You are planting a vegetable garden on a plot of land that is a sector of a circle, as shown below.
You want fencing along only the curved edge of the garden.
a. Use the figure to find the length of fencing you will need.
15 ft
75°
b. How much area will be available for planting?
Answers
Answer:
(a) 19.63 ft
(b) 147.26 ft^2
Step-by-step explanation:
(a) 75/360 degrees . 2 . pi . 15 = 19.63
(b) 75/360 degrees. pi . 15^2 = 147.26
Answer:
a) 19.63 ft (2 dp)
b) 147.26 ft² (2 dp)
Step-by-step explanation:
To find the length of the curved fence, use the formula for arc length of a circle.
To find the area of the vegetable garden, use the formula for area of a sector of a circle.
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 75°r = 15 ft[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (15)\left(\dfrac{75^{\circ}}{360^{\circ}}\right)\\ & = 30 \pi \left(\dfrac{5}{24}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf ft\:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{75^{\circ}}{360^{\circ}}\right) \pi (15)^2\\& = \left(\dfrac{5}{24}\right)\pi \cdot 225\\& = \dfrac{375}{8} \pi\\& = 147.26\: \sf ft^2 \:(2\:dp)\end{aligned}[/tex]
Related Questions
Pranay's school is selling tickets to the annual talent show. On the first day of ticket sales the
school sold 9 senior citizen tickets and 10 student tickets for a total of $113. The school took in
$64 on the second day by selling 2 senior citizen tickets and 10 student tickets. What is the price
each of one senior citizen ticket and one student ticket?
Answers
Answer:
Price of senior citizen ticket = $7
Price of student ticket = $5
Step-by-step explanation:
Let:
senior citizen ticket price = astudent ticket price = bEquations formed :
9a + 10b = 1132a + 10b = 64Subtract : Equation 1 - Equation 2
9a + 10b - 2a - 10b = 113 - 647a = 49a = 7Finding b
2(7) + 10b = 6410b = 50b = 5Solution
Price of senior citizen ticket = $7Price of student ticket = $5Answer:
Senior tickets would be 7 dollars
and
Student ticket prices would be 5 dollars
Step-by-step explanation:
Determine the equation of the circle graphed below.
Answers
Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2
(h, k) = center of the circle
r = radius of the circle
Center = (2, 0)
Radius = 7
Equation: (x - 2)^2 + (y - 0)^2 = 49
Answer: (x - 2)^2 + y^2 = 49
Hope this helps!
How do I solve for 4h=57.6
Pls explain bc I don’t understand Does h = 14.4
Answers
Answer:
h = 14.4
Step-by-step explanation:
4h=57.6
Divide each side by 4
4h/4 = 57.6/4
h = 14.4
Answer:
See explanation
Step-by-step explanation:
Always divide the constant by itself and the value it equals.
1) Divide both sides by 4.
[tex]h=\frac{57.6}{4}[/tex]
2) Simplify [tex]\frac{57.6}{4}[/tex] to [tex]14.4[/tex].
h = 14.4
To check our answer,
4h = 57.6
1) Let h = 14.4
4 * 14.4 = 57.6
2) Simplify 4 × 14.4 to 57.6.
57.6 = 57.6
Susan, Frank, and Dan sent a total of 83 text messages over their cell phones during the weekend. Susan sent 7 more messages than Frank. Dan sent 4 times
as many messages as Susan. How many messages did they each send?
Number of text messages Susan sent:
Number of text messages Frank sent:
Number of text messages Dan sent:
Answers
Step-by-step explanation:
Susan message=34.66
Frank message=27.6
Dan message=28
What is the total of the new purchases Jessica made during the month?
A.
$123.09
B.
$125.00
C.
$210.30
D.
$210.52
Answers
2. If A and B are square matrices of the same order, then (A + B) (A - B) is equal to (a) A²– B² (b) A– BA – AB - B² (c) A² - B² + BA – AB (d) A² - BA +B+ AB
Answers
Correct option is C) A² - B² + BA – AB
Step-by-step explanation:
(A+B)(A−B)=A(A−B)+B(A−B).........because matrix product is distributive.
=A² + BA - AB - B²
And as matrix product is not commutative, so AB¦=¦BA
Hence option C is correct.
Watch help video
Find an expression which represents the sum of (x – 2y) and (-10x + 6y) in
simplest terms.
+
a
Answers
Answer:
-9x + 4y
Step-by-step explanation:
Adding expressions:
Like terms have same variable with same power.Combine like terms.
Here, x and (-10x) are like terms &
(-2y) and 6y are like terms
x - 2y + (-10x + 6y) = x - 2y - 10x + 6y
= x - 10x - 2y + 6y
= -9x + 4y
A cube of side 3cm contains a sphere within it.if the sphere touches each face of the cube,find the volume of the space between the cube and the sphere
Answers
Answer:
6.86cm^3
Step-by-step explanation:
In order to do this problem you must first find the volume of the cube and subtract the volume of the sphere within it.
Volume of a cube is S^3
using the given 3×3×3= 27cm^3 volume of cube
volume of a sphere is 4/3 pir^3
4/3 × pi x 1.5^3 = 14.14cm^3 volume of sphere
now simply subtract
27-14.14= 6.86 cm^3
I chose B as an answer but I’m not sure
Answers
Answer:
hy the answer is C. a car maintained constant speed
Answer:
c.A car maintained constant speed
Step-by-step explanation:
according to the graph,velociry is always in a straight line over time.
so the velocity is constant
so A car maintaned constant speed
You roll a number cube twenty times and it lands on a 3 five times. What is the
experimental probability that it ends on a 3 the next time you roll?
Answers
Answer:
Hence, a fair dice has a probability of 16 to land on any predetermined number 1 through 6. Therefore, to land on 3 the probability is 16
Step-by-step explanation:
help me out here guys
Four functions are listed below.
f(x) | (x^2-4) (x-1)
g(x) | (x+4) (x-6)
h(x) | (x^2+6)
k(x) | x (x^2-25)
Which two functions, when graphed, have the same number of x-intercepts?
A.
f(x) and g(x)
B.
g(x) and h(x)
C.
h(x) and k(x)
D.
k(x) and f(x)
Answers
f(x) can be written as (x+2)(x-2)(x-1)
by using difference of two squares to expand x^2 - 4 whch yields 3 x intercepts
similarly, k(x) can be written as
x(x+5)(x-5) which also yields 3
x intercepts (0,-5, and 5)
The altitude of an equilateral triangle is 7 units long. The length of one side of the triangle is ____ units. 7 14
Answers
The length side of equilateral triangle is 8.08 units
What is Altitude?The altitude or height of an equilateral triangle is the line segment from a vertex that is perpendicular to the opposite side.
Here, let the side of the equilateral triangle be x units
given altitude of the equilateral triangle = 7 units
we know,
Altitude = √3/2 X side
7 = √3/2 X x
x = 7 X 2 / √3
x = 14/√3
x = 8.08 units
Thus, the length side of equilateral triangle is 8.08 units.
Learn more about Altitude from:
https://brainly.com/question/18530806
#SPJ1
Find the product and simplify. (3c-5) ^2
Answers
Answer:
9c² -30c + 25
Step-by-step explanation:
Perfect square trinomial: (a - b)² = a² - 2ab + b²
(3c - 5)²
(3c)² -2(3c * 5) + 5²
9c² -2(15c) + 5²
9c² -30c + 25
Final answer: 9c² -30c + 25
Hope this helps!
Hi!
Given:
[tex](3c-5)^2[/tex]
As this is squared, we are simply multiplying the given expression by itself, like so:
[tex](3c-5)(3c-5)[/tex]
Now, we can use the Distributive Property to solve, using the FOIL Method:
[tex](3c-5)(3c-5)[/tex]
[tex]9c^2-15c-15c+25[/tex]
Combine like terms:
[tex]9c^2-30c+25[/tex]
For a similar problem, see:
https://brainly.com/question/15639394
What is the value of x in this figure?
O x=85
O x= 90
O x= 95
Answers
35° + 60° + x° = 180°
95° + x° = 180°
x° = 180° - 95°
x° = 85°
In any triangle, the sum of its interior angles measures 180º.
The coordinates of the vertices of quadrilateral HIJK are H (-2, -1), I (2, 1), J (5, 0), and K (-1, -3). Isabella states that quadrilateral HIJK is a parallelogram. Is Isabella correct? Support your answer and show all work.
Answers
Answer:
Step-by-step explanation:
Suppose you buy 3 pizzas for a party. Each pizza is cut into 8slices. Twenty slices are eaten. How many pizzas
were eaten?
Answers
Answer:
2 and a half pizzas were eaten
Step-by-step explanation:
3 pizzas divided into 8 slices is equal to 24 slices. So if 20 slices were eaten, we can do simple math to solve this
There are two ways to do this:
A. divide 20 by 8 to get 2.5
B. subtract a pizza (8 slices) from 20 to get 12. Subtract another pizza (8 more slices) to get 4. The 4 slices left are equal to another half pizza. So in total, there were 2.5 pizzas eaten
Tom volunteered 1 out of the last 12 days at the school store. Which shows the decimal form of this ratio?
Answers
Answer:
0.0833
Step-by-step explanation:
1 out of 12 can be written as a fraction 1/12
Now we convert the fraction to a decimal with division. Using long division the 12 goes outside the division symbol and 1 on the side. 12 doesn't go into 1 so we add a decimal to the answer and a 0 after the 1. 12 doesn't go into 10 so we add another 0. 12 goes into 100 8 times. 8 goes on top after 0.08 and then we finish the long division. We would have 4 remaining. Add another 0. 12 goes into 40 3 times. This is then where the division becomes repetitive. With more threes. Depending on where youryou're supposed to Round to the answer is 0.0833
which expression shows the raltinship between 1 and 2 and 6 and 3
Answers
Step-by-step explanation:
THREE SOLUTION TO PROVE ITS FALSE
1:2
Multiply by 3 on each side
1*3 : 2*3 = 3:6
This is not the same as 6:3
3 apple:6 bananas is not the same as 6 apples: 3 bananas
1:2 is equivalent to 6:12 not 6:3
because 1x6=6 2×6=12 =6:12
3)
however when we solve mathematically
1/2=6/3
1/2=2
The sides are not equa so its false
There are eleven divers on a swim team. If the team can only send four divers to a competition, how many ways can they send four?.
Answers
PLEASE HELP GIVING BRAINLIST!!!!! What is the perimeter of the shape below?
Answers
Area of the rectangle
LB92(40)3680ft²Area of trapezoid
1/2(sum of parallel sides)(Height)1/2(5+92)(40-5)1/2(97)(35)3395/21697.5ft²Total
3680-1697.51982.5ft²Solve this problem and get 15 points
Answers
d. 32.6°
explanation:
tan(×)= 0.6396
tan(x)= 0.6396/1000
tan(×)= 1599/2500
(×)= arctan (1599/2500)
(×)≈ 0.569029 or 32.6°
The diagram shows a regular pentagon.
a)
Work out the sum of the interior angles.
b)
Work out the size of one interior angle.
Answers
Answer:
a) 540° b) 108°
Step-by-step explanation:
Formula: (n-2)×180°
a) (5-2)×180°
3×180°=540°
b) 540°÷5=108°
n means nr of sides
SOMEBODY PLS HELP ME
Answers
Answer:
I would say 6m because i measured the side that is labeled 6m, and DE is also 6m.
( I hope I'm right ^^)
( I hope this helps ^^)
Select the correct answer. The graph below shows the height of a seat on a Ferris wheel as the Ferris wheel goes through its rotation. The function describing this graph is a transformation of the parent sine function, y=sin(x). Which value best describes the maximum of the transformed function?
Answers
Answer:
105 feet
Step-by-step explanation:
Got it right
Answer:
105
Step-by-step explanation:
correct
7
——
math
math geniuses pls help!!!
——
pls check other questions as well thanks,!
Answers
Answer:
The time spent by a physician with a patient
Step-by-step explanation:
Option C is the answer
find the surface area of the composite figure. 5 cm 6 cm 4 cm 20 cm 12 cm R6 cm 5 cm 4 cm
help pls fast
Answers
Answer:
644 cm^2
Step-by-step explanation:
20*5*2 = 200
6*5*2 = 60
20*6 = 120
6*8 = 48
12*4*2 = 96
6*4*2 = 48
12*6 = 72
The store opened at 8:15 a.m. and closed at 11:45 p.m. how long was the store opened?
Answers
Answer:
3 hours and 30 minutes
Step-by-step explanation:
8:15+3=11:15
11:15+30=11:45
Answer:
15 hr 30 min
Step-by-step explanation:
8:15 - 9 am = 45 min
9 am to 11 pm = 14 hours
11pm - 11:45 pm = 45 min
90 min = 1 hr 30 min
14 hr + 1 hr 30 min = 15 hr 30 min
what is the solution for x? 6(x+4)=3x-2
Answers
Step-by-Step Explanation:
= 6(x + 4) = 3x - 2
= 6 * x + 6 * 4 = 3x - 2
= 6x + 24 = 3x - 2
= 6x - 3x + 24 = -2
= 6x - 3x = -2 - 24
= 3x = -26
= x = -26/3
Therefore, x = -26/3
#81 will gove brainliest to best answer
Answers
To solve this problem, we need to factor both
⇒ numerator: [tex]x^2-4x+4[/tex]
⇒ denominator: [tex]x^2-4[/tex]
Let's factor:
⇒ [tex]x^2-4x+4=(x-2)(x-2)\\[/tex]
⇒ [tex]x^2-4=(x+2)(x-2)[/tex]
Let's put it back into the fraction:
[tex]\frac{x^2-4x+4}{x^2-4}=\frac{(x-2)(x-2)}{(x+2)(x-2)} =\frac{x-2}{x+2}*\frac{x-2}{x-2} =\frac{x-2}{x+2} *1=\frac{x-2}{x+2}[/tex]
Answer: Choice (3) or [tex]\frac{x-2}{x+2}[/tex]
Answer:
[tex]\frac{x-2}{x+2}[/tex]
Step-by-step explanation:
First, let's factor out the fraction into [tex]\frac{(x-2)^2}{(x+2)(x-2)}[/tex], now we can cancel out the [tex]x-2[/tex]. After we do that, our final answer is [tex]\frac{x-2}{x+2}[/tex].
Hope this helps! :)
DUE SOON PLEASE HELP
Kayla has some colored marbles that are the same size and shape. Use
the information below to determine which is closest to the probability
that Kayla will randomly select a marble that is NOT red, replace it, then
randomly select a marble that is yellow?
.
The probability of randomly selecting a red marble is 30%.
The probability of randomly selecting a yellow marble is 13%.
9%
26%
4%
61%
Answers
Answer:
9% sry if im wrong
Step-by-step explanation:
Kayla has some colored marbles that are the same size and shape. Use
the information below to determine which is closest to the probability
that Kayla will randomly select a marble that is not red, replace it, then
randomly select a marble that is yellow?
The probability of randomly selecting a red marble is 30%.
The probability of randomly selecting a yellow marble is 13%