
y=1.25x+7.45
We are looking to see how much a pizza is with 5 toppings, so we plug 5 into x
y=1.25(5)+7.45= 13.7
3. Flyn is ordering t-shirts for all 8th graders at his school: T-shirts R-Us charges
$6.25 per shirt with a one-time embroidery fee of $19. T-shirts Galore charges
$4 75 per shirt with a one-time embroidery fee of $43. Which inequality can be
used to find x, the minimum number of shirts that can be ordered so that the total
charge at T-shirts R-Us is less than the total charge at T-shirts Galore?
A. 6.25 + 19x < 4.75 + 43x
B. 6.25x + 19 < 4.75 + 43x
C. 6.25 + 19x < 4.75x + 43
D. 6.25x + 19 < 4.75x + 43
Answers
Answer:
the answer is a
Step-by-step explanation:
Simplify 123 over 3
Answers
Answer:
The answer is 41
Step-by-step explanation:
Answer: 123/3 simplified is 41 or 41/1
Step-by-step explanation:
What is the square root of 1,567?
Answers
Answer:
39.585
Step-by-step explanation:
What is the slope of this line?
−3
3/4
4
−3/4
Number graph ranging from negative 5 to 5 on both the x and y axis. A line passes through the point begin ordered pair 0 comma 2 end ordered pair and the point begin ordered pair 4 comma negative 1 end ordered pair
Answers
find the vertex f(x)=2(x+14)^2-6
Answers
Answer:
(-14,-6)
Step-by-step explanation:
Which layer of a soil profile forms first from the bedrock?
A. A horizon. B.B horizon C.C horizon D. humus
Answers
Felicia has grown five pumpkins. The first is 25.34 pounds. The second
weighs 10.23 pounds less than the first. Both the third and fourth pumpkin
are 13.2 pounds. If the combined weight of the pumpkins is 71.87 pounds,
how much does the fifth pumpkin weigh?
Answers
Answer:
5.02
Step-by-step explanation: