Given circle O lies perfectly within square ABCD. If side BC = 6.84, then what is the area of the orange region?
Answers
What we get to know by looking at picture :
There are two figures: 1. square 2. circle inside it touching all square's wall.As O is center of circle (given) ∴ OP is radius of circleAs the sides are of square , therefore AB = BC = DC = AD[tex] \\ \\\\ [/tex]
To find :
Area of orange region[tex] \\ \\ \\ [/tex]
Given:
O is the center of the circle.ABCD is squareLength of BC is equal to 6.84.[tex] \\ \\ \\ [/tex]
Concept:
So as we can orange doesn't lies inside circle. And the wall of circle touches all four sides of circle. So first we have to find area of circle and then Area of square. And then we will subtract the ares. The result will be Area of orange part.
[tex] \\\\ \\ [/tex]
Solution:[tex] \\ \\\\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of circle: }}}[/tex]
[tex] \\ [/tex]
To find area of circle we need radius of it i.e Length of OP.
As BC = AB
∴AB = 6.84
As O is the center of square ∴it's center of circle too
Therefore:
AB = 2 OP6.84 = 2 OPOP = 6.84/2OP = 684/2 × 10OP = 342/10OP = 3.42[tex] \\\\ [/tex]
Now Let's find area :
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~circle = \pi {r}^{2} }[/tex]
here :
r is the radius of circle.[tex] \\ [/tex]
[tex]: \implies\sf Area~of~circle = \pi {r}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times11.7\\\\\\: \implies\sf Area~of~circle = \dfrac{257.4}{7} \\ \\ \\ : \implies \boxed{ \orange{\tt{ Area~of~circle = 36.6 \{approx \}}}} \bf \dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of square: }}}[/tex]
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~square = {side}^{2} }[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area~of~square = {side}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84} \times 6.84 \\ \\ \\ : \implies \boxed{\tt{ \orange{Area~of~square = 46.8 \{aprox \}}}}\bf\dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of orange \: part: }}}[/tex]
[tex] \\ [/tex]
[tex] \star\sf \boxed{ \rm Area_{(orange \: part)} = Area_{(square)} - Area_{(circle)}}[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area_{(orange \: part)} = 46.8 - 36.6 \\ \\ \\ : \implies \boxed{ \blue{\tt{Area_{(orange \: part)} = 10.2}}}\bf\dag[/tex]
Related Questions
Find the surface area and the volume of the cylinder below.
Answers
Answer:
70
Step-by-step explanation:
10x7=70. basically, bxh base 10 height 7
Volume is 549.78cm^3
i need help please thanks
I will give brainlessly
Answers
~Answer~
_____________________________________
1. yes ±4
2. no, it's between 9 and 4
3. no, it's between 25 and 9
4. yes ±7
5. yes ±11
6. no, it's between 81 and 64
~Step-by-step explanation~
_____________________________________
ok I'll walk you through this
1. x²=16
x = ±4 because (-4)(-4) is 16 and (4)(4) is also 16
4. x²=49
x=±7 because (-7)(-7)=49 and (7)(7) is also 49
5. x²=121
x=±11 because (-11)(-11)=121 and (11)(11)=121.
_____________________________________
Hope this helps and have a good day!
P.S. Brainliest :)
Keller has $15 from babysitting. He spends $3 on a cat toy and
$3 on markers.
Match the model to the correct equation showing how much
money Keller has left.
$15
15 = m +3+3
15 + 6 = m
15 - 3 - 3 m
3+3+15 m
Subre
Answers
Answer:
c.
Step-by-step explanation:
15-3-3=9...........
Bridget can type 2400 words in 40 minutes.
Krutika can type 2750 in 50 minutes.
Jim can type 3500 words in 70 minutes.
Who types at the fastest rate of words per minute?
Answers
Answer:
bridget types at the fastest rate as he can type 60 words per minute
NEED HELP PLEASE ANSWER ASAP! (43)
Answers
Answer:
43. (2) $2.00
Step-by-step explanation:
Question 43
Let cheese pizza be c and mushroom pizza be m3c + 4m = 12.503c + 2m = 8.50Subtract Equation 2 from Equation 1.
3c + 4m - 3c - 2m = 12.50 - 8.502m = 4.00m = $2.00(2) $2.00Answer:
(2) $2.00
Step-by-step explanation:
Jack's order
3 slices of cheese pizza and 4 slices of mushroom pizza = $12.50
Grace's order
3 slices of cheese pizza and 2 slices of mushroom pizza = $8.50
The difference between the two orders is 2 slices of mushroom pizza.
The difference between the cost of the two orders is:
$12.50 - $8.50 = $4.00
Therefore, 2 slices of mushroom pizza costs $4.00
So the cost of 1 slice of mushroom pizza is:
$4.00 ÷ 2 = $2.00
Please help with my math
Answers
[tex]7 \times {10}^{ - 3} [/tex]
Hopefully you got what I meant, this is easy.
C. A store window has a perimeter of 18 feet. The width
is 6 feet. Find the length and the area.
211 +18).
Answers
The length is 3
The area is 18
I'm in 7th grade and am doing high school math! Help!
Answers
Answer:
Step-by-step explanation:
(x - 5)(x + 2) = 0
x - 5 = 0
x = 5
x + 2 = 0
x = -2
x = 5, -2
The height of a burning candle can be modeled by a linear function.
Candle A has an initial height of 201 millimeters, and its height
decreases to 177 millimeters after 4 hours of burning. The height, h,
in millimeters, of Candle B can be modeled by the function
h = 290-5t, where t is the time in hours. Which of the following
statements are true? Select all that apply.
the initial
Answers
Answer:
below
Step-by-step explanation:
• We know that the initial height of Candle A is 201 millimeters and of Candle B is 290 millimeters which means the first statement is not true.
• To find the rate at which the Candle A is decreasing, we simply have to divide 201 - 177 with 4.
24 / 4 = 6
As we can see Candle A is decreasing at a faster rate of 6 than the rate of decreasing of Candle B which is 5. This means that second statement is true.
• To find out after how many hours will the Candle B burn out we simply have to divide the initial value with the rate of change which is 5.
290 / 5 = 58
Candle B will burn out after 58 hours. This statement is true.
• We simply have to multiply the rate of change with 10 and after that subtract the value that we get from the initial value of Candle A.
10 x 6 = 60
201 - 60 = 141
After 10 hours the height of Candle a will be 141 millimeters. This statement is true.
• We know that Candle A is burning out at a faster rate and that the Candle B was higher at start which means that
Candle A will burn out before Candle B. This statement is true.
Determine the next two terms in the arithmetic sequence.
5, 11, 17, 23,
The sequence is add 6 so the answer is 29 and 35
Answers
Answer:
Next two will be 41, 47
Step-by-step explanation:
5+6= 11
11+6= 17
17+6= 23
23+6= 29
29+6= 35
35+6= 41
41+6= 47
Answer:
29 and 39
Step-by-step explanation:
[tex]10/7 + 2/20 + 7-4[/tex]
Answers
[tex]\dfrac{10} 7 + \dfrac 2{20} +7 - 4\\\\\\=\dfrac{20(10)+7(2)}{140}+3\\\\\\=\dfrac{200+14+140(3)}{140}\\\\\\=\dfrac{634}{140}\\\\\\=\dfrac{317}{70}[/tex]
-6-5 (subtracting integers))
Answers
Just adding both the numericals because they both have same sign that is negative
-6-5
-11 answer
Answer:
-11
Step-by-step explanation:
Change the minus sign to addition
6 + 5
= 11
= -11
it is negative 11 because since the signs are the same in front of the 2 numbers (negative sign) they both add together and keep the negative in front of it
Answer = -11
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
It’s a Pythagorean theorem problem, so you add together the squares of each leg to get the square of the hypotenuse. In this case you have to do it backwards by subtracting one leg squared from the hypotenuse squared
A fair coin is flipped 120 times. Estimate the expected number of ‘heads’.
Answers
Answer:
76.47
How I did it(using a specific range)
(n, 54, 66 (120 C)) 2¹²⁰ = 0.76 × 100 ≈ 76.47
Kellie bought 8 towels and spent $39.60.Each towel costs the same amount.
Part B
What is the price, in dollars, of 11 towel?
Answers
Answer: $54.45
Step-by-step explanation:
First, we will find the price of one towel.
-> We will divide the cost by the towels bought.
$39.60 / 8 = $4.95
Now, we can find the price of 11 towels.
-> We will multiply the cost of one towel by 11 to find the total cost.
$4.95 * 11 = $54.45
Answer:
$54.45
Step-by-step explanation:
Given:
Number of towels = 8
Money spent on towels = $39.60
To Find:
What is the price, in dollars, of 11 towel?
Solve:
Since, each towels cost the same amount then we can divide the cost by number of towels.
39.60/8 = 4.95
Thus, Each towel costs $4.95
Then we are trying to find the price in dollars of 11 towels.
Knowing that 1 towels cost $4.95 then 11 towels:
4.95 × 11 = $54.45
Kavinsky
What are the solutions of the equation x^4+3x^2+2=0? Use u substitution to solve.
Answers
Answer:
Option BStep-by-step explanation:
Solve the equation in steps below
[tex]x^4+3x^2+2=0[/tex][tex]x^4+x^2+2x^2+2=0[/tex][tex]x^2(x^2+1)+2(x^2+1)=0[/tex][tex](x^2+2)(x^2+1) = 0[/tex][tex]x^2+2=0[/tex] or [tex]x^2+1=0[/tex][tex]x^2=-2[/tex] or [tex]x^2=-1[/tex][tex]x=\sqrt{-2}[/tex] or [tex]x=\sqrt{-1}[/tex][tex]x=\pm\ i\sqrt{2}[/tex] or [tex]x=\pm\ i[/tex]Correct choice is B
From her eye, which stands 1.69 meters above the ground, Sadie measures the angle
of elevation to the top of a prominent skyscraper to be 36º. If she is standing at a
horizontal distance of 275 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary.
Answers
The height of the skyscraper is 201.5 meters, if the angle of elevation to the top of a prominent skyscraper to be 36º
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Angle of elevation = 36 degree
Horizontal distance of 275 meters from the base of the skyscraper
From the tan ratio:
tan36 = x/275
x = 275(tan36)
x = 199.79 meters
The height of the skyscraper = 199.79+ 1.69 = 201.48 ≈ 201.5 meters
Thus, the height of the skyscraper is 201.5 meters if the angle of elevation to the top of a prominent skyscraper to be 36º
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Answer:I just got it wrong the answer is 201.49
Step-by-step explanation:
What is the surface area of the prism in square inches? A prism is made up of 3 rectangles and 2 triangles. A rectangle has a base of 14 inches and height of 8 inches. A rectangle has a base of 14 inches and height of 5 inches. A rectangle has a base of 14 inches and height of 5 inches. 2 triangles have a base of 8 inches and height of 3 inches. 60 square inches 168 square inches 276 square inches 304 square inches.
Answers
Answer:
c: 275
Step-by-step explanation:
Complete the recursive formula of f (n)
Answers
The value of the given function will be written as:-
a) f(1)= 12
b) [tex]f(n-1)= -48(\dfrac{-1}{4})^{n-1}[/tex]
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The given function is :-
[tex]f(n)= -48(\dfrac{-1}{4} ) ^{n}[/tex]
So the value of the given function f(1) will be:-
[tex]f(1)= -48(\dfrac{-1}{4} ) ^{1}=12[/tex]
The value of the function f(n-1) will be:-
[tex]f(n-1)= -48(\dfrac{-1}{4})^{n-1}[/tex]
To know more about functions follow
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The length of time it takes a worker to assemble a large product is assumed to be normally distributed. a random sample of 25 workers a were selected, and their times to assemble the product were recorded. the mean and variance for this sample were 3 and 0.5 hours, respectively.
the 90 percent confidence interval for the mean length of time (in hours) it takes a worker to assemble the product _____ hours to ______ hours
Answers
Using the t-distribution, it is found that the 90% confidence interval is of 2.71 hours to 3.29 hours.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 25 - 1 = 24 df, is t = 2.0639.
The other parameters are given as follows:
[tex]\overline{x} = 3, s = \sqrt{0.5} = 0.707, n = 25[/tex]
Hence the bounds of the interval are given as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3 - 2.0639\frac{0.707}{\sqrt{25}} = 2.71[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3 + 2.0639\frac{0.707}{\sqrt{25}} = 3.29[/tex]
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Which one 3, 4, 6, or 7
Answers
Answer:
i think that it is 6
Step-by-step explanation:
hope this helps
Please give me Brainlist
For a charity initiative, 420 t-shirts were made; in the morning 1/3 of the t-shirts is sold and in the afternoon 4/7 of the remaining ones. How many shirts are left to sell at the end of the day?
Answers
1/3 * 420 = amount of t-shirts sold in the morning
1/3 * 420 = 420/3 = 140 t-shirts
140 t-shirts were sold, so remaining is 420 - 140
420 - 140 = 280 remaining t-shirts
4/7 * 280 = amount of t-shirts sold in the afternoon
4/7 * 280 = (280/7) * 4 = 40 * 4 = 160 t-shirts
160 t-shirts were sold, so remaining is 280 - 160
the remaining t-shirts = 120 t-shirts
120 t-shirts are left to sell at the end of the day
+) First, simplify the fraction.
180
?
t
4
m
Answers
Answer:
hope this will help you
[tex] \frac{180}{t} = \frac{?}{4} \\ t = 180 \times 4 \\ t = 720[/tex]
use the dots for one and two. what is the difference between the ranges
a. 20 points
b. 5 points
c. 10 points
d. 35 points
Answers
Answer:
a. 20 points
Step-by-step explanation:
Range = Largest given value - Smallest given value.
Identifying the range of test 1
Looking at the dot plot the lowest test grade appears to be 50 while the highest is 90.
So range of test 1 = 90 - 50 = 40
Identifying the range of test 2
Looking at the plot the lowest test grade appears to be 40 while the highest appears to be 100
So range = 100 - 40 = 60
Identifying the differences between the ranges
Test 1 range : 40
Test 2 range : 60
Difference between the two : 60 - 40 = 20 points
Math hw 2
Probability Distributions
pls help me with my homework!!
thanks,
Answers
In the given question, to approach this, we should have a little understanding of what is a random variable. The random variable here is the distance travelled by the tee shots in a golf.
What is a Random Variable?A random variable is a numerical description of the outcome of a statistical experiment. A random variable that may assume only a finite number or an infinite sequence of values is said to be discrete; one that may assume any value in some interval on the real number line is said to be continuous.
We are given two scenarios in which we are to identify the random variable here.
The number of hits for the players of a baseball teamThe distance travelled by the tee shots in a golfIn the above scenarios, the random variable here is the distance travelled by the tee shots in a golf. The reason is that we can never give an exact value the distance and would lead to an assumption of a finite number of value or an infinite sequence of values to determine this.
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Can someone help me with the steps to create the formula? It involves quadratics
Answers
The formula of the quadratic function passing through the points (-2,0), (8,0) and (2, -24) is f(x) = x² - 6x - 16
How to create the formula?The points are given as:
(-2,0) , (8,0) and (2, -24)
The points (-2,0) and (8,0) are the zeros of the function.
So, we have:
f(x) = a(x + 2)(x -8)
Substitute (2, -24) in the above equation
-24 = a(2 + 2)(2 -8)
Evaluate the sum and the difference
-24 = a(4)(-6)
Divide both sides by -24
a = 1
Substitute a = 1 in f(x) = a(x + 2)(x -8)
f(x) = (x + 2)(x -8)
Expand
f(x) = x² + 2x - 8x - 16
Evaluate the like terms
f(x) = x² - 6x - 16
Hence, the formula of the quadratic function is f(x) = x² - 6x - 16
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PLEASE HELP ASAP!! DUE BY THE END OF THE NIGHT (LOOK AT PICTURE)
Answers
Simplify 12.4 and 12.39
Answers
Answer:
12.4 and 12.39 = 4.836x12
Step-by-step explanation:
5 The diagram shows three identical shapes. į of
shape A is shaded and of shape C is shaded.
What fraction of shape B is shaded? ......
Answers
Answer:
7/24
Step-by-step explanation:
The total amount of unshaded area of shape B is the sum of the areas of the unshaded regions of shapes A and B.
Unshaded area in A: 1 - 2/3 = 1/3
Unshaded area in C: 1 - 5/8 = 3/8
Sum of unshaded areas of A and B: 1/3 + 3/8 = 8/24 + 9/24 = 17/24
Shaded area of B: 1 - 17/24 = 24/24 - 17/24 = 7/24
A savings account offers 0.8% interest compounded bimonthly. If Bob deposited $300 into this account, how much interest will he earn after 10 years?
Answers
Answer:
$288
Step-by-step explanation:
We first need to find what 0.8% of 300 makes and to do that we multiply 300 with 0.8 and divide that by 100
300*(0.8)/100 = 2.4 this is the monthly interest
Now we need to find how much it'd be after 10 years
There are 10*12 = 120 months in 10 years
120*(2.4) = 288 is the interest Bob will earn after 10 years
