Answer:
The volume of a 3D figure can be determined by the sum of all the cross-sections of that 3D figure parallel to the base
Step-by-step explanation:
We need to understand what a cross-section of a 3D figure ?
A cross section is the shape we get when cutting straight through an object
and in geometry it is the shape made when a solid is cut through by a plane.
=> the cross section is parallel to the base of the figure.
So that the area of the cross-section is determined by its shape
Hence, The volume of a 3D figure can be determined by the sum of all the cross-sections of that 3D figure parallel to the base
The shape of a cross-section parallel to the base of a 3D figure determines its volume, as the volume is calculated by multiplying this area by the figure's height. For parallelepiped figures, the cross-sectional area is found using the magnitude of the cross product of base side vectors.
Understanding the relationship between the shape of a cross-section and the volume of a three-dimensional figure involves recognizing that for solids with parallel sides, such as a cylinder or parallelepiped, the cross-section parallel to the base will have the same shape as the base. When this cross-section is multiplied by the height of the figure, the result is the volume of that shape (V = Ah). In terms of vectors representing the base in three-dimensional space, for a parallelepiped, the cross-sectional area can be found by the magnitude of the cross product of vectors given by the sides forming the base.
Moreover, regardless of changes in length or width, as shown in Table 3, if a volume is kept constant but the shape is altered to be elongated or flattened, the shape of the cross-section parallel to the base still determines the volume through the base area times the height formula.
This is significant in various fields, including physics, engineering, and architecture, where understanding the volume and dimensions of structures and shapes is crucial.
In the diagram above, O is the centre of circle, PAQis the tangent to the circle at A, AD is parallel to OC and ∠PAD = 28°. Find,
(i) ∠ABC
(ii) ∠OAC
(iii) ∠OCD
The answer is attached.
Complete the following statement.
-0.3 is graphed to the______ of 0.
Right
Left
Answer:
left
Step-by-step explanation:
because -0.3 is a negative number, it will be on the left side of the x axis.
JI kkk dm em an s k. Gn dnzexnexnrxnex
Answer:
6
Step-by-step explanation:
The mode of a set of data values is the value that appears most often. ^ appers 4 times.
On Monday sue young ran 2.5km on Tuesday she ran another 3.6 km and on Wednesday she ran 4.1 how much farther did sue young ran on Wednesday than on Monday
Answer:
1.6 km
Step-by-step explanation:
subtract 2.5 from 4.1
Need help with this
Answer:
6.169
-1.009= 5.1 48
Step-by-step explanation:
I did it backwards
Answer:
Top = 6.157 bottom =5.148
Step-by-step explanation:
Sarah is renting a cabin for vacation and has two choices. Cabin Arents for $100 per day and has a
$50 insurance fee. Cabin B rents for $120 per day and has a $10 insurance fee. Which system of
equations below will determine when the two choices will have the same cost?
Answer:
x = 2 days
y = 250 $
Step-by-step explanation:
We call "y" total renting costs and "x" total vacation days
according to that in first case we have:
y = 100*x + 50
And for the second case
y = 120*x + 10 (1)
That two equation system represent the equation system of the situation, therefore if we solve that system we will determine the choises with same costs
equating these two equations:
100*x + 50 = 120*x + 10
50 - 10 = 120*x - 100*x
20*x = 40
x = 2 days
Plugging that value in any of the equation (1) or (2) we get y value
y = 120*2 + 10
y = 250 $
Write the expression for when you translate the graph of y =|3x| − 5 one unit to the right.
Answer:
The answer is |3x-3|-5
I have RSM too it’s irritating
Answer:
y=|3x-3|-5
Step-by-step explanation:
y=|3x-3|-5
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Surface area of Square and Triangular Pyramids
Due 05/08/20 11:59pm
Use the figure to answer exercises 6-7.
12 ft
7 ft
6. Dennis drew a square pyramid and its net to represent a fort. Complete the net by filling in the
missing measure. Choose the correct answer below.
A
C.
D.
a
75ft
12ft
3.56
Cck to select your answers)
Rew
progress
& Back
Next
Answer:
B
Step-by-step explanation:
A car Travels at a speed of 65 miles per hour. How far will it travel in 5hours?
b(n)=−1(2) ^n−1
What is the 5th term in the sequence?
Answer:
8
Step-by-step explanation:
aₙ = 2ⁿ⁻¹
a₅ = 2⁴⁻¹ =2³=8
I need help ASAP please
which of these is the best estimate of the volume of this cereal box?
Answer:
234 cubic inches
Step-by-step explanation:
12.9 will round to 13
9.2 will round to 9
2.2 will round to 2
the equation for volume is [tex]V=whl[/tex] which mean you will multiply all three of the numbers to get 234 cubic inches
i hope i could help :)
The equation y = log b^x
is equivalent to the exponential form
If [tex]\(y = \log_b(x)\)[/tex], then [tex]\(b^y = x\)[/tex] is the equivalent exponential form.
The logarithmic equation [tex]\(y = \log_b(x)\)[/tex] is equivalent to the exponential form [tex]\(b^y = x\)[/tex]. These two forms are related by the definition of logarithms.
In the logarithmic form [tex]\(y = \log_b(x)\)[/tex], [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(x\)[/tex] is the argument of the logarithm, and [tex]\(y\)[/tex] is the exponent to which the base [tex]\(b\)[/tex] must be raised to obtain [tex]\(x\)[/tex].
In the exponential form [tex]\(b^y = x\)[/tex], [tex]\(b\)[/tex] is the base, [tex]\(y\)[/tex] is the exponent, and [tex]\(x\)[/tex] is the result of raising the base [tex]\(b\)[/tex] to the power of [tex]\(y\)[/tex].
So, if [tex]\(y = \log_b(x)\)[/tex], then [tex]\(b^y = x\)[/tex] is the equivalent exponential form.
The probable question may be:
"What is the exponential form equivalent to the logarithmic equation [tex]\(y = \log_b(x)\)[/tex], where [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(x\)[/tex] is the argument, and [tex]\(y\)[/tex] is the exponent? Provide the expression in the form [tex]\(b^y = x\)[/tex]."
The equation [tex]\(y = \log_b^x\)[/tex] can be represented in exponential form as [tex]\(b^y = x\).[/tex]
Explanation:When dealing with logarithms and exponential functions, there exists an inverse relationship between them. The logarithm is the inverse of the exponential function, and vice versa. In the given equation [tex]\(y = \log_b^x\),[/tex] the logarithm is in base \(b\) with an exponent of \(x\). To rewrite this equation in exponential form, we need to switch from logarithmic notation to exponential notation.
In exponential form, the base[tex](\(b\))[/tex]is raised to the power of the logarithm ((y)), resulting in [tex]\(b^y\).[/tex] The result of this exponential expression is the value (x\), which is the argument of the logarithm. This transformation showcases the fundamental relationship between logarithms and exponentials, demonstrating that they are different representations of the same mathematical concept.
Expressing the equation as[tex]\(b^y = x\)[/tex]in exponential form clarifies how the logarithmic statement[tex](\(y = \log_b^x\))[/tex] translates into an equivalent exponential form. It emphasizes the reciprocal relationship between logarithms and exponentials, providing a clear understanding of how these forms interrelate in mathematics.
This transformation from logarithmic to exponential form serves to simplify expressions, solve equations, and understand the fundamental connection between logarithms and exponentials in mathematical operations.
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Can someone help me please?
Answer:
l
Step-by-step explanation:ll
In boot camp, a cadet must use a rope swing to cross an obstacle without falling into the water hazard below. Unfortunately, they miss the platform on the other side and swing back to where they started. If it takes the cadet 3.5 seconds to swing from one side of the obstacle to the other and back, how Lind is the rope swing? Use the formula: T= 2 pi square root over L/9.8
Answer:
3.04m
Step-by-step explanation:
Time taken to swing the rope = 3.5s
Length of the rope = L
T = 2π√(L / 9.8)
3.5 = 2π√(L / 9.8)
take the square of both sides
(3.5)² =[2π√(L/9.8)]²
12.25 = 39.48 × (L / 9.8)
12.25 = 39.48L / 9.8
39.48L = 12.25 × 9.8
39.48L = 120.05
L = 120.05 / 39.48
L = 3.04m
The length of the rope is 3.04m
Answer:
Step-by-step explanation:
3.0meters
What is mArc B C? 50° 80° 100° 130°
Answer:
130
Step-by-step explanation:
The measurement of arc BC is 130°.
Step-by-step explanation:
Given : circle with origin O, with two line segments AC and BD which are also diameters.
Measurement of arc AB = (3 x -70)° =
Measurement of arc DC= (x +10)° = ∠3
To find : Measurement of arc BC = ∠2 =?
Solution:
Let angle subtended by the arc AC = ∠1 = (3 x -70)°
Let angle subtended by the arc BD = ∠2
Let angle subtended by the arc DC = ∠3 = ( x + 10)°
Let angle subtended by the arc AD = ∠4
AC and BD are intersecting each other at O.
So, ∠1 = ∠3 (vertically opposite angles)..[1]
∠2 = ∠4 (vertically opposite angles)..[2]
(3 x -70)° = (x +10)° (from [1])
3x - x = 10 + 70
∠1 = ∠3 = (x +10)° = (40 +10)° = 50°
∠1 + ∠2 + ∠3 + ∠4 = 360°
50° + ∠2 + 50° + ∠2= 360° (from [2])
2∠2 = 360° -50° - 50°
2∠2 = 260°
∠2 = 260° ÷ 2
∠2 = 130°
The measurement of arc BC is 130°.
The measurement of arc BC is 130°.
A circle with origin O, with two line segments AC and BD which are also diameters.
Measurement of arc AB = (3 x -70)° =
Measurement of arc DC= (x +10)° = ∠3
Measurement of arc BC = ∠2 =?
Let angle subtended by the arc AC = ∠1 = (3 x -70)°
Let angle subtended by the arc BD = ∠2
Let angle subtended by the arc DC = ∠3 = ( x + 10)°
Let angle subtended by the arc AD = ∠4
AC and BD are intersecting each other at O.
So, ∠1 = ∠3 (vertically opposite angles)..[1]
∠2 = ∠4 (vertically opposite angles)..[2]
(3 x -70)° = (x +10)° (from [1])
3x - x = 10 + 70
What is the circumference?
The circumference of the circle is 360 degrees the circle.
∠1 = ∠3 = (x +10)° = (40 +10)° = 50°
∠1 + ∠2 + ∠3 + ∠4 = 360°
50° + ∠2 + 50° + ∠2= 360° (from [2])
2∠2 = 360° -50° - 50°
2∠2 = 260°
∠2 = 260° ÷ 2
∠2 = 130°
The measurement of arc BC is 130°.
To learn more about the circle visit:
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What is the value of x? A) 10 B) 12 C) 15 D) 17
Answer:
c) 15
Step-by-step explanation:
Which situation can be represented by the equation below?
15 - x = 63.75
Answer:
The last one
Step-by-step explanation:
The first one would be multiplication because you want to find the total thickness, the second one is division because it gives the total value and the amount of bags, the third one is addition because it gives you a starting value and says that they work this amount more in this month, and the last one is subtraction because he first pays with a gift card, and then with cash.
Hopefully that helped
The situation that can be represented by the equation 15 - x = 63.75 is (d)
How to determine the situation?The equation is given as:
15 + x = 63.75
The above equation is a addition equation.
This means that the situation or scenario that describes the situation must illustrate addition.
From the list of given option, the option (d) perfectly describes the scenario.
This is so because 15 represents the worth of gift card, 63.75 represents the total amount and x represents the amount spent in cash
Read more about linear equations at:
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find the area of the shaded region. round to the nearest hundredth. use 3.14 for pi.
7.1 in.
The base of the rectangular pyramid shown has an
area of
Sulare in
5.6 in.
5 in.
10 in.
5.6 in.
A triangular face with a base of 10 inches has an area
of square inches.
A triangular face with a base of 5 inches has an area of
square inches.
The total surface area of the pyramid is
square inches.
7.1 in.
5 in.
10 in.
Answer:
1:The base of the rectangular pyramid shown has an area of 50 square inches
2:A triangular face with a base of 10 inches has an area of 28 square inches
3:A triangular face with a base of 5 inches has an area of 17.75 square inches
4:The total surface area of the pyramid is 141.5 square inches.
Step-by-step explanation
How would you slice through a cube such that the figure formed by the intersecting plane is a triangle?
A. from the upper left edge of the cube to the lower right edge
B. perpendicular to the base
C. parallel to the base
D. passing through three intersecting edges
Answer: passing through three intersecting edges
Step-by-step explanation:
To create a triangle by slicing a cube, D. pass the slicing plane through three intersecting edges, such as AB, FE, and DH, to intersect the cube and form a triangular cross-section.
To slice through a cube such that the figure formed by the intersecting plane is a triangle, you would need to follow option D, passing through three intersecting edges. Imagine the cube has vertices labeled A to H, with ABCD and EFGH being the top and bottom faces respectively, and the vertical edges connecting the corresponding vertices of these two faces.
By slicing through edge AB, edge FE, and edge DH, you would create a plane that intersects the cube in such a way that the section of the cube cut by this plane is a triangle with vertices at the points where the plane cuts through the edges AB, FE, and DH.
Which of these probability values fit the tree diagram?
(Tree Diagram picture included)
Answer:
your awnser would be be
Step-by-step explanation:
it would be b because i took this test
how many cubic feet of water can the following in ground swimming pool hold
a)42 ft3
b)144 ft3
c)303 ft3
d)528 ft3
The mean age of a student book club is 14.2 years. A 27-year-old teacher is
invited to join the club. How does the teacher's age affect the mean?
Answer: The teacher's age increases the mean.
Step-by-step explanation:
14.2 + 27 = 41.2 years
41.2/2 = 20.6 years
20.6 years > 14.2 years
Adding the 27-year-old teacher to the student book club, which has a current mean age of 14.2 years, will increase the mean age of the club.
Explanation:When a 27-year-old teacher is invited to join the book club with an average age of 14.2 years, the teacher's age will increase the mean (average) age of the club members. This occurs because the mean age is calculated by adding all of the ages together and dividing by the total number of individuals in the group. Adding a number that is significantly higher than the current mean will raise the overall total, which, when divided by the new total number of individuals, will result in a higher average age than 14.2 years. We do not have the exact number of original club members, so we cannot calculate the new mean exactly, but we can confidently say the mean age will increase due to the addition of the 27-year-old teacher's age.
compare 6.2054 to 5.3115
Answer: 6.2054 > 5.3115
Compare 6 and 5
6 > 5
Therefore 6.2054 > 5.3115
Answer:
[tex]6.2054 > 5.3115[/tex]
Step-by-step explanation:
[tex]6.2054 > 5.3115[/tex]
it's easy, first compare Number 6 and 5
[tex]6 > 5[/tex]
Which expression represents “6 more than x”? A. x−6 B. 6ix C. x+6 D. 6 − x
Answer:
D. -6.
Step-by-step explanation:
The inverse is the number when added to 6 results in 0.
So it is 0 - 6 = -6. (6 + -6 = 0)
Answer: x+6
Step-by-step explanation:
6 more than (+) x
If the distance from the center of a regular pentagon to one of the vertices is 15 units, what is the length of one of the sides?
Select one:
A. 15.4
B. 17.6
C. 19.0
D. 24.3
Answer:
B. 17.6
Step-by-step explanation:
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Which symbol makes this statement true?
7.1 _____ -7.1
>
<
=
The greater than sign is what makes it true because a positive number is always greater than a negative number.
7.1 > -7.1
Answer:
> is the answer
Step-by-step explanation:
Some times it is hard to understand which symbol it is. - 7.1 is left of the number line, so that mean its is less that a whole number/ full decimal.
Pls mark me as brainliest, thank you have a wonderful day!
Passengers of flyaway airlines can purchase tickets for either business class or economy class. On one particular flight there were 154 passengers. Let x be the number of business class passengers and y be the number of economy class passengers on this flight.
Use the information above to write down an equation in x and y.
On this flight the cost of a ticket for each business class passenger was 320 euros and the cost of a ticket for each economy class passenger was 85 euros. The total amount that Flyaway Airlines received for these tickets was 14970 euros.
Use this information about the cost of the tickets to write down a second equation in x and y.
Find the value of x and the value of y.
The airlines finance officer write down the total amount received by the airline for these tickets as 14270 euros.
Find the percentage error.
Answer:
x = 8
y = 146
Error = 4.86%
Step-by-step explanation:
Number of business class passenger = x
and the economy class passenger = y
Total number of passengers = 154
x + y = 154 ------(1)
Cost of business class tickets and economy class tickets are €320 and €85 respectively.
Total amount received by airlines is €14970.
320x + 85y = 14970
64x + 17y = 2994 --------(2)
Multiply equation (1) by 17 and subtract from equation (2)
(64x + 17y) - (17x + 17y) = 2994 - 2618
47x = 376
x = 8
From equation (1),
8 + y = 154
y = 154 - 8
y = 146
Airline officer wrote down the amount received as €14270
Then difference from the actual amount received = 14970 - 14270
= €700
% Error = [tex]\frac{\text{Difference in amount}}{\text{Actual amount}}\times 100[/tex]
= [tex]\frac{700}{14970}\times 100[/tex]
= 4.676
≈ 4.68%
Therefore, x = 8 and y = 146
and % error = 4.68%
combine like terms. x + 8y - 5y + 5y
Answer:
x+8y
Step-by-step explanation:
add them all together