A lawn sprinkler sprays water 8 feet at full pressure as it rotates 360 degrees. If the water pressure is reduced by 50%, what is the difference in the area covered?
Answers
so, if the pressure is halfed, then the radius covered would be halfed
now, if 64π is the 100%, what is 16π in percentage?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 64\pi &100\\ 16\pi &x \end{array}\implies \cfrac{64\pi }{16\pi }=\cfrac{100}{x}\implies \cfrac{4}{1}=\cfrac{100}{x}\implies x=\cfrac{1\cdot 100}{4}[/tex]
Answer:
[tex]150.72 feet^2[/tex] is the difference in the area covered.
Step-by-step explanation:
A lawn sprinkler sprays water 8 feet at full pressure, P.
A lawn sprinkler rotates 360 degree which means area covered by sprinkler is of circular shape. Since the sprinkler is in center and sprays the the water 8 feet away in all the direction while rotating.
Radius of the circle = 8 feet
Maximum pressure = P
As we know that higher the pressure higher will the force by which water will move out of the sprinkler. And with more force, sprinkler will able to spray water farther.
So we this we can say that pressure of the sprinkler is directly proportional to the radius of the circle in which water sprayed
[tex]pressure\propto Radius[/tex]
[tex]P\propto r[/tex]
[tex]\frac{P_1}{r_1}=\frac{P_2}{r_2}=constant[/tex]
[tex]P_1=P.P_2=P-50\%\times P=0.5 P[/tex]
[tex]r_1=8 feet.r_2=?[/tex]
[tex]r_2=\frac{0.5 P\times 8 feet}{P}=4 feet[/tex]
Area when , [tex]r_1= 8 feet[/tex] (Area of circle=[tex]\pi (radius)^2[/tex])
[tex]A=\pi r_1^{2}=\pi (8 feet)^2[/tex]
Area when ,[tex]r_2= 4 feet[/tex]
[tex]A'=\pi r_1^{2}=\pi (4 feet)^2[/tex]
Difference in Area = A- A'
[tex]\pi (8 feet)^2-\pi(4 feet)^2=\pi(48 feet^2)=150.72 feet^2[/tex]
[tex]150.72 feet^2[/tex] is the difference in the area covered.
Related Questions
Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a2?
Answers
a^2=4^2+4^2-2*4*4*cos45°
a^2=32-32cos45°
a^2=32(1-cos45°)
a=√(32(1-cos45°))
a≈3.06 units (to nearest hundredth of a unit)
Keeping in mind that a functions rate of change is measure of how fast the function is increasing or decreasing what does the slope of a linear function indicate?
Answers
Answer: A linear function is represented as a straight line. The slope of the line gives the function’s rate of change.
Step-by-step explanation: Plato sample answer
The extreme rock climbing club planned a climbing expedition. The total cost was $5000, which was to be divided equally among the members going. Prior to the trip, 3 members decided not to go. If the cost per person increases by $375, how many people went on the expedition?
Answers
Atmospheric pressure decreases by about 11.8% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 4000 meters.
(Express your answer in millibars rounded correctly to the nearest tenth.)
Answers
[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\to &1013\\ I=\textit{initial amount}\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &0\\ p=period\to &1000 \end{cases} \\\\\\ 1013=I(1-0.118)^{\frac{0}{1000}}\implies 1013=I\cdot 1\implies 1013=I[/tex]
so, the inital amount is 1013, when t = 0,
[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1- r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1013\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &t\\ p=period\to &1000 \end{cases} \\\\\\ A=1013(1-0.118)^{\frac{t}{1000}}\implies A=1013(0.882)^{\frac{t}{1000}}[/tex]
now, to check the atmospheric pressure at 4000, simply set t = 4000, to get A.
a triangular prism has height of 10cm and a base area of 12cm. a rectangular prism has height of 10cm and base dimensions of 3 cm and 4 cm. do the solids have the same volume?
Answers
notice, the base area of the rectangular prism is just 3x4.
Find a_1 and d for an arithmetic sequence with these terms. a_4=9and a_7=18
Answers
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ n=7\\ d=3 \end{cases} \\\\\\ a_7=a_1+(7-1)d\implies 18=a_1+(7-1)3\implies 18=a_1+18 \\\\\\ 18-18=a_1\implies \boxed{0=a_1}[/tex]
A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width
Answers
Plug these values into the Perimeter equation P = 2(length) + 2(width):
P = 2(5x) + 2(x), or P = 12x, and this is known to have the value 192 units. Solve for the width, x:
(192 units) = 12x gives us x = 16 units. Then the length is 5(16 units) = 80 units.
Check: Does 2(80 units) + 2(16 units) = 192 units? If so, then our width (16) and length (80) are correct.
The axis of symmetry for a quadratic equation can be found using the formula x =-b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?
2x
–2x
1/2x
–1/2x
Answers
So the denominator is -2x because it has to take the minus sign that the numerator refused to take ;-)
The answer is B on edgen.
The volume of the Moon is about 2.18×10102 cubic kilometers. The volume of Earth is about 1.09×10121 cubic kilometers. The number of Moons that can fit inside Earth can be found by dividing Earth's volume by the Moon's volume. About how many Moons can fit inside Earth?
Answers
Volume of Earth is 1.09×1012 cubic kilometers
Volume of Moon is 2.18×1010 cubic kilometers
Hence number of Moons that can fit in Earth is
1.09×10122.18×1010
= 1012−102 as 2.18=1.09×2
= 1022
= 1002=50
Answer:
50 moons
Step-by-step explanation:
cause i got it right on the test
Evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim h→0 (5 + h)−1 − 5−1 h
Answers
[tex]\displaystyle=-\lim_{h\to0}\frac h{5(5+h)h}[/tex]
[tex]\displaystyle=-\lim_{h\to0}\frac1{5(5+h)}=-\frac1{25}[/tex]
Alternatively, recall that if [tex]f(x)=\dfrac1x[/tex], then [tex]f'(x)=-\dfrac1{x^2}[/tex], and so
[tex]f'(5)=\displaystyle\lim_{x\to5}\frac{\frac1x-\frac15}{x-5}[/tex]
Take [tex]h=x-5[/tex], so that [tex]x=h+5[/tex], and we have the original limit. So the limit is equivalent to the value of [tex]f'(5)[/tex], i.e.
[tex]f'(5)=-\dfrac1{5^2}=-\dfrac1{25}[/tex]
What's the answer to the equation;
√2y+3=11
Answers
The course for a walkathon is 6 miles long. If Chloe wants to walk 50 miles during the walkathon, how many times must she walk the course?
Answers
divide 50 by 6
50/6 = 8.333
so she has to walk it 8.33 times
round answer as needed.
What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters? 8.75 meters 12.25 meters 26.25 meters 52.5 meters
Answers
simplify away.
Since this cylinder has a radius of 6 meters, its height is equal to 8.75 meters.
Given the following data:
Radius of cylinder = 6 m.
Volume of cylinder = 315π m.
How to calculate the height of this cylinder?Mathematically, the volume of a cylinder is calculated by using this formula:
V = πr²h
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
315π = π × 6² × h
315π = 36πh
h = 315/36
Height, h = 8.75 meters.
Read more on cylinder here: brainly.com/question/21367171
#SPJ2
write each fraction as a sum or difference
2m-5/9
Answers
So we can simply divide each term of numerator by denominator because we can write [tex] \frac{a+b}{c} = \frac{a}{c}+ \frac{b}{c} [/tex]
So we can write given fraction as
[tex] \frac{2m-5}{9} = \frac{2m}{9} - \frac{5}{9} [/tex] which is expressed as a difference.
Kathy walked 3 1/2 miles per hour for 1 1/4 hours. During 1/2 of her walking time it rained. How many miles did she walk while it was raining?
Answers
1 1/4 = 5/4 * 1/2 = 5/8
3 1/2 = 7/2 * 5/8 = 35/16 = 2 3/16 miles
Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: "When I multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produce a sum of 12. When I add my first lucky number and twice my second lucky number, the sum is 5." Which twin is talking? How do you know?
Answers
The solve the next problem, the second lucky number (1) twice is 2. When added to the first lucky number, the sum is 4. This is tricky, because if the first lucky number was multiplied by 2 and added to the second lucky number, the sum would be 5.
In this case, the twin that lies is talking.
Which of the following gives all of the sets that contain -1/2?
A.the set of all rational numbers and the set of all real numbers
B.the set of all natural numbers and the set of all irrational numbers
C.the set of all integers and the set of rational numbers
D.the set of all natural numbers, the set of rational numbers, and the set of all real numbers
Answers
Answer:
Option A is Correct Option.
Step-by-step explanation:
Given: [tex]\frac{-1}{2}[/tex]
[tex]\frac{-1}{2}[/tex] is a rational no.
Option A:
Given no is a rational no.
⇒ Both Set of rational no and real nos. contain rational nos..
Thus, Correct Option.
Option B:
set of natural nos and irrational nos does not contain rational nos.
Thus, Not correct option.
Option C:
Set of integers does not contain rational numbers.
Thus, Incorrect Option.
Option D:
Set of all Natural Nos. does not contain rational nos.
Thus, This option is not correct option
Therefore, Option A is Correct Option.
The perimeter of a rectangular field is 168 feet. The field is 36 feet wide. How long is the field
Answers
Length= Peremiter/2 - width
L = P/2 - W
L = 168/2 - 36
L = 84 - 36
L = 48
The length is 48
Out of 30 students surveyed 17 have a dog based on these results predict how many of the 300 students in the school have a dog
Answers
17/30 = 0.5666 so about 57% of the sample had dogs
300 x 0.57 = 171 would have dogs
PLEASE help me...Suck at math. find the following using the given triangle.
Answers
5+5+6 = 16
To find the area, you need to use the following formula
[tex] area = \frac{1}{2}bh[/tex]
we know b but we need to find the height. We can find the heigh by using pythagorean theorem [tex]a^2 + b^2 = c^2[/tex]
height = [tex] a^2 + 3^2 = 5^2 [/tex]
[tex] a^2 + 9 = 25 [/tex]
[tex] a^2 = 25 - 9[/tex]
[tex] a^2 = 16 [/tex]
[tex] a = \sqrt{16} = 4 [/tex]
h = height = 4
[tex] area = \frac{1}{2}\times 6\times 4 = 12cm^2[/tex]
Cost:
6.00 per cm^2 = 6.00 x 12 = $72.00 dollars
what's the cost? well is $6 per square foot, what area did you get? well, say you got A, so the cost is just A * 6.
The total ages of 2 buildings is 201 years. if one building is twice as old as the other, what are the ages of 2 buildings?
Answers
In this case, you are given the buildings sum ages ( building A ages+ building B ages = 201 years) and the building ratio ( Building A ages= 2x Building B ages).
To answer the question, you simply need to insert the second equation into the first. It would be:
building A ages + building B ages= 201
2x building B ages + building B ages= 201
building B ages= 67 years.
Then building A ages= 2x 67 years= 134 years.
The ages of the two buildings are 67 and 134 years. This is found by setting up an algebraic equation where the sum of their ages is 201, and one is twice as old as the other.
Finding the Ages of Two Buildings
If the total ages of two buildings is 201 years and one building is twice as old as the other, then we can express the ages of the buildings using algebra. Let's denote the age of the younger building as y years. The older building is twice as old, so its age would be 2y years. The equation based on their total ages would be:
y + 2y = 201 years
Solving this equation:
Combine like terms: 3y = 201.
Divide both sides by 3 to isolate y: y = 201 / 3.
Calculate the exact value: y = 67 years.
So, the younger building is 67 years old, and the older building, being twice as old, is 134 years old.
how many miles can you drive with 13.2 gallons of gasoline
Answers
Certain cars burn more gasoline than others. You also may burn more or less gasoline depending on your speed. Slower speeds burn less, whereas faster speeds burn more.
What statement regarding the diagram is true?
Answers
What property describes the number sentence? 6+0=6
Answers
the property describes the number sentence 6+0=6 is : " 0 Neutral element for addtion"
A math teacher gave her class two tests. 76% of the class passed the first test. 58% of the class passed both tests. What is the approximate probability that a student who passed the second test, given that he passed the first test.
Answers
P(test 2 | test 1) = 0.58 ÷ 0.76
P(test 2 | test 1) = 0.76 ≈ rounded to two decimal places
a car dealership has 55 cars and 11 vans.what is the ratio of cars to vans? wriiten as a fraction in simplest form?
Answers
You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 5 days later you determine that it has decayed down to 0.7 grams. What is its half-life? (Round your answer to three significant digits.)
Answers
t(1/2)=[tln2]/[lnN-lnN(t)]
where;
t=time
N=initial amount
N(t)=final amount
thus the half-life of our material will be as follows:
t=5 days
N=1 g
N(t)=0.7 g
N(1/2)=[5*ln2]/[ln1-ln0.7]
=9.717
Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?
Answers
45x = money Matt has
45x =50(x-.1)
45x =50x -5
5 =5x
x=$1
45x= $45
the cost of each car is $1
You deposit $5000 in an account earning 2% interest compounded continuously. How much will you have in the account in 15 years?
Answers
A=p(1+r/100)^n
where:
A=future amount
p=principle
r=rate
n=time in years
Therefore given that, p=$5000, r=2% and n=15 years, the amount after 15 years will be:
A=5000(1+2/100)^15
A=5000(1+0.02)^15
A=5000(1.02)^15
A=6,729.34
We conclude that the amount after 15 years will be $6,729.34
A wheelchair access ramp has an angle of elevation of 20°. If the ramp reaches to the top of a 33 inch high porch, how long is the ramp?
Answers
length=height/sinα, we are given that α=20° and h=33 in
length=33/sin20° in
length≈96.49 in (to nearest hundredth of an inch)
Sin(20) = 33/x
x*Sin(20) = 33
x = 33/Sin(20)
x = 96.49in long.
*This answer is the length of the SLOPE of the ramp.