A sprinkler rotates through an angle of 115° spraying water outward for a distance of 12 ft. find the exact area watered, then round the result to the nearest tenth of a square foot.
Answers
Therefore the radius of the circular section is 12 ft as shown in the diagram below.
The total circle occupies 360°. Therefore the area watered is
A = (115/360)*π*(12 ft)²
= 144.513 ft²
Answer: 144.5 ft (nearest tenth)
Related Questions
evaluate a/z+bw^2 for a=21 b=3 w=6 z=7
Answers
(6)^2 = 36
3+3(36) = 111
I REALLY NEED THIS ONE IT'S MY LAST ONE.
Verify the identity. Justify each step.
please help and show your work.
Answers
[tex]\bf \cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}-\frac{cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}+\frac{cos(\theta )}{sin(\theta )}}\implies \cfrac{\frac{1}{cos(\theta )}}{\frac{1-cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1+cos(\theta )}{sin(\theta )}} \\\\\\ \cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1-cos(\theta )}-\cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1+cos(\theta )}[/tex]
[tex]\bf \cfrac{sin(\theta )}{cos(\theta )[1-cos(\theta )]}-\cfrac{sin(\theta )}{cos(\theta )[1+cos(\theta )]} \\\\\\ \cfrac{sin(\theta )[1+cos(\theta )]~-~sin(\theta )[1-cos(\theta )]}{cos(\theta )[1+cos(\theta )][1-cos(\theta )]} \\\\\\ \textit{notice that }[1+cos(\theta )][1-cos(\theta )]\textit{ is a difference of squares}[/tex]
[tex]\bf \cfrac{\underline{sin(\theta )}+sin(\theta )cos(\theta )\underline{-sin(\theta )}+sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]} \\\\\\ \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]}\\\\ -------------------------------\\\\ \textit{recall that }sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\qquad thus\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[sin^2(\theta )]}\implies \cfrac{2\underline{sin(\theta )cos(\theta )}}{\underline{cos(\theta )sin(\theta )} sin(\theta )}\implies \cfrac{2}{sin(\theta )} \\\\\\ 2\cdot \cfrac{1}{sin(\theta )}\implies 2\cdot csc(\theta )\implies 2csc(\theta )[/tex]
What is the abbreviation for SI unit of mass
Answers
This is probably not right but I tried.
Good Luck!
Kg I think I did this last year sk
What is the algebraic expression for the following word phrase: the quotient of j and 8
A.j-8
B.j+8
C.j
-
8
D.8j
Answers
[tex] \frac{j}{8} [/tex]
This is the correct algebraic expression for the quotient of j and 8. Quotient is just a fancy term for the answer to a division problem.
Answer:
[tex]\frac{j}{8}[/tex]
Step-by-step explanation:
the quotient of j and 8
We need to write the given word phrase in algebraic expression
Algebraic expression contains terms with numbers and variables with operators in between.
In the given word phrase , 'j' is the variable
quotient occurs only on division . so we divide 'j' and 8
The expression for word phrase the quotient of j and 8 is
[tex]\frac{j}{8}[/tex]
Please help with both questions thank you.
Answers
2(3) + 2(7)
6 + 14
20!
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a + 3.75b = 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
adult tickets
Answers
Answer: There are 168 adult tickets that were sold.
Step-by-step explanation:
Let the number of adult tickets were sold be 'a'.
Let the number of student tickets were sold be 'b'.
Since we have given that
The ticket sales for opening night totaled as
[tex]10.50a+3.75b=2071.50[/tex]
And the number of students attended = 82
so, b = 82
So, we will put the value of b in the above equation:
[tex]10.50a+3.75\times 82=2071.50\\\\10.50a+307.5=2071.50\\\\0.50a=2071.50-307.5\\\\10.50a=1764\\\\a=\dfrac{1764}{10.50}\\\\a=168[/tex]
Hence, there are 168 adult tickets that were sold.
A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a _____ conjecture. transformation. tessellation. composition.
Answers
Answer:A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.
Step-by-step explanation:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes are called tiles, without overlaps or gaps.They can be generalized to higher dimensions and a variety of geometries.Therefore, A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.
The difference between Alan's and Bea's age is three years. The sum of their ages is twenty-seven years. How old are they if-
A. Alan is older than bea?
B. Bea is older than Alan?
Answers
a + b = 27
--------------add
2a = 30
a = 30/2
a = 15 <=== alan is 15
a + b = 27
15 + b = 27
b = 27 - 15
b = 12 <=== bea is 12
Simplify r^4st^7 / 5r^5st^3
Simplify 7x^3y^9z^4 /28x^8y^2
Simplify 3a^3b * 2a^2b^4 / a^10b^3c^2
Explain if you can thankyou!!
Answers
1) r^4st^7 / 5r^5st^3 = st^4 / 5r
2) 7x^3y^9z^4 /28x^8y^2 = y^7z^4 /4x^5
The last one you need to multiply the factors first (add exponents of common factors)
3) 3a^3b * 2a^2b^4 / a^10b^3c^2 = 6a^6b^5/a^10b^3c^2 = 6b^2/a^4c^2
Hope this helps, let me know if you need more explanation!
Simplify -|-5 + 2|.
a)-7
b)-3
c)3
d)7
Answers
if it would have been | - (-5 + 2) | ur answer would have been 3 because the negative sign fell in ur absolute value bars.
[tex]-|-3|[/tex]
Step 2. Simplify [tex]|-3|[/tex] to [tex]3[/tex]
[tex]-3[/tex]
Done! :)
Martin is logging the number of strikes he bowls per hour. He has determined the function to be f(x) = 2x + 5, where x represents hours and f(x) represents the number of strikes he has bowled. Which of the following options describes the restrictions to the domain and range correctly?
Domain, nonnegative values; range, values greater than −2.5
Domain, nonnegative values; range, values greater than or equal to 5
Domain, nonnegative values; range, values less than −2.5
Domain, nonnegative values; range, values less than or equal to 5
Answers
range (f(x) values are : values greater then or equal to 5
Answer:
B. Domain, nonnegative values; range, values greater than or equal to 5
Step-by-step explanation:
Basically, domain is the set of values that x can take and range is the set of values that the result of f(x) can be.
Since x is the time Martin spends bowling, it cannot be negative. The least he can bowl is zero hours, so x cannot be a negative number.
For the lowest x can be (zero), f(x) is calculated as:
f(x) = 2(0)+5 = 0+5 = 5
For higher values of x, the equation can only yield higher results because the 2 that is multiplying it is positive. Multiplying a two positive numbers (2 and x, which cannot be negative) will always give a positive number. In other words, f(x) is directly proportional to x because its coefficient 2 is positive, which means that when x grows, f(x) grows.
This means that f(x) can never be lower than 5.
The best description is, then, nonnegative values for the domain and values greater or equal to 5 for the range.
Is an equation with an integer coefficient will always have an integer solution true or false?
Answers
4 x = 5 ( 4 is an integer coefficient )
x = 5 : 4 = 1.25 ( not an integer )
Answer:
This is false.
Determined whether the graphs of each pair of equations are parallel, perpendicular or neither
Answers
What is the period of the function y=5/2 cos x/4?
Answers
...............................
A ball is launched into the sky at 19.6 feet per second from a 58.8 meter tall building. The equation for the ball’s height, h, at time t seconds is h = -4.9t2 + 19.6t + 58.8 . When will the ball strike the ground?
Answers
Is that a typo, or a real mixture of units?
The equation is only good if the launch speed is actually 19.6 m/s, so I'll assume that.
It will strike the ground when the ball's height = 0 m !!!
-4.9t² +19.6t + 58.8 = 0
You can always use the "quadratic formula" if you want to, but ...
This set of numbers is beloved by physics teachers everywhere. Everything divides by -4.9
t² - 4t -12 = 0
...and factorizes easily:
(t + 2)(t - 6)
So t = 6 or t = -2 Disregard the negative solution.
The ball will strike the ground at t = 6 seconds
Look at the following expression, then factor the sum of terms as a product of the GCF and a sum. 4x + 12 = 4(____ + 3) What term is missing from the solution
Answers
Select the graph that best represents the solution set for 5x+1≤11
Answers
[tex]5x+1-1 \le 11-1[/tex] Subtract 1 from both sides
[tex]5x \le 10[/tex]
[tex]\frac{5x}{5} \le \frac{10}{5}[/tex] Divide both sides by 5 to isolate x
[tex]x \le 2[/tex]
To graph this, draw out a number line. Plot a closed circle at 2 on the number line. The closed circle indicates we include this value in the solution set. This is the endpoint. We shade to the left of the endpoint to represent all of the values smaller than 2. The endpoint is included because of the "or equal to" portion of the inequality sign.
How to get the B by itself
Answers
(a + b + c)/3 x 3 = A x 3
a + b + c = A(3)
a- a + b + c - c = A(3) - a - c
b = A(3) - a - c
hope this helps
( i dont know if the A is suppose to be there or not sorry)
A baseball team has home games on thursdaythursday and saturdaysaturday. the two games together earn $4285.004285.00 for the team. thursdaythursday's game generates $295.00295.00 less than saturdaysaturday's game. how much money was taken in at each game?
Answers
1,995+1,995=3,990
3,990+295=4,285.00
Out of 32 students in the class 5 said they rode their bikes to school based on their results how many of the 800 students in the school rode their bikes toschool
Answers
To make this equivalent we need to find the ratio between 800 and 32:
800/32
25
Now, multiply 5 and 25
25*5
125
Hope this helped!
The next train will arrive in 32 minutes and 30 seconds.
In how many seconds will the next train arrive?
____Seconds
Answers
You can convert time from minutes to seconds by multiplying the number of minutes by 60. Therefore, if the train is due in 32 minutes and 30 seconds, the train will arrive in 1950 seconds.
Explanation:To answer your question, we need to understand that 1 minute is equal to 60 seconds.
So, if the train arrives in 32 minutes, then it will arrive in 32 minutes * 60 seconds per minute, which equal 1920 seconds. And we have additional 30 seconds. So, the total time the train will arrive in is 1920 + 30 = 1950 seconds.
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Solve algebraically for x
Answers
3x + 1 = x^2 - 2x + 1
0 = x^2 -5x
0 = x(x-5)
x = 0,5
Hope this helps!
What is the measure of 1 (1 point) 45 60 120 125?
Answers
Answer:
120°
i finished the quiz and that what i got
and for the rest
1.b
2.d
3.a
4.c
and number 5 is the first answer that i wrote
Step-by-step explanation:
A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
Answers
Answer:
The restaurant needs to earn $839 on Sunday.
Step-by-step explanation:
Consider the provided information.
Let $x needs to earn on Sunday, to average $1000 per day .
It is given that the average earn should be $1000
[tex]Average=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]
[tex]Average= \frac{1240+921+x}{3}[/tex]
[tex]Average= \frac{2161+x}{3}[/tex]
The average should be $1000, so substitute 1000 for average and solve for x.
[tex]\frac{2161+x}{3} =1000\\\\ 2161+x=3000\\\\x=3000-2161\\\\x=839[/tex]
Thus, the restaurant needs to earn $839 on Sunday.
The required equation is [tex]\frac{1240+921+x}{3}=1000[/tex].
Help me plz? I have no clue how
Answers
(3, 9) and (0, 3)
Slope = (Y2 -Y1) ÷ (X2 -X1)
Slope = (3-9) / (0-3)
Slope = -6 / -3
Slope = 2
The equation will have the form y = mx + b
We can rearrange this to b = y -mx
Let's take one of the points (3, 9) and the slope (m) and enter it into the formula:
b = -9 -2*3
b= -3
Now we enter all that data into b = y -mx
and get
y = 2x -3
the sum of 18 and the number of x in algebriac expression
Answers
What makes an irrational number irrational?
Answers
Answer:
Step-by-step explanation:
The sum of the page numbers on the facing pages of a book is 629. what are the page numbers
Answers
So you can just divide this by 2, and then add one to the second number.
629/2 = 314 R1
So the first page number is 314, and for the second one, just add one, and you get 315.
The number of pages of the book is 315.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the sum of the page numbers on the facing pages of a book is 629.
Basically, these numbers have to be consecutive because they're facing pages.
To calculate the number of the pages divide this by 2, and then add one to the second number.
N = 629/2 = 314
Therefore, the number of pages of the book is 315.
To know more about an expression follow
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Leon correctly found the slope and y-intercept of the line that passes through the points (9, –8) and (3, 4) as follows.
m = -8, -4 = -12
9-3 -6 =-2
y = -2x+b
-8=-2(9)+b
-8= -18+b
10=b
a)y=-2x+10
B) y=-2x+10
C) y= 10x-2
D)y=10x +2
Answers
Answer:
[tex]\displaystyle y = -2x + 10[/tex]
Step-by-step explanation:
The work is already done. This is EXACTLY how you find the parallel line, however, two answer choices are an EXACT REPLICA of each other. Perhaps there was a typographical error?
I am joyous to assist you anytime.
the correct answer is option
a)y=-2x+10.
How do you locate the slope?pick factors on the line and decide their coordinates. determine the difference in y-coordinates of these two factors (upward thrust). determine the difference in x-coordinates for those two factors (run). Divide the difference in y-coordinates by means of the difference in x-coordinates (upward thrust/run or slope).
How do u find slope-intercept shape?resolve for the slope (m). recollect, the slope is equal to the alternate in y divided with the aid of the change in x (upward push overrun).remedy for the y-fee of the y-intercept (b). replace m and b with their values inside the y=mx+b system.Learn more about slope-intercept shape here: https://brainly.com/question/1884491
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During a storm, why do you see the flash of lightning before you hear the roar of thunder? What would it mean if you saw the flash of lightning and heard the roar of thunder at the same time? What would it mean if there were many seconds in between the flash of lightning and the roar of thunder?
Answers
T/5=miles away when T is time from the strike of lightning to hearing thunder
Final answer:
You see lightning before hearing thunder due to the faster speed of light compared to sound. A simultaneous occurrence suggests the lightning is very close, while a delay indicates distance, with every five seconds equaling approximately one mile.
Explanation:
During a storm, you see the flash of lightning before you hear the roar of thunder because light travels much faster than sound. Lightning, a massive discharge of electricity, heats and expands the air rapidly, creating the sound of thunder. The difference in the travel speeds of light (3 × 10⁸ meters per second) and sound means that we perceive these events at different times.
If you saw the flash of lightning and heard the roar of thunder at the same time, it would mean that the lightning strike occurred very close to your location, practically overhead. Conversely, a noticeable delay between the flash of lightning and the sound of thunder indicates that the lightning strike is farther away. Each 5-second gap between seeing lightning and hearing thunder equates to approximately one mile distance from the lightning strike.
To estimate the distance of a storm, you only need to know the speed of sound, as the speed of light is so fast that the time it takes for light to reach you is negligible for this calculation. This method of estimating distance helps understanding the physical phenomena and ensuring safety during storms.