The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, each cross section perpendicular to the x -axis is a semicircle. What is the volume of the solid?
Answers
Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]
The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:
[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]
Substitute:
[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]
Simplify:
[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]
Integrate:
[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]
Evaluate:
[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]
The volume of the solid is π/40 cubic units.
Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
How to find the volume of a three dimensional region bounded by curves?For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.
We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.
The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1
Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.
If we take [tex]dx[/tex]x-axis, then the curve [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]
Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:
[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).
Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
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Related Questions
The height between two floors of a building is 10 feet. How many stairs would be required
if the rise of each stair is 8 inches?
Note: 1 foot = 12 inches
Answers
Answer:
15 stairs would be needed
Step-by-step explanation:
10x12= 120
15 x 8 = 120
the following sorting algorithm is stable and in runs in place. none of the others quicksort counting sort mergesort. true or false
Answers
A stable sorting algorithm is one that keeps the relative order of two equal elements. Quicksort is a sorting algorithm that has a high degree of instability, which means that it may alter the relative order of two equal components.
Which sorting algorithm is stable?The Merge Sort, Timsort, Counting Sort, Insertion Sort, and Bubble Sort are just a few examples of popular sorting algorithms that are by their very nature stable. Others, like Quicksort, Heapsort, and Selection Sort, are erratic. Stable sorting algorithms can be modified to be more efficient.
Because we swap elements according on the location of the pivot, QuickSort is an unstable algorithm (without considering their original positions). A sorting algorithm is said to sort in-place if it never stores more than a fixed number of input array members outside of the array. If the order of elements with the same value is not altered by a sorting technique, it is stable. Binary insertion sort is the only stable algorithm available from the options offered.
Therefore the correct answer is false.
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Give slope for these points blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
Answers
The slope equation is: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
The slope of the points (0, 2) and (1, -3) is: -5
The slope of the points (-5, -8) and (10, 12): 4/3
First graph: m = 1
Second graph: m = -2/3.
What is the Slope of a Line?The slope of a line is calculated using the formula below:
Slope (m) = rise/run = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Therefore, the equation of the slope is expressed as: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Find the slope of the points (0, 2) and (1, -3):
m = change in y / change in x = (-3 - 2) / (1 - 0)
m = -5/1
Slope (m) = -5
Find the slope of the points (-5, -8) and (10, 12):
Slope (m) = (12 -(-8)) / (10 - (-5))
m = 20/15
m = 4/3
Find the slope of the first graph:
Slope (m) = rise/run = 1/1
m = 1
The slope of the second graph = rise/run = -2/3.
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I found it is 273 Megabytes is being download if the download is 17.7% completed how many megabytes have been downloaded Round your answer to the nearest 10th
Answers
The megabytes that have been downloaded will be 48 megabytes.
How to depict the percentage?Based on the information, percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since 273 megabytes is being download if the download is 17.7%, the megabytes that have been downloaded will be:
= 17.7% × 273
= 48 megabytes.
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Based on the relative frequency histogram below , which of the following statements is supported by the plot? i. The IQR of the distribution is roughly 10
ii. There are no outliers in the distribution.
iii. It is not possible to estimate the median without knowing the sample size. iv. The distribution is multimodal v. The mean of the distribution is smaller than its median.
Answers
The statement supported by the plot is that the IQR of the distribution is roughly 10. It is possible to estimate the median from the plot, and the distribution appears to be unimodal, with the mean being smaller than the median. There are no outliers shown in the plot.
The relative frequency histogram provides a visual representation of the distribution of the data. From the plot, it is possible to estimate the median, which is the middle value of the distribution, as well as the interquartile range (IQR), which is the difference between the upper and lower quartiles. The IQR of the distribution is roughly 10, which can be seen by the distance between the upper and lower quartiles in the plot. Additionally, the distribution appears to be unimodal, which means that it has only one mode or peak. It is also apparent that the mean of the distribution is smaller than its median, as the peak is shifted to the left of the median. Finally, there are no outliers shown in the plot, as all of the values appear to be within the range of the distribution.
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What is the equation for the line that passes through the points (3, 4) and (5,8)
Answers
The equation of a line is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To find the equation of the line that passes through the points (3, 4) and (5, 8), we need to first calculate the slope of the line.
The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we have:
m = (8 - 4) / (5 - 3) = 4/2 = 2
Now that we know the slope of the line, we can use one of the given points to find the y-intercept. Let's use the point (3, 4). If we plug the values of x and y into the equation y = mx + b, we get:
4 = 2 * 3 + b
4 = 6 + b
-2 = b
Therefore, the equation of the line that passes through the points (3, 4) and (5, 8) is:
y = 2x - 2
Let ƒ(x) = 8(1/4)^X+³ — 4.
The graph of f(x) is translated 4 units down to form the graph of g(x).
Answers
The function f(x) is translated by 4 units down to form a function g(x) will be written below.
[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4[/tex]
Simplify the equation, then we have
[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4\\\\\\f(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4[/tex]
The function f(x) is translated by 4 units down to form a function g(x) will be given as,
[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4-4\\\\\\g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8[/tex]
The function f(x) is translated by 4 units down to form a function g(x) will be [tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]. The graph is drawn below.
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The sum of heart rate readings taken five times for of Kundaval and Kulazhi are 400 and 360 respectively. And their projected deviations are 3,16 and 2.0 respectively. If you were. a doctor, who would you treat immediately?.
Answers
If i were a doctor, the person I would treat immediately is; Kundaval because he has higher heart rate and larger projected deviation.
We are given that;
Sum of heart rates taken 5 times for Kundaval = 400
Sum of heart rates taken 5 times for Kulazhi = 360
Projected deviation for Kundaval = 3.16
Projected deviation for Kulazhi = 2.0
Now, mean simply means the average of a set of given data while standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Thus, as a doctor, I would prioritize the treatment of the patient that has higher heart rate and larger projected deviation. Thus, we would conclude that Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16 would be the one that should be treated first.
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A rectangular walkway is 38 feet long and has a perimeter of 80 feet the department of public works wants to spread gravel on the walkways how many square feet of gravel are needed to cover the entire walkway ?
Answers
Answer:
76 [tex]ft^{2}[/tex]
Step-by-step explanation:
We are looking for the area of the walkway.
Area = length times width.
We know the length, we need to find the width.
Perimeter is the distance around the rectangle. It is two length and two widths.
p = 2l + 2w
80 = 2(38) + 2W
80 = 76 + 2W Subtract 76 from both sides.
80 - 76 = 76 - 76 + 2w
4 = 2w Divide both sides by 2
[tex]\frac{4}{2}[/tex] = [tex]\frac{2w}{2}[/tex]
2 = w
Now that we know the width we can find the area
a = 38 x 2
a = 76 [tex]ft^{2}[/tex]
Answer:
Length=38 ft
breadth=?
Perimeter=80 ft
we know,
Perimeter= 2(length+breadth)
or,80ft=2(38 ft + breadth)
or,40 ft=38ft + breadth
or,breadth=40 ft-38 ft
:. breadth=2 ft
Now,
Area of walkway= length ×breadth
=38 ft×2 ft=76 ft²
Hence,72 square feet of gravel is required to cover the entire walkway.
Which of these expressions is equivalent to 5.8 ÷ 1.15 ?
0.58÷115 5.8÷115 58÷115 580÷115
Answers
The expression that is equivalent to 5.8 ÷ 1.15 is 580 ÷ 115
What are equivalent expressions?Equivalent expressions are expressions that have equal values when compared
How to determine the equations that are equivalent?From the question, we have the following parameters that can be used in our computation:
5.8 ÷ 1.15
Divide both sides of the equation by 1/10
So, we have the following representation
5.8 ÷ 1.15 = 5.8/(1/10) ÷ 1.15/(1/10)
Evaluate the quotients
So, we have the following representation
5.8 ÷ 1.15 = 58 ÷ 11.5
Multiply both sides of the equation by 10
So, we have the following representation
5.8 ÷ 1.15 = 580 ÷ 115
Hence, the equivalent equation is 580 ÷ 115
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what is the measure of angle x
Answers
Answer:
61 degrees
Step-by-step explanation:
sum of all angles of a triangle is 180 degrees
82+37+x=180
119+x=180
-119. -119
x=61
hopes this helps
180 Degrees
[tex]37+82+x=180[/tex]
[tex]119+x=180[/tex]
[tex]x+119=180[/tex]
Subtract 119 from both sides:
[tex]x+119-119=180-119[/tex]
[tex]\fbox{x = 61}[/tex]
find the measure of m< VTK
Answers
Measure of angle VTK is 90°.
Define angle.Angles come in many different varieties in geometry. Angle is among the most crucial and fundamental units. Two rays or lines are linked at their shared terminus when they create an angle. We use angles in many facets of our daily lives, starting with the construction of buildings, dams, and monuments, not only in mathematics. The study of angles is essential to civil engineering. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Given
∠VTK = 90°
∠VMK = 90°
∠VTK is given
∠VTK = 90°
Measure of angle VTK is 90°.
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Determine a series of transformations that would map Figure T onto Figure U.
Press "try" to test a transformation or sequence of transformations.
Answers
The series of transformations that would map Figure T onto Figure U are:
Rotation TranslationWhat is rigid transformation?
Transformation is a process in which the dimensions of an object is resized, or its orientation is changed.
Rigid transformation is a topic that involves resizing an object, or changing its orientation. Some common methods used in transformation are: reflection, dilation, rotation and translation.
Reflection is the process in which a given object is turned about a reference point or line.Dilation involves changing the dimensions of a given object. Thus its size will be affected.
Rotation involves turning an object at a certain angle. Translation implies moving a whole object in a given direction and number of units.
In the given question, the required series of transformation are:
i. First rotating figure T at an angle of 90 degrees using its base as the reference line.
ii. Then translating the image some units.
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tan^2x/sec^2x + cot^2x/csc^2x
Answers
The value of the trigonometric expression will be 1. Then the correct option is C.
What is trigonometry?Mathematical capabilities inspect the collaboration between the aspects and points of a three-sided structure.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
⇒ tan²x / sec²x + cot²x / cosec²x
Simplify the expression, then the value of the expression is given as,
⇒ tan²x / sec²x + cot²x / cosec²x
⇒ (sin²x × cos²x) / cos²x + (cos²x × sin²x) / sin²x
⇒ sin²x + cos²x
⇒ 1
The worth of the mathematical articulation will be 1. Then, at that point, the right choice is C.
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Consider the following three polynomial functions.
f(x) =3x3 +5x-2
9 (x) =582-3x +2 m(x) =2x2 - 2x
Write an expression to represent f(x) + [g (x) - m(x)].
Use the carrot (^) for exponents and leave no spaces between terms.
Answers
The Solution for the given problem is 6x² +4x
What is Polynomial?
A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Solution:
We are given with the values of the following terms f(x), g(x), and m(x)
f(x) = 3x² + 5x - z
g(x) = 5x² - 3x + z
m(x) = 2x² - 2x
To find: f(x) + [g(x) - m(x)]
so, we need to put the respective values in the equation and simplify it
3x² + 5x - z + [5x² - 3x + z - 2x² + 2x]
3x² + 5x - z + [3x² - x + z]
6x² +4x
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Tim has 42 marbles. He divides them equally into 7 bags. How many marbles are in each bag?
Answers
Answer:
6 marbles per bag
Step-by-step explanation:
42 marbles * 1 bag / 7 bags =
42 * 1/7 =
42/7 = 6 marbles per bag
1 bag represents each bag of the 7 total bags.
Multiply 1 bag / 7 bags with 42 marbles(total amount of marbles) to get the marbles in EACH bag.
Answer:
let x = marbles in a bag
x = 42/7
x = 6
There are 6 marbles in each bag for 7 bags(6) + (6) + (6) + (6) + (6) + (6) + (6)
This is 7 bags, total of 42 marbles
this is my own explanation moderator, please dont delete just because its almost the same with previous answer. well its because its the only way to solve it hehe but i add another explanation, i really dont want to get warnings for this kind of questions you knoww..
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-How many groups of \dfrac{7}{4}
4
7
start fraction, 7, divided by, 4, end fraction are in 111?
Answers
There are two groups of [tex]\dfrac{7}{4}[/tex], an integer which is equal to 1, and 0.75 which is decimal.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
The given fraction is,
[tex]\dfrac{7}{4}[/tex].
To find the groups of fraction,
Simplify the fraction,
[tex]\dfrac{7}{4} = 1 \dfrac{3}{4}\\\\ = 1.75[/tex]
There are two groups in the fraction of [tex]\dfrac{7}{4}[/tex] ,
Integer part which is 1.
And decimal part which is 0.75.
Hence, there are two groups of fraction [tex]\dfrac{7}{4}[/tex].
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the value of y varies exponentially with respect to x and the 1 -unit growth factor is 1.8 . which of the following is the best explanation for the meaning of this growth factor?
Answers
We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
Given that,
With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.
We have to find which of the following best describes the significance of this growth factor.
We know that,
The required expression for y with respect to x is
y=(1.8)ˣ------>equation(1)
1.8=1- unit growth factor.
Whenever x changes by 1.
x=x-1----->equation(2)
Putting equation (2) in (1)
y'=1.8ˣ⁺¹
y'=1.8ˣ×1.8----->equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ
y'=(1.8)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.
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y=(1.8)ˣ equation(1)
1.8=1- unit growth factor.
Whenever x changes by 1.
x=x-1 equation(2)
y'=1.8ˣ⁺¹
y'=1.8ˣ×1.8 equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ
y'=(1.8)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.
The greatest common factor of 250 and 300 is?
Answers
Answer:
GCF: 50
Step-by-step explanation:
Let's test
50 ( 5 + 6)
= 250 + 300
So, my answer is correct!
How many positive integers have distinct prime digits?
Answers
Answer:
64
Step-by-step explanation:
There are 4 prime digits: 2, 3, 5, and 7.
If the number is one digit, there are 4 possible numbers.
If the number is two digits, there are 4(3)=12 possible numbers.
If the number is three digits, there are (4)(3)(2)=24 possible numbers.
If the number is four digits, there are (4)(3)(2)(1)=24 possible numbers.
Taking the sum, the answer is 64.
What is the value of x in the triangle?
3√2
A. 3√2
B. S
C. 6
D. 6√2
E. 2√2
Answers
Answer: D
Step-by-step explanation:
Santa Santa can deliver presents to 15 children per hour. What is the maximum number of presents Santa can deliver to children’s in three hours?
Answers
Answer:
45
Step-by-step explanation:
15(3) = 45
determine the equation of the parabola that opens up, has vertex (7,7) and a focal diameter of 16.
Answers
The equation of a parabola that opens up and has a vertex at (7,7) can be written in the form
y = a(x - 7)^2 + 7.The focal diameter of the parabola is 16, which means that the distance from the vertex to the focus is 8 (since the focal diameter is the sum of the distances from the vertex to the focus and from the vertex to the directrix).
To find the equation of the parabola, we need to determine the value of a that will give us the correct focal diameter. The distance from the vertex to the focus is given by the equation sqrt(4a(y - 7)), so we can set this equal to 8 and solve for a:
sqrt(4a(y - 7)) = 8
4a(y - 7) = 64
a(y - 7) = 16
a = 16 / (y - 7)
Substituting this value of a back into the equation for the parabola gives us:
y = (16 / (y - 7))(x - 7)^2 + 7
This is the equation of the parabola that opens up, has a vertex at (7,7), and a focal diameter of 16.
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{20 PTS}
4/6 = ??? x 1/6
what number makes this equation true? fill in the blank
Answers
Hope this helps :)
Choose the function whose graph is given by:
A. y=-3.5cos x
B. y=3.5sin x
C. y=sin(3x)
D. y=2.5sin x
Answers
Answer:
A a option is right because cause 3 is near to zero that's value one and y 3.5 x 1near equal to 3 something
Using the year 2000 as the base year, compute
- nominal GDP [1 point]
- real GDP [1 point]
- GDP de
ator [1 point]
Answers
1) Nominal GDP = Current year price* Current year quantity
= 500*3000 + 400,000*20
= 1,500,000 + 8,000,000
= $9,500,000
2) Real GDP = Base year price* Current year quantity
= 500*2000 + 400,000*10
=1,000,000 + 4,000,000
= $5,000,000
3) GDP Deflator = Nominal GDP/Real GDP
=9,500,000/5,000,000
statistics that specify how likely findings are to be true for other populations or in other locales is called statistics.
Answers
The study of data collection, analysis, presentation, and interpretation is known as statistics.
Given,
What is statistics?
Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activity and census data.
Types of statistics;
Based on the characteristics, the various statistical kinds are divided: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as using pie charts, bar graphs, or tables.
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1. What is the vertical distance between (5, –12) to (5, 17)?
2. What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?
3. The point (–7, 6) was reflected over an axis to become the point (7, 6). Which axis was it reflected over? Explain.
Answers
The required solutions for each of the questions are obtained as 29 units, 235.2 cubic yards and y axis respectively.
What is the distance formula?The distance formula in coordinate geometry is used to find the distance between two points whose coordinates are given as (x₁, y₁) and (x₂, y₂) as √((x₁ - x₂)^2 + (y₁ - y₂)^2).
By knowing the sides, the area of different polygons can be found.
(1) The vertical distance between points (5, –12) and (5, 17) is given by distance formula as below,
√((5 - 5)² + (-12 - 17)²) = 17
(2) The volume of the rectangular prism is given as,
Volume = Area of base × Height of the prism
= 14(¹/₅) × 7 × 8
= 21/5 × 56 = 235.2
(3) The given points are (–7, 6) and (7, 6).
It is clear that after reflection y coordinate does not change.
Which implies that the axis of symmetry is y axis.
Thus, the axis of reflection is y axis.
Hence, the vertical distance between points, the volume of the prism and the axis of reflection are 29 units, 235.2 cubic yards and y axis respectively.
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Which of the following functions is graphed below?
Answers
Answer:
D
Step-by-step explanation:
Looking at the graph, when x <= 1, the line is x + 6. Only one answer has this option.
I really need help with these questions please help
Answers
The area, lengths and dimensions of the plot of land and the situation picture are as follows;
a. 282.2 ft
b. 2330 ft²
c. 42.8 ft
Exercise 364
The true statements are;
The perimeter of ΔPQU is greater than 13 units
The perimeter of ΔPQR is 12 units
The area of ΔPST is 7.5 square units
What is the perimeter of a shape or figure?The perimeter of a shape or figure is the length or distance of the edge boundary of the shape.
a. The perimeter of the plot of land, P, can be found as follows;
P = (70 - 0) + (60 - 0) + (80 - 0) + √((80 - 60)² + (0 - 70)²) ≈ 282.8
The perimeter of the fencing is approximately 282.8 feet
b. The shape of the plot of land is a trapezium
Area of the plot of land is therefore; A = 0.5 × (60 + 80) ×70 = 4900
The shape of the Parking Area is a trapezium, therefore;
Area of the Parking Area = 0.5 × ((49 - 8) + (60 - 8)) ×(70 - 50) = 930
The shape of the Warehouse is a square, therefore;
Area of the Warehouse = (49 - 8) × (50 - 10) = 1640
Area of the plot of land that does not include the warehouse and the parking area is therefore;
Required area = 4900 - (930 + 1640) = 2330
The area of the plot of land that does not include the warehouse and the parking area is 2330 ft²
c. The sum of the length of the legs of the parking area trapezoid, L, can be found as follows;
L = (70 - 50) + √((70 - 50)² + (60 - 49)²) ≈ 42.8
The total length of fence needed is about 42.8 ft
Exercise 364
The true statements are found as follows;
The perimeter of the ΔPQU = 4 + 4 + 4·√2 ≈ 13.66 > 13The perimeter of the ΔPQR = 3 + 4 + √(3² + 4²) = 12The perimeter of QRSTU = 3 + √(5² + 2²) + √(3² + 4²) + 4·√2 + √(5² + 2²) ≈ 24.43
The perimeter of QRSTU > 24
The area of ΔPRS = 0.5 × 3 × 5 = 7.5
The area of triangle ΔPST = 0.5 × 3 × 5 = 7.5Learn more about finding the area of shapes on the coordinate plane here:
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