14. The figure shows a slice of an apple pie in the shape of a sector of a circle with centre O and radius 8cm. A cut is made along AB to remove some of the crust
Given that AB = 7 cm find:
(i) AOB in radians
(ii) the maximum number of slices that can be obtained from one full pie.
(iii) the area of the shaded segment that has been removed
Answers
Step-by-step explanation:
(i) Using the law of cosines, we can find that
[tex]cos(O) = \frac{8^{2}+8^{2} - 7^{2}}{8*8*2}[/tex] ≈ 0.62, so O ≈ 0.9
(ii) Since the whole pie has 2π radians (or 360 degrees), we can divide 0.9 by 2π to get around 6.9 slices from the pie
(iii) The area of the shaded segment can be found by finding sector OAB and subtracting triangle OAB from that. Sector OAB can be found by finding the area of the pie (π*8², since 8 is the radius) and dividing that by 6.9, so we get 64π/6.9 ≈ 29. Then, the area of the triangle is √p(p-a)(p-b)(p-c), with p being the perimeter and a, b, and c being the sides. Plugging 7, 8, and 8 in, we get 25.1781 as our area, so the difference is around 3.8
Related Questions
please help(lots of pts) which table represents the increasing linear function with the greatest unit rate?
A.
x y
2 16
5 10
B.
x y
2 14
6 12
C.
x y
2 -24
5 -15
D.
x y
2 -12
6 -16
E.
x y
2 -19
6 -17
Answers
Answer:
I believe the answer is B
Step-by-step explanation:
Hope this helps :D
Pls help. I’m begging you.
Answers
Answer:
n=6
Step-by-step explanation:
Given: f(x) = 2x^2 - 2x - 4
a.explain how to create a table value for f(x) and make a table for f(x).
b. Explain how to graph using the table and graph f(x).
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I need help I would really appreciate it !!
Answers
Help needed ASAP! Please
Answers
Answer:
r =5
Step-by-step explanation:
Write the algebraic expression for... 16 less than a number n
Answers
Answer: n-16
Step-by-step explanation:
The algebraic expression for 16 less than a number n is thesame thing as subtracting 16 from n which will be represented as: n - 16.
Therefore, the algebraic expression for 16 less than a number n will be = n - 16
Which system of linear inequalities is represented by the graph?
y > x – 2 and y x + 1
y x + 1
y > x – 2 and y < x + 1
Answers
Answer:
D) y > x – 2 and y < x + 1
Step-by-step explanation:
- Graph each system of linear inequalities.
- Examine each graphed system of linear inequalities
- Match the system of linear inequalities that looks the same as the graph shown
Remember:
> and < are dashed lines
≥ and ≤ are solid lines
if y is ≥ or > , then the shaded region is above the graphed line
if y is ≤ or <, then the shaded region is below the graphed line
m = slope
b = y intercept
change the inequality sign into an equal sign to check the y intercept.
use the equation y = mx + b to check each one
Hope this helps!
Answer:
Answer:
D) y > x – 2 and y < x + 1
Step-by-step explanation:
- Graph each system of linear inequalities.
- Examine each graphed system of linear inequalities
- Match the system of linear inequalities that looks the same as the graph shown
Remember:
> and < are dashed lines
≥ and ≤ are solid lines
if y is ≥ or > , then the shaded region is above the graphed line
if y is ≤ or <, then the shaded region is below the graphed line
m = slope
b = y intercept
change the inequality sign into an equal sign to check the y intercept.
use the equation y = mx + b to check each one
Step-by-step explanation:
How much should be added to the sum of 25 1/6 and 7 2/5 to get 60?
Answers
Answer:
3.77 should be added
hope it helps.
Answer:
823/30
or 27 13/30
decimal: 27.43
Step-by-step explanation:
(25+7)+ (1/6 + 2/5)
32+ (5/30 + 12/30)
32+ 17/30
= 32 17/30
60- 32 17/30
= 1800/30 - 977/30
= 823/30
= 27 13/30
Solve the system of equations:
y = 2x
y=x2-3
A. (-1,2) and (3, 2)
B. (-2, -4) and (2, 4)
C. (-2, 1) and (2, 1)
D. (-1, -2) and (3, 6)
Answers
Answer:
D. (-1, -2) and (3, 6)
Step-by-step explanation:
y = 2x
y = x² - 3
2x = x² - 3
x² -2x - 3 = 0
(x + 1)(x - 3) = 0
x = -1 or x = 3
y = -2 or y = 6
Question 3 (4 points)
(04.01 LC)
Which of the following types of rocks are likely to disintegrate by weathering and erosion? (4 points)
a
Igneous rocks only
b
Metamorphic rocks only
c
Both igneous rocks and metamorphic rocks
d
Neither igneous rocks nor metamorphic rocks
Answers
help this is geometry
Answers
Answer:
a=corresponding sides of congruent triangles
b= by SAS condition ( ac=ce, acb=oce,oc=cb)
Function w gives the weight of a cat, in kilograms, when it is m months old.
Which statement represents the meaning of the equation w(7) = 4 in this situation?
A) The cat weighs 7 killograms when it is 4 months old.
B) The cat weighs 4 kilograms when it is 7 months old.
C)The weight of the cat has been 7 kilograms for 4 months.
D) The cat weighs 4 kilograms when it is 7 years old.
Answers
Option B) The cat weighs 4 kilograms when it is 7 months old. is correct answer.
Given that:w gives weight of cat, in kgs, when it is m months old.
To find:What does w(7) = 4 represents.
Explanation:It is already given that w gives weight in kilograms.
It outputs weight when we tell the age in months, thus, this is what we treat as input.
w(7) means weight when cat is 7 months old.
and w(7) = 4 represents that the cat weighs 4 kilogram when the age of cat is 7 months.
Thus, Option B) The cat weighs 4 kilograms when it is 7 months old. is correct answer.
Learn more about functions here:
https://brainly.com/question/24846347
The correct option is Option B) The cat weighs 4 kilograms when it is 7 months old.
The following information should be considered:
The equation is w(7) = 4.Here car weight should be 4 kilograms at the time of 7 months old. Since w denotes the weight of the cat and m denotes the months.Learn more: https://brainly.com/question/4804019?referrer=searchResults
is it one to one or onto? why?
Answers
Answer:
Step-by-step explanation:
Given quadratic function is,
f(x) = -x² - x + 1
Range of the function has been defined as (-∞, [tex]\frac{5}{4}[/tex] ]
Domain of the function is a set of all real numbers.
From the graph of this function,
At x = -3 and x = 2, value of y = -5
But for one to one functions, every x value should map to a different value of y.
Therefore, function is not one to one.
Since, every value of domain (x-value) maps the range (y-value) in the given range (-∞, [tex]\frac{5}{4}[/tex] ], function will be defined as onto.
Therefore, this function is ONTO, but NOT ONE TO ONE.
OREGON TRAIL! (pls help)
So far you have completed 816 miles
which is 54% of the trail.
Can you find about how many miles for the total trip?
Answers
ion understand this one
Answers
Answer:
114
Step-by-step explanation:
\+_+/
114 is the answer if you are confused just look at it it is the same angle
One grain of this sand approximately weighs 6 x 10^-6g.
b) How many grains of sand are there in 7200 kg of sand?
Give your answer in standard from.
Answers
Answer:
1.2×10¹² grainsStep-by-step explanation:
1 grain = 6×10⁻⁶ g
7200 kg = 7200000 g = 7.2×10⁶ g = 7.2×10⁶ ÷ 6×10⁻⁶ = (7.2÷6)×10⁶⁻ ⁽⁻⁶⁾ =1.2×10¹² grainsHow can you tell if a table represents a proportional relationship?
Answers
Answer:
from my knowledge i have made a sample here it is:
To see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportional ratios.
Step-by-step explanation:
brainliest?
Jimmy walked 5 miles east from his campsite. Then from his current location he decided to walk 3 miles south. Determine Jimmy’s Bearing From his current location to his campsite
Answers
The class has 12 girls and 16 boys. What is the ratio of total students to boys in simplest form?
Answers
Answer:
7:4 is the simplest form.
Step-by-step explanation:
total number of students is 28 and number of boys is 16 which makes the ratio 28:16
when we simplyfy it we get 7:4.
If you were to use the substitution method to solve the following system, choose the new
equation after the expression equivalent to x from the second equation is substituted into the
first equation.
2x – 3y = -29
x + 4y = 13 (6 points)
1) 2(4y + 13) – 3y = -29
2) 2(-4y + 13) – 3y = -29
3) 2x - 3(4y + 13) = -29
O4) 2x - 36-4y + 13) = -29
Answers
Answer:
Option 2
Step-by-step explanation:
We will use the substitution method, as the question asks for. The second equation (where x or y is isolated on one side) will be susbstituted as the x or y in the first equation.
2x-3y=-29
x+4y=13
let's isolate x onto one side in the second equation.
Subtract 4y from both sides
x=-4y+13
now we can substitute the expression as x in the first equation
2(-4y+13)-3y=-29
it's the 2nd option
Hope this helps!
Find the value of x in the proportion. Check your answer.
30
15
14
Х
x=0
what is x?
Answers
Answer:
Step-by-step explanation:
Which trigonometric functions have a domain of [–1, 1]?
A.) y = arcsinx and y = arccosx
B.) y = arccosx and y = arctanx
B.) y = arcsinx and y = arctanx
D.) y = arcsecx and y = arccscx
Answers
Answer:
The answer is A. y = arcsinx and y = arccosx
Step-by-step explanation:
How would I divide decimals by a whole number?
Answers
Answer:
divide the two numbers ignoring the decimal point and then place the decimal point in the quotient in the same position as in the dividend
hi can anyone plz help me with this and can you explain how you got it
Answers
Answer:
x = 62
Step-by-step explanation:
Since the 2 legs of the triangle are congruent, both 6 , then the triangle is isosceles and the base angles are congruent, that is
x = [tex]\frac{180-56}{2}[/tex] = [tex]\frac{124}{2}[/tex] = 62
ssssssssssssssssssssssssssshhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhStep-by-step explanation:
Anybody know the answers to this
Answers
Answer:
no sorry
Step-by-step explanation:
1,615×10 to the power of 2
Answers
is 0.21 greater than 0.27
Answers
Answer:
no
Step-by-step explanation:
0.27 is greater than 0.21
hope it helps
What is the equation of the given linear function? x y 0 8 1 17 2 26 -3 -19
A. f(x)=8x+9
B. f(x)=9x+8
C. f(x)=9x
D. f(x)=17x
Answers
Answer:
Step-by-step explanation:
Need help answer ASAP
Answers
Answer:
.1i01390
Step-by-step explanation:
The length, l, of the shadow cast by an object varies directly as the height, h, of the object. If k is the constant of variation, which equation represents this situation?
A.
l + h = k
B.
lh = k
C.
l = hk
D.
l = h + k
Answers
Answer:
C. l = hk
Step-by-step explanation:
the equation for direct variation is y = xk (or y/x = k) so you just replace y and x with l and h
The length of the shadow cast l represents by situation l = hk. Hence, option (C) is correct.
What is the linear relation of an equation?An equation has a linear relation if a variable from that equation varies linearly with the other variable.
for example, x is varied linearly with y then we can write
x ∝ y
x = yk where k will be the constant of variation.
Given that length, l is varies directly as the height h
Hence, l = hk will be the correct representation.
For more information about direct variation.
https://brainly.com/question/14254277
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