The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.
To find the diameter, circumference, and area of the circle watered by the lawn sprinkler, we can use the formulas:
1. **Diameter [tex](\(d\)) = \(2 \times \text{radius}\)[/tex]
2. **Circumference [tex](\(C\)) = \(2 \times \pi \times \text{radius}\)[/tex]
3. **Area [tex](\(A\)) = \(\pi \times \text{radius}^2\)[/tex]
Given:
Radius[tex](\(r\)) = 40 feet[/tex]
1. Diameter:
[tex]\[d = 2 \times r\]\[d = 2 \times 40 \text{ feet}\]\[d = 80 \text{ feet}\][/tex]
2. Circumference:
[tex]\[C = 2 \times \pi \times r\]\[C = 2 \times \pi \times 40 \text{ feet}\]\[C \approx 2 \times 3.14159 \times 40 \text{ feet}\]\[C \approx 251.327 \text{ feet}\][/tex]
3. Area:
[tex]\[A = \pi \times r^2\]\[A = 3.14159 \times 40^2 \text{ square feet}\]\[A = 3.14159 \times 1600 \text{ square feet}\]\[A \approx 5026.548 \text{ square feet}\][/tex]
Answer:
The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.
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Answer:
1/4
Step-by-step explanation:
help plsss need this for tomorrow
Can someone please help? In the circle at right, AZB is a(n): (A) minor arc, (B) central angle, (C) major arc, (D) arcezoid, or (E). None of these? Thanks
In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.
As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.
Therefore, Option A, minor arc is the correct answer.
If a circle has an diameter of 14, what would the area be?
Use 3.14 for π
Please help!! Which of the following could represent the scale factor of the smaller figure to the larger figure?
Smaller figures volume is 216in.^3
Larger figures volume is 343in.^3
The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.
Explanation:The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.
Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.
To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.
One number is one less than five times another. if their sum is decreased by three, the result is eight. find the numbers.
Can anyone answer this for me?
Can anyone help me!?!?!?!?! Here is my question:
Compare the functions shown below:
f(x) = 4 sin (2x − π) - 1
g(x)
x y
-1 6
0 1
1 -2
2 -3
3 -2
4 1
5 6
h(x) = (x − 2)2 + 4
Which function has the smallest minimum y-value?,
For what values of b will F(x) = logb x be an increasing function?
A. b < 0
B. b > 0
C. b < 1
D. b > 1,
Final answer:
The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)
Explanation:
The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.
Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.
Line r passes through points (2, 11) and (10, 4). Line s is perpendicular to r. What is the slope of line s?
what is the sum of the arithmetic series 18 t=1 (3t-4)
a. 234
b. 441
c. 25.5
d. 49
The given arithmetic series is
[tex] \sum_{t=1}^{18} (3t-4) [/tex]
When t =1, we will get the first term,a, which is
[tex] 3(1)-4 =3-4=-1 [/tex]
When t =18, we will get the last term,l , which is
[tex] 3(18)-4 = 50 [/tex]
Now we use the formula of sum of n terms which is
[tex] S = \frac{t}{2} (a+l) [/tex]
Substituting the values of t,a and l, we will get
[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]
Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]
Let t=1 in the given series, we get
first term = [tex] a_{1} [/tex] = 3-4 = -1.
Let t=2 in the given series, we get
second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]
Let t=3 in the given series, we get
third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]
Now, let t=18 in the given series, we get
last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]
We get the series as
-1, 2, 5,..... 50
Sum = [tex] \frac{n}{2}(a+l) [/tex]
= [tex] \frac{18}{2}(-1+50) [/tex]
= [tex] = 9 \times 49 [/tex]
= 441
Therefore, the sum of the given arithmetic series is 441.
How far does a ball that is hit from a height of 3 feet at a speed of 120 feet per second travel before it hits the ground if it is hit at an angle of 45 degrees? Round your answer to the nearest integer.
A) 376 Feet
B) 395 Feet
C) 426 Feet
D) 453 Feet
Select ALL the correct answers.
The square of the sum of a number and 6 plus twice the number is equal to 189.
Which equations could be used to represent this relationship?
(3x + 6)2 = 189
(x + 6)2 + 2x = 189
(x + 6)2 = 189 + 2x
x2 + 10x + 36 = 189
x2 + 14x + 36 = 189
x2 + 2x + 6 = 189
Answer:
[tex](x+6)^{2}+2x=189[/tex]
and
[tex]x^{2}+14x+36=189[/tex]
Step-by-step explanation:
Let
x -----> the number
we know that
The equation that represent the situation is
[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]
therefore
The equations that could be used are
[tex](x+6)^{2}+2x=189[/tex] and [tex]x^{2}+14x+36=189[/tex]
Answer:
(x+6)^{2}+2x=189
and
x^{2}+14x+36=189
Step-by-step explanation:
HELP ASAP WILL MARK AS BRAINILEST TO WHOEVER GETS IT RIGHT
according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction
see the attached figure to better understand the problem
we know that
[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.
Hence
The probability that they buy both fiction and paperback is equal to
[tex]0.65*0.45=0.2925[/tex]
the answer is
[tex]0.2925[/tex]
The asymptote of the function f(x) = 3x + 1 – 2 is_________ . Its y-intercept is_____ .
Options for the first blank is
y= -2
y= -1
y= 1
y= 2
Options for the second is
(0,-2)
(0,-3)
(0,1)
(0,-1)
Answer:
In first blank : y = - 2,
In second blank : ( 0, 1 )
Step-by-step explanation:
Given function is,
[tex]f(x)=3^{x+1}-2[/tex]
The horizontal asymptote of the function f(x),
[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]
[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]
[tex]y=3^{\infty+1}-2[/tex]
[tex]y=3^\infty - 2[/tex]
[tex]y=0-2[/tex]
⇒ y = -2
First option is correct.
Also, the function has no vertical asymptote,
2. For finding the y-intercept, x = 0,
[tex]f(0)=3^{0+1}-2=3-2=1[/tex]
Hence, the y-intercept = (0,1)
Third option is correct.
Final answer:
The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).
Explanation:
The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.
Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.
To find the y-intercept, we set x equal to 0 and solve for f(0):
f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.
Therefore, the y-intercept of the function is the point (0, – 1).
MATH HELP PLEASE LOOK AT THE PICTURES BELOW!!!
5 QUESTIONS
Cassandra lives in Oklahoma and makes $60,000 a year. If the median annual income in Oklahoma is $64,105 and the median annual income in the United States as a whole is $50,233, is Cassandra likely to qualify for Chapter 7 bankruptcy?
Answer:
Cassandra is likely to qualify for Chapter 7 bankruptcy.
Step-by-step explanation:
Given scenario is : Cassandra lives in Oklahoma and makes $60,000 a year. The median annual income in Oklahoma is $64,105.
A person qualifies for chapter 7 bankruptcy, if his annual median income is below the median income of his state. So, here the annual median income of Cassandra is below the median income of her state, Oklahoma.
So, she will qualify for chapter 7 bankruptcy.
What is the slope-intercept form for each equation in this system? Compare the slopes and y-intercepts to describe the graph of the system. 3x - 4y = 28 4x + 10y = 20 A) y = 3 4 x − 7; y = −2 5 x + 2; one line B) y = - 3 4 x − 7; y = −2 5 x + 2; parallel lines Eliminate C) y = 3 4 x − 7; y = 2 5 x + 2; intersecting lines D) y = 3 4 x − 7; y = −2 5 x + 2; intersecting lines
The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]
Given the standard form of the equations :
3x - 4y = 28 - - - - (1)4x + 10y = 20 - - - - - (2)The General form of a slope - intercept equation :
y = bx + cFor equation (1) :
3x - 4y = 28
Make y the subject
-4y = 28 - 3x
Divide both sides by - 4 to isolate y
y = -7 + 3/4x
[tex]y = \frac{3}{4} x - 7 [/tex]
For equation (2) :
4x + 10y = 20
Make y the subject
10y = 20 - 4x
Divide through by 10 to isolate y
y = 2 - 2/5x
[tex]y =- \frac{2}{5} x + 2[/tex]
Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]
Learn more :
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solve the system of equations y=2x^2-3 y=3x-1
Solve by factoring write the steps.
x2−7x+10=0
Please help show me all the steps and the answers
K - 263.48 = 381.09 solve this equation
Please help me out :)
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
I have the same problem but with 14 being 15 in and 9 being 7 in, can someone help?
What is the value of x?
Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3 n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6 –2m6 – 5m3n3 + 14m2n4 + 7mn5 + n6 14m2n4 + 7mn5 – 6m6 – 5m3n3 + n6 n6 – 6m6 + 7mn5 + 14m2n4 – 5m3n3
The correct combining of like term is
f(m, n) = [tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
What is polynomial equation?A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.
Given:
8m[tex]n^{5}[/tex] - 2[tex]m^{6}[/tex] +5m²[tex]n^{4}[/tex] - m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] + 9m²[tex]n^{4}[/tex] - m[tex]n^{5}[/tex] - 4m³n³
Now, Combining the like terms
(8m[tex]n^{5}[/tex] - m[tex]n^{5}[/tex]) + 5m²[tex]n^{4}[/tex] + 9m²[tex]n^{4}[/tex] - m³n³ - 4m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
=7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ - 6 [tex]m^{6}[/tex] + [tex]n^{6}[/tex]
now, arranging according to their powers
[tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
Learn more about polynomials here:
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Jalen traded $4100 for Mexican pesos, immediately changed his mind, and then promptly traded his Mexican pesos back into dollars. Which of these amounts is he most likely to have?
A. More than $0 but less than $4100
B. $0
C. $4100
D. More than $4100
APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX
More than $0 but less than $4100
Find the perimeter of the rectangle.
If the rectangle has vertices M(−2,4), N(1,5), O(3,−1), and P(0,−2), what is the perimeter of the rectangle?
Round each side length to the nearest tenth, if necessary.
Find the probability that when a couple has four four children, at least one of them is a girl girl. (assume that boys and girls are equally likely.)
What is the equation, in slope-intercept form, of the line that is perpendicular to the line Y-4=-2/3(X-6) and passes through the point (-2,-2)
Answer:
d
Step-by-step explanation: