A square lawn has area 512 ft squared .ft. a sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. what is the radius of the circle?
Answers
Answer:
Radius of circle = 16 ft
Step-by-step explanation:
Refer figure for the arrangement.
Area of square = 512 ft²
Side of square [tex]=\sqrt{512}=22.63ft[/tex]
From figure see that
Diagonal of square = Diameter of circle
[tex]\texttt{Diameter of circle}=\sqrt{22.63^2+22.63^2}=32ft[/tex]
Radius of circle [tex]=\frac{32}{2}=16ft[/tex]
Related Questions
Assume that the committee consists of 6 Republicans
and 8 Democrats. A subcommittee consisting
of 7 people is to be selected.
(1) How many such subcommittees are possible
if each subcommittee must contain exactly 3
Republicans and 4 Democrats?
(1) How many such subcommittees are possible
if each subcommittee must contain at least 1 and
no more than 3 Republicans?,
Answers
The question requires the application of combination formulas to calculate the number of possible subcommittees with specific party member composition requirements.
Explanation:The question deals with combinations in mathematics, specifically combinatorial calculation to determine the number of ways a subcommittee can be formed given certain restrictions on a party composition.
Part 1:
To find out how many subcommittees can be formed containing exactly 3 Republicans and 4 Democrats, we use the combination formula which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial. There are 6 Republicans, so we can choose 3 of them in C(6, 3) ways and there are 8 Democrats from which we can choose 4 in C(8, 4) ways. The total number of such subcommittees is the product of these two combinations.
Part 2:
For the second part, we consider subcommittees with at least 1 and no more than 3 Republicans. This means we must calculate the sum of subcommittees for when there are exactly 1, 2, or 3 Republicans, combined with the appropriate number of Democrats to make a total of 7 members. We use the combination formula again for each scenario and add the results together.
The rate, r, at which people get sick during an epidemic of the flu can be approximated by r = 1600te^(−0.5t), where r is measured in people/day and t is measured in days since the start of the epidemic.
(a) When are people getting sick the fastest?
(b) How many people get sick altogether?,
Answers
a group of 31 friends gets together to play a sport. first people must be divided into teams. each team has to exactly 4 players, and no one can be on more than one team. how many can they make? (it is possible that not everyone can be on a team.)
Answers
Total people: 31
People per team: 4
The number of teams will then be:
N = (31) / (4)
N = 7.75
Round to the previous whole number.
N = 7
There are 7 teams.
Answer:
they can make about 7 teams.
which expression is equivalent to -3(2m-1)-n
6m-n-3
6m-n+3
-6m-n-3
-6m-n+3
Answers
by order of operations
-3(2m-1)-n=-6m+3-n=-6m-n+3
Distribute:= (−3)(2m)+(−3)(−1)+−n=− 6m + 3 + −n
Answer: D= −6m − n +3
B). -3(2m-1)-n Final result : -6m - n + 3 Step by step solution : Step 1 :Equation at the end of step 1 : (0 - 3 • (2m - 1)) - n Step 2 : Step 3 :Pulling out like terms : 3.1 Pull out like factors :
-6m - n + 3 = -1 • (6m + n - 3)
Final result : - 6m - n + 3
PLEASE PLEASE HELP ME!!!!
Answers
180 - 35-52 = 93
Now we can solve for x.
3(x + 2) = 93
3x + 6 = 93
3x = 87
x = 29
A. x = 29
B. C = 93
Hope this helps =)
3x + 93=180
3x = 87
x = 29
<C = 3(29+2) = 3(31) = 93
An isosceles triangle has perimeter T and sides of length x, x, and y. Which of the following represents x in terms of T and y? (10 POINTS + BRAINLIEST ANSWER)
A. x = T - y
B. x = T - 2y
C. x = T - 2y/2
D. x = T - y/2
Answers
the correct answer is C. x = (T - 2y) / 2.
To find the value of x in terms of T (the perimeter) and y for an isosceles triangle with two sides of length x and one side of length y, we use the fact that the perimeter is the sum of all three sides. The equation representing the perimeter of the triangle is T = x + x + y, which simplifies to T = 2x + y. To solve for x, we rearrange the equation to x = (T - y) / 2. Therefore, the correct answer is C. x = (T - 2y) / 2.
The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. What is $a+b$?
Answers
The value of [tex]$a + b$[/tex] is 9.
To solve this problem
We can use the fact that the roots of the equation are given as[tex]$2 - 3i$ and $2 + 3i$.[/tex]
Quadratic equation roots occur in pairs of complex conjugates. Since[tex]$2 - 3i$[/tex] is the first root in this instance,[tex]$2 + 3i$[/tex] is the other root.
We now understand that the coefficient of the [tex]$z$[/tex] term is equal to the opposite of the sum of the roots of a quadratic equation. Stated otherwise, the total of the roots equals [tex]a[/tex] Thus, the two roots can be added together:
[tex]$(2 - 3i) + (2 + 3i) = 4$[/tex]
Therefore[tex], $-a = 4$, or $a = -4$.[/tex]
Next, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of the [tex]$z^2$[/tex]term.
[tex]$(2 - 3i)(2 + 3i) = 4 - 6i + 6i - 9i^2 = 4 + 9 = 13$[/tex]
So, [tex]$b = 13$.[/tex]
Finally, we can find the sum[tex]$a + b$:[/tex]
[tex]$a + b = -4 + 13 = 9$[/tex]
Therefore, the value of [tex]$a + b$[/tex] is 9.
The annual interest rate of Paul's savings account is 7.2%,and simple interest is calculated monthly. What is the periodic interest rate of Paul's account?
A. 0.9%
B. 0.6%
C. 0.4%
D. 1.8%
Answers
The periodic interest rate is found by dividing the annual interest rate by the number of times per year it is compounded.
7.5/12 = 0.625, rounded to 0.6.
PLEASE HELP ME WITH THIS....
BRAINLIEST AVAILABLE
Answers
Answer A
[tex]V= \dfrac{ \pi *r^2*h}{3} \\\\ 3*V= \pi *r^2*h\\\\ \boxed{ \dfrac{3*V}{\pi*r^2}=h }[/tex]
helpppppppppppppppppppppppp
Answers
For the first pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.
For the second pair of points: the first point has a tangent value of -sqrt(3), while the second has a tangent value of -1/sqrt(3), so these are not identical.
For the third pair of points: the first point has a tangent value of sqrt(3), while the second also has a tangent value of sqrt(3), so these have the same reference angle.
For the fourth pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.
So the only correct answer is the third choice.
Quadratic Equations Solve for x. x2+2=102 Enter the solutions for the equation in the boxes.
Answers
X= 10, and -10
The given quadratic equation is :
[tex] x^{2}+2=102 [/tex]
We have to solve the given quadratic equation for the value of 'x'.
[tex] x^{2}+2=102 [/tex]
[tex] x^{2}=102-2 [/tex]
[tex] x^{2}=100 [/tex]
[tex] x=\sqrt{100} [/tex]
x= [tex] \pm 10 [/tex]
So, the value of 'x' in the given quadratic equation are 10 and -10.
What are all solutions to the equation 2 cos Θ = 1 for 0 ≤ Θ ≤ 2pi? Round to the nearest hundredth.
θ ≈ 1.32, 4.97
θ ≈ 1.05, 5.24
θ ≈ 0.52, 2.62
θ ≈ 0.05, 2.89,
Answers
Answer:
1.a
2.d
3.c
4.a
5.b
Step-by-step explanation:
Please help me with #1!!!!
Answers
When finding the value of a function with a given number, always replace the variable (for x) and simplify. As we can see in your problem, f(x) is being replaced with "4", so substitute "x" with 4.
This leaves us with:
5(4) - 5. All we need to do now is simplify.
5(4) - 5
20 - 5
15.
From the work above, we can see that the function of f(4) has a value of 15.
I hope this helps!
12 stamps increased by 125%
Answers
The answer to this is 27.
12 x 2 = 24
12 ÷ 4 = 3
24 + 3 = 27
which of the following is an x-intercept of the function f(x)=x^2-25
A.-5
B.-20
C.-25
D.-15
Answers
Replace y with 0 in the equation. You get the following.
[tex]x^2-25=0[/tex]
Add both sides by 25
[tex]x^2=25[/tex]
Take the square root.
[tex]x= \pm \sqrt{25} [/tex]
[tex]= \pm 5[/tex]
This means that the x-intercepts are 5 and -5.
A is your answer.
The x-intercept of the function f(x) = x^ 2-25 is -5. The correct option is A.
What is the intercept function?A rational function's intercept is the location on its graph where it crosses either the x- or y-axis. When the independent variable is 0, use the intercept function to find the value of the dependent variable (zero).
For instance, if your data points were collected at room temperature and above, you can use the intercept function to forecast a metal's electrical resistance at 0°C.
The x-intercept of a function is when the y-value is 0.
Replace y with 0 in the equation. You get the following.
[tex]x^2 - 25 = 0[/tex]
Add 25 to both sides
[tex]x^2 = 25[/tex]
Take the square root.
[tex]x = - \sqrt{25}[/tex]
[tex]x = -5[/tex]
Therefore, the correct option is A. -5.
To learn more about the intercept function, refer to the link:
https://brainly.com/question/11872755
#SPJ2
Which parent function has a graph that is located in Quadrants I and III?
A. reciprocal
B. quadratic
C. exponential
D. square root
Answers
An reciprocal function, as for instance
[tex]f(x) = \frac{1}{x} [/tex]
is located in the Quadrants I and III.
A <<<< answer.
2.3,
12
5
,
5
2
, 2.2,
21
10
least to greatest
Answers
Can any one help me with this! Please look at the picture below just the circled numbers!!
Answers
If Ge=46 and dh=15 find gf
Answers
GE=46
DH=15
GF=?
we know that
the rhombus has two perpendicular diagonals
and
GE=GH+HE
GH=HE
DF=DH+HF
DH=HF
so
GE=46------------> GH=46/2------------> GH=23
DH=15-------------> HF=15
so
applying the Pythagorean theorem
GF²=GH²+HF²----------> 23²+15²----------> 754
GF=√754----------> GF=27.46 in
the answer is
GF=27.46 in
Answer:
GF=26.4
Step-by-step explanation:
21^2+16^2=C^2
441+256=c^2
697=c^2
GF=26.4
I hope this helps
Who, in 1706, first gave the greek letter "pi" its current mathematical definition? *?
Answers
It was previously known as Ludolph's constant (in honor of the mathematician Ludolph van Ceulen) or as a constant of Archimedes (not to be confused with Archimedes' number).
Jones poses the name and symbol of this number in 1706 and Euler begins to spread it in 1736.
Answer:
Welsh mathematician William Jones
Which of the two functions below has the largest maximum y-value?
f(x)=-x^4-2
g(x)=-3x^3+2
A. There is not enough information to determine
B. The extreme maximum y-value for both f(x) and g(x) is infinite
C. f(x)
D.g(x)
Answers
APEX
Answer: D. g(x)
Step-by-step explanation: since,f(x)=-x^4-2
x^4>=0 for all x so,-x^4<=0 for all x
⇒ -x^4-2<=-2 for all x
⇒ f(x)<=-2 for all x so, maximum possible value of f(x)=-2
whereas g(x)= -3x^3+2 can take values from (-∞,∞)
so, g(x) has the maximum y value
A hybrid car averages 600 miles on a 12.9 gallon tank of gas. Manuel is planning a 1240-mile vacation in his hybrid car. Find how many gallons of gas he can expect to burn.
Answers
amount of gas used up - 12.9 gallons
therefore when he travels 600 miles he uses up 12.9 gallons
for every mile the amount of gas used up - 12.9 gallons / 600 miles = 0.0215 gallons / mile
therefore 0.0215 gallons used up per mile
so when he's going for 1240 miles - gas used up is 0.0215 gallons/ mile x 1240 miles = 26.66 gallons
amount of gas needed is 26.66 gallons
Answer:
26.66 gallon of gas
Step-by-step explanation:
A car uses 12.9 gallons of gas for travelling 600 miles
For travelling one mile , the car will use gas = 12.9 gallon of gas/600 miles
= 0.0215 gallon of gas /mile
For travelling 1240 miles, gallon of gas required =
= 0.0215 gallon of gas /mile x 1240 miles
= 26.66 gallon of gas
The center of a circle is located at (3,8) and the circle has a radius that is 5 units long What is the general form of the equation for the circle
Answers
1 question. 11 points. thanks for the help
The equation p = 1.7t² + 18.75t + 175 approximates the average sale price p of a house (in thousands of dollars) for years t since 2010.
What is the best estimate for the price of the house in year 2020
Answers
I can't really explain it very well but I just took my test and I got it right
The equation [tex] p= 1.7t^{2}+18.75t+175 [/tex] approximates the average sale price p of a house (in thousands of dollars) for years t since 2010.
We have to calculate the best estimate for the price of the house in year 2020.
So, we have to calculate the best price of the house after 10 years.
So, putting the value t=10 in the given equation.
[tex] p= 1.7t^{2}+18.75t+175 [/tex]
[tex] p= (1.7 \times 100)+(18.75 \times 10)+175 [/tex]
p = 532.5= 533 (Rounded)
Since it approximates the average sale price p of a house (in thousands of dollars).
Therefore p=$533,000
Therefore, the best estimate for the price of the house in year 2020 is $533,000.
Please show all sork
Answers
a) Second differences are 2.
b) The next three numbers will be
.. 30+12 = 42
.. 42+14 = 56
.. 56+16 = 72
c) There are a number of ways to write an equation for this. One of the simpler ones is to let a graphing calculator perform quadratic regression and tell you the equation.
.. a[n] = n(n +1)
d) 117 is not in the sequence. The sequence consists only of even numbers, of which 117 is not one.
e) 10100 is in the sequence. It is 100*101, hence the 100th term of the sequence.
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
Answers
Please note that odd numbers differs by 2...1,3,5,7,9etc....
If the first odd integer Is x
The next(consecutive one) = x+2
The third = (x+2)+2 = x+4
The fourth one = (x+4)+2 = x+6..
The sum of all this equals to - 72 that is......
x+x+2+x+4+x+6 =-72
4x+12 = - 72
4x=-72-12
4x=-84
x=-84/4
x= -21...
x+2 = - 21+2 = -19
x+4 = -21+4 = -17
x+6 = -21+6 = -15
Those number have been highlighted above..
Hope this helped....
Answer: n + n+2 + n+4 + n +6 = 4n + 12 = -72 4n = -84 n = -21 -21,-19,-17 and -15
helpppppppppppppppppppppppppppppp
Answers
4/9
Explanation:
For the left hand side:
log base 2 of (6x) - log base 2 of (√x) = log base 2 of (6x / √x)
Equating this to the right hand side we will get:
log base 2 of (6x / √x) = 2
Converting this into exponent form, we will get:
2^2 = 6x/√x
4 √x = 6x
4√x - 6x = 0
√x (3√x - 2) = 0
either √x = 0....> This value is rejected as the log base 2 of zero is undefined
or √x = 2/3 which means that x = 4/9
Hope this helps :)
111 is what percent of 300
Answers
Answer:
37
Step-by-step explanation:
bc its 37
99 points
What is the approximate volume of the cone?
Use 3.14 for π
1272 cm³
2120 cm³
4239 cm³
6359 cm³
Answers
And from doing and plugging in all of this, our answer would give us [tex](2120 \ cm^3)[/tex]
Your answer: (second option)
v=3.14(225)(3)
v=2119.5
v=2120
The answer is B
A man is in a tree house 7 ft above the ground. He is looking at the top of another tree that is 24 ft tall. The bases of the trees are 40 ft apart. What is the angle of elevation from the man's feet to the top of the tree? Round to the nearest degree.
A. 23
B. 31
C. 67
D. 59
Answers
Final answer:
The angle of elevation from the man's feet to the top of the tree is approximately 31 degrees.
Explanation:
To find the angle of elevation from the man's feet to the top of the tree, we can use the tangent function.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (24 ft) and the adjacent side is the horizontal distance between the two trees (40 ft).
Therefore, tan(angle) = opposite/adjacent = 24/40 = 0.6.
Taking the inverse tangent, we get angle = arctan(0.6).
Rounding to the nearest degree, the angle is approximately 31 degrees.