Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
Answers
Answer:
(a) (x - 3)² + (y + 4)² + (z - 5)² = 25
(b) (x - 3)² + (y + 4)² + (z - 5)² = 9
(c) (x - 3)² + (y + 4)² + (z - 5)² = 16
Step-by-step explanation:
The equation of a sphere is given by:
(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ---------------(i)
Where;
(x₀, y₀, z₀) is the center of the sphere
r is the radius of the sphere
Given:
Sphere centered at (3, -4, 5)
=> (x₀, y₀, z₀) = (3, -4, 5)
(a) To get the equation of the sphere when it touches the xy-plane, we do the following:
i. Since the sphere touches the xy-plane, it means the z-component of its centre is 0.
Therefore, we have the sphere now centered at (3, -4, 0).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;
\(d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}\)
\(d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}\)
\(d = \sqrt{(0)^2+ (0)^2 + (-5)^2}\)
\(d = \sqrt{(25)}\)
d = 5
This distance is the radius of the sphere at that point. i.e r = 5
Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 5²
(x - 3)² + (y + 4)² + (z - 5)² = 25
Therefore, the equation of the sphere when it touches the xy plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 25
(b) To get the equation of the sphere when it touches the yz-plane, we do the following:
i. Since the sphere touches the yz-plane, it means the x-component of its centre is 0.
Therefore, we have the sphere now centered at (0, -4, 5).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;
\(d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}\)
\(d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}\)
\(d = \sqrt{(-3)^2 + (0)^2+ (0)^2}\)
\(d = \sqrt{(9)}\)
d = 3
This distance is the radius of the sphere at that point. i.e r = 3
Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 3²
(x - 3)² + (y + 4)² + (z - 5)² = 9
Therefore, the equation of the sphere when it touches the yz plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 9
(b) To get the equation of the sphere when it touches the xz-plane, we do the following:
i. Since the sphere touches the xz-plane, it means the y-component of its centre is 0.
Therefore, we have the sphere now centered at (3, 0, 5).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;
\(d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}\)
\(d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}\)
\(d = \sqrt{(0)^2 + (4)^2+ (0)^2}\)
\(d = \sqrt{(16)}\)
d = 4
This distance is the radius of the sphere at that point. i.e r = 4
Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 4²
(x - 3)² + (y + 4)² + (z - 5)² = 16
Therefore, the equation of the sphere when it touches the xz plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 16
By using the general sphere equation and what we know about planes, we will get:
a) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2b) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2c) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2.General sphere equation.The general sphere of radius R centered in the point (a, b, c) is given by:
(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2
If we want a sphere centered in (3, -4, 5) we will have:
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = R^2
a) We want the sphere to touch the xy-plane, (with z = 0) then the radius must be at least equal to the z-component of the point, so we have R = 5, then the equation is:
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2
b) This time is the yz-plane, so the radius must be equal to the x-component.
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2
c) Finally, the xz-plane, this time the radius must be equal to the y-component.
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2
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Related Questions
Anna volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 382 people went to The Youth Wing, 461 people went to Social Issues, and 355 went to Fiction and Literature. On Sunday, the library had 800 total visitors. Based on what Anna had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number.
Answers
Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.
Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:
\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)
Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)
Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:
\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)
Calculating the proportion:
\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)
Calculating the estimated number of visitors to The Youth Wing on Sunday:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)
Simplifying the equation:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)
Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)
Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
In a recent frisbee tournament, Hybrid scored 2 less points than Rival. Their combined scores were 28. Let h represent Hybrid and r represent Rival Which pair of equations can be used to determine their scores?
h + r = 28 h = r - 2
h + r = 28 h + r = 2
h + 28 = r h = 2
h - r = 28 h = r - 2
Answers
The pair of equations that can be used to determine their scores is h + r = 28 h = r - 2. The correct option is a.
What is an equation?Equations that happen simultaneously or a system of equations The simultaneous solution of two or more equations is necessary for algebra (i.e., the solution must satisfy all the equations in the system).
For a system to have a unique solution, the number of equations must equal the number of unknowns.
Variable h: number of points scored by Hybrid.
Variable r: number of points scored by Rival.
Hybrid scored 2 fewer points than Rival, hence:
h = r - 2.
Their combined scores were 28, hence:
h + r = 28.
Therefore, the correct option is a. h + r = 28 h = r - 2.
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The population of a town is predicted to grow according to the following model:
P = 15e0.012r
where P represents the number of people in thousands and t is the number of years since 2020. Find
the predicted population in the year 2030. Round your answer to nearest person
O 16,912 people
O 16,913 people
O 16 people
O 17 people
Answers
The predicted population in the year 2030 is 10 people
How to determine the predicted population in the year 2030From the question, we have the following parameters that can be used in our computation:
Population function, P(t)= 15е⁻⁰.⁰¹²⁺
Also from the question, we have
The variable t represents the number of years since 2020
This means that the value of t in 2030 is
t = 2030 - 2020
t = 10
So, we have
P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰
Evaluate the above products
P(10)= 15е⁻⁰.¹²
Evaluate the exponents
P(10)= 13.30
Approximate the above expression
P(10) = 13
This means that the number of people is 13
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Which polynomial functions have only the roots 1
and 4? Check all that apply.
f(x) = (x - 1)(x – 4)
f(x) = 3(x + 1)(x + 4)
f(x) =(4x - 1)(x – 4)
f(x) = 3(x - 1)(x – 4)
f(x) = 6(x - 1)(x-4)
Answers
Answer:
Hey there!
Your answer would be f(x) = (x - 1)(x – 4), 3(x - 1)(x – 4), and 6(x - 1)(x-4) .
The polynomial roots can be found by finding the values of x that make the equation equal to 0. We know that when two items are multiplied, and one of them is zero, the result is 0. Thus, we have to make only one of the items equal to 0. To make the roots 1 and 4, we have to have (x-1) and (x-4).
4-4=0, x=4
1-1=0, x=1
Answer:
A,D,E
second answer is : f(x) = (x – 3)(x – 3)(x – 6)
Step-by-step explanation:
got it right on edg2020
Q6 : "Social media has become a ubiquitous part of modern life, allowing people to connect with friends, family, and strangers from all around the world. However, social media use has been linked to a number of negative mental health outcomes, including increased rates of depression, anxiety, and stress. This is due in part to the constant pressure to present a perfect image of oneself, leading to feelings of inadequacy and self-doubt. Additionally, the endless stream of news and information on social media can be overwhelming and lead to feelings of information overload and burnout. However, not all social media use is negative. Research has also shown that social media can be a valuable tool for promoting social support and connection, particularly among marginalized communities. It can also be a source of education and awareness, allowing people to learn about important issues and engage with social and political causes." What is one negative mental health outcome associated with social media use?"
Increased social support and connection
Greater awareness of social and political issues
Higher rates of depression and anxiety
Improved self-esteem and self-worth
Answers
Higher rates of depression and anxiety are one negative mental health outcome associated with social media use
Social media and modern life:The paragraph discusses the role of social media in modern life and its impact on mental health. It notes that social media has become a ubiquitous part of life that allows people to connect with others from around the world, including friends, family, and strangers.
However, the paragraph goes on to mention that social media use has been linked to negative mental health outcomes such as depression, anxiety, and stress.
These negative outcomes may be due to the pressure individuals feel to present a perfect image of themselves online, leading to feelings of inadequacy and self-doubt.
Despite these negative outcomes, the paragraph notes that social media can also be valuable for promoting social support and connection, especially among marginalized communities.
Furthermore, it can be a source of education and awareness, allowing people to learn about important social and political issues and engage with them.
Hence,
Higher rates of depression and anxiety are one negative mental health outcome associated with social media use
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Three equations model this situation: 14 is 4 more than 2 times a number. Which equation does NOT?
Answers
Answer:
2x-4=14
Step-by-step explanation:
Harry asked a sample of 444 people how many siblings they had. Here are their responses: 0, 0, 1, 30,0,1,30, comma, 0, comma, 1, comma, 3 The mean is \bar x =1 x ˉ =1x, with, \bar, on top, equals, 1 sibling. Which of these formulas gives the standard deviation? Choose 1 answer:
Answers
The formulas give the standard deviation will be sₓ=√(0-1)²+(0-1)²+(1-1)²+(3-1)²/4.Option C is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
\(\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}\)
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that, Harry asked a sample of 4 people how many siblings they had. Here are their responses:0,0,1,3 The mean is 1 sibling.
\(\bar x =1 \\\\ n =4\)
The formulas give the standard deviation as,
\(\rm s_x = \sqrt{\frac{(x_1-\bar x)^2+(x_2-\bar x)^2 +(x_3- \bar x)^2 }{n-1} } \\\\ s_x = \sqrt{\frac{(0- 1)^2+(0-1)^2 +(1- 1)^2 + (3-1)^2}{3} }\)
Thus, the formulas give the standard deviation will be sₓ=√(0-1)²+(0-1)²+(1-1)²+(3-1)²/4.Option C is correct.
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The axis of symmetry!
Answers
Answer:
x = - 1
Step-by-step explanation:
Just by looking, we can tell that the axis of symmetry in this graph is going to be a vertical line. to make vertical lines, we start with:
x = ____
For a quadratic, the vertical line always hits the vertex. The x value of the vertex is - 1.
Therfore, the equation of the axis of symmetry is x = - 1
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Match the vocabulary to the correct operation PLZ ANSWER:(
Answers
Sum=addition
Difference=subtraction
Quotient=division
Quantity=parentheses
A direct variation includes the points (2,18) and (n,9). Find n?
Answers
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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PLEASE HURRRY
if m abd = 74 what are m abc and dbc whats the degrees of m
Answers
The correct measure of m<ABD = 79degrees
The measure of m<DBC and m<ABC are 45 and 34degrees respectively.
Find the diagram to the question attached.
From the diagram, we are given the following measures;
m<DBC = 5x + 4
m<ABC = 8x - 3
m<ABD = 79degrees
From the diagram, we can see that;
m<DBC + m<CBA = m<ABD
5x + 4 + 8x - 3 = 79
13x + 1 = 79
13x = 79 - 1
13x = 78
x = 78/13
x = 6
Get the measure of m<ABC
m<ABC = 8x - 3
m<ABC = 8(6) - 3
m<ABC = 45 degrees
Get the measure of m<DBC
m<DBC = 5x + 4
m<DBC = 5(6) + 4
m<DBC = 34degrees
Hence the measure of m<DBC and m<ABC are 45 and 34degrees respectively.
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A cone with a diameter of 16 centimeters has a volume of 320(pie)cubic centimeters. Find the height of the cone.
Answers
A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.
What is volume of cone?A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.
Cone volume is calculated using the method V=1/3πhr².
Given that,
diameter(d) = 16 cm
radius (r) = d/2 = 8 cm
volume = 320π cubic centimeters
πr²h/3 = 320π
or, [π × (8)² × h]/3 = 320π
or, h = (3 × 320)/(8)²
or, h = 15 cm
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Two wires are attached to a pole and create similar triangles with the ground. The longer wire is attached to the ground 32 feet from
the base of the pole and the shorter wire is attached to the ground 16 feet from the base of the pole.
If the cosine of the angle formed by the shorter wire and the ground is 8/41, what is the length of the longer wire?
Please help im so confused!
Answers
The length of the longer wire is 82 feet.
Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.
We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.
In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:
cos(θ) = adjacent/hypotenuse = 16/L
Given that cos(θ) = 8/41, we can substitute this value into the equation:
8/41 = 16/L
To solve for L, we can cross-multiply and solve for L:
8L = 41 * 16
L = (41 * 16)/8
L = 82
Therefore, the length of the longer wire is 82 feet.
In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.
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What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest! hundredth. 5 m cubic meters
Answers
We will have the following:
\(V=\frac{4}{3}\pi r^3\)Now, we replace the values and solve:
\(V=\frac{4}{3}(3.14)(5)^3\Rightarrow V\approx523.33\)So, the volume of the sphere is approximately 523.33 cubic meters.
***Example with an 8 m radius***
If the radius of the sphere were of 8 meters, we would have:
\(V=\frac{4}{3}(3.14)(8)^3\Rightarrow V\approx2143.57\)So, the volume of such a sphere would be approximately 2143.57 cubic meters.
What is the equation of the line that passes through the points (2,4) and (5, 13)?
Answers
Answer:
y = 3 x − 2
Step-by-step explanation:
I Use the slope formula and slope-intercept form y = m x + b to find the equation.
Hope this helps:)
The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches
Answers
Since the volume of the pyramid is 18 cubic inches, then the volume of the prism is 3 times that amount which is 54 cubic inches 2.
Therefore, the answer is D. 54 cubic inches.
The table shows the proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
hurry pls
Buckets 3 5 7
Price (dollars) 28.50 47.50 66.50
Determine the constant of proportionality.
Answers
The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.
Given that,
The table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.
We have to find the constant of proportionality.
We know that,
What are ratio and proportion?A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.
The table displays the proportional relationship between the price for a particular quantity of golf ball cans at a driving range.
Buckets 3 5 7
Price (dollars) 28.50 47.50 66.50
The constant of proportionality is calculated as,
⇒ 25.8 / 3
⇒ 9.5
Therefore, The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.
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Answer:
9.5
Step-by-step explanation:
I took the exam and got it right
Simplify.
2x + 6x2
10 + 4x2 – 3x + (-6) =
Answers
Answer: 14x,4+4x ^2-3x
Step-by-step explanation:
1. Simplify 6x\times 26x×2 to 12x12x.
2x+12x,10+4{x}^{2}-3x-6
2x+12x,10+4x
2
−3x−6
2 Simplify 2x+12x2x+12x to 14x14x.
14x,10+4{x}^{2}-3x-6
14x,10+4x
2
−3x−6
3 Collect like terms.
14x,((10-6)+4{x}^{2}-3x)
14x,((10−6)+4x
2
−3x)
4 Simplify (10-6)+4{x}^{2}-3x(10−6)+4x
2
−3x to 4+4{x}^{2}-3x4+4x
2
−3x) Hope that helps
a car uses 1 9/8 of gasoline to travel 50 3/4. how far can the car travel in miles on 1 gallon of gasoline
Answers
Answer: 30 miles
Step-by-step explanation:A typical car can travel 30 miles on just one gallon of gasoline
Question 3 of 56
Triangle ABC has vertex coordinates A(-5, 2), B(-1, 3), and C(-1, 1). It is
rotated 90° clockwise around the origin. What are the coordinates of C?
Answers
Answer:1,1
Step-by-step explanation:if you do it 90 degrees all the way around ur gonna get 1,1.
Answer:
The coordinates of A' are (-1,-3) , B' are (-2,-2) , C' are (-4,-3).
Step-by-step explanation:
1/4 times 2/2 PLS HURRY
Answers
Answer:
answer is 2/8 or simplified is still 1/4
Step-by-step explanation:
1/4
STEP BY STEP:
look at image
just remember that 2/8 can reduce to your answer, 1/4
(Pls help me! I don’t understand!) it’s as image btw
Answers
Mark used the computer for 12 hours. If the average power use of a computer per hour is 299 watts, how much power did Mark use?
Answers
Answer:
Step-by-step explanation:
To be able to solve, you need to multiply 12 (the amount of hours he used) by 299 (since he used 299 per hour) this would result in you getting a answer of 3,588 watts of power.
What is the equation of the line that passes through the point (4, -2) and has a
slope of -22
Answers
Answer:
y = - 22x+86
Step-by-step explanation:
Slope is - 22 so we solve the equation for any unknown points x and y
What’s the area of the arrows
Answers
Answer:
60 inches squared
Step-by-step explanation:
This problem can be solved by splitting the arrow into a triangle and a rectangle, and then adding the areas together.
For the rectangle, you can multiply 4 (the base) by 12 (the height) in order to get 48 inches squared.
Then, for the triangle, you can split it into two right triangles since you know that half of the base is 6, and the height is 4. Then, you would get 24 inches squared. Ordinarily you would multiply the height and base of a triangle and then divide by two to get the area, but as both right triangles are exactly the same you would end up getting double of what you dividing by two anyways.
Finally, after adding 48 and 24, you get 72 inches squared.
Select all composite numbers shown:
11
12
13
14
15
16
17
18
19
20
Answers
Answer:
12,14,16,18,20
Step-by-step explanation:
Answer:
just 20
Step-by-step explanation:
Ez
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
the object will fall a distance of 1024 feet in 8 seconds. So the answer is (C) 1024 ft.
what is distance ?
Distance is a scalar quantity that refers to the total length traveled by an object or person, without considering the direction. It is a measure of the path length between two points, usually measured in units such as meters (m), feet (ft), or kilometers (km).
In the given question,
The formula t = √(d/16) relates the time t (in seconds) it takes an object to fall a distance d (in feet) to the acceleration due to gravity, which is approximately 32.2 feet per second squared.
To find how far the object will fall in 8 seconds, we can rearrange the formula to solve for d:
t = √(d/16)
t² = d/16 (Squaring both sides)
d = 16t² (Multiplying both sides by 16)
Substituting t = 8 into the formula, we get:
d = 16(8)² = 1024
Therefore, the object will fall a distance of 1024 feet in 8 seconds.
So the answer is (C) 1024 ft.
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If you estimate that a piece of wood measures 5.5cm if it actually measures 5.62cm what is the percent error of the estimate
Answers
The percent error of the estimate is -2.14%
How to determine the percent error of the estimate?In this question, the figures are given as
Estimate = 5.5 cm
Actual = 5.62 cm
The percentage of the error is then calculated using the following equation
Error percentage = (Estimate - Actual)/Actual * 100%
Substitute the known values in the above equation, so, we have the following representation
Error percentage = (5.5 - 5.62)/5.62 * 100%
Evaluate
Error percentage = -2.14%
Hence, the error percentage is -2.14%
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The mean monthly rainfall is 3.245 inches.
How to find the mean of the monthly rainfall?For a set of N numbers {x₁, x₂, ...}, the mean of these N numbers is:
M = {x₁ + x₂ + ...}/N
Here we want to find the mean of the rainfall in inches, then we just need to add the 12 values in the table and then divide by 12, we will get:
M = (2.22+1.51+1.86+2.06+3.48+4.57+ 3.27 + 5.40 + 5.45 + 4.34+2.64+ 2.14)/12
M = 3.245
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