What are the indices for the directions indicated by the two vectors in the following sketch?
Answers
The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].
Miller Indices of Direction Vector:
The Miller indices of direction are rationalized components of the direction vectors taken in all crystallographic directions. They are indicated by [[u v w ]]. They are always defined as the smallest integers, so if they occur in fractional or decimal form, we need to convert them into the smallest integral value by algebraic manipulation.
The indices of direction 1.
Let the length of direction 1 along the x-axis be X units. The length of the vectors along the y and z axes is 0.
[ X 0 0 ]
⇒ [tex]\left[\begin{array}{ccc}0&0&0\\X'&X'&X'\\\end{array}\right][/tex]
Divide each length by X to convert it into the smallest integer.
⇒ [1 0 0]
And, this is the Miller indices of the direction vector 1.
So, the Miller indices of the direction vector 1 are [ 1 0 0].
Direction 2
The indices of direction 2.
Let the length of direction 2 along the x-axis be X units. The length of the vector along the y and z axes are 0.
[ 0.2 0 0.3 ]
⇒[ 2 0 3 ]
Multiply each fractional length by 10 to convert it into the smallest integer.
So, the Miller indices of the direction vector 2 are [ 2 0 3].
Therefore, The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].
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Related Questions
100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
Answers
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
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You Draw two marbles (without replacement) from a bag containing 4 green 2 yellow and 6 red marbles.what is the probability that both marbles are yellow? round to the nearest thousand
Answers
The probability of drawing two yellow marbles is 0.015 to the nearest thousandth.
What is the probability?The probability of drawing two yellow marbles after drawing a yellow marble on the first draw and without replacement drawing another yellow marble is determined as follows:
Total number of marbles in the bag = 4 + 2 + 6
Total number of marbles in the bag = 12 marbles in the bag.
P(Yellow on first draw) = 2/12 or 1/6
P(Yellow on second draw | Yellow on first draw) = 1/11
The probability of both marbles being yellow will be:
P(Both marbles yellow) = (1/6) * (1/11)
P(Both marbles yellow) = 1/66 or 0.015
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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!
Answers
Answer:
∆ABC ~ ∆QPR by SSS since 6/8 = 9/12.
Find the midpoint (-3,-5)(4, 5)
Answers
The midpoint of this line segment (-3, -5) and (4, 5) is (0.5, 0).
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
By substituting the given end points into the formula for the midpoint of a line segment, we have the following;
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(-3 + 4)/2, (-5 + 5)/2]
Midpoint = [(1)/2, 0/2]
Midpoint = (0.5, 0).
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Identify the pairs of alternate exterior angles in the given figure.
A) ∠2 and ∠7; ∠1 and ∠8
B)∠3 and ∠6; ∠4 and ∠5
C) ∠3 and ∠5; ∠4 and ∠6
D) ∠1 and ∠7; ∠2 and ∠8
Answers
The pairs of alternate exterior angles in the given figure is Option D) ∠1 and ∠7; ∠2 and ∠8
Alternate exterior angles are a pair of angles formed by a transversal line intersecting two parallel lines and located on opposite sides of the transversal and on the exterior of the parallel lines. In other words, if two parallel lines are intersected by a third line (the transversal), then the pairs of angles on opposite sides of the transversal and outside the parallel lines are alternate exterior angles. These angles are congruent to each other.
In the given figure two parallel lines, which are crossed by a transversal line which forms angles.
Now according to the given figure
so, answer is Option D) ∠1 and ∠7; ∠2 and ∠8
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PLEASE HELP WITH SURFACE AREA!! This is my project and I need the awnser quick!! Pls help me marking brainliest if the awnsers r right !
Answers
The surface areas and volumes of the solids are listed below:
Case 1: A = 118 cm², V = 70 cm³
Case 2: A = 121.5 in², V = 91.125 in³
Case 3: A = 192 m², V = 144 m²
Case 4: A = 480 ft², V = 576 ft³
Case 5: A = 87.965 yd², V = 62.832 yd³
How to determine the surface area and the volume of solidsIn this problem we need to determine the surface area and the volume of each solid. The surface area is the sum of the areas of all faces. The area and volume formulas required to answer this question are shown below:
Area
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Circle
A = π · r²
Lateral face of a cylinder
A = 2π · r · h
Volumes
Prism
V = A · h
Where:
w - Widthl - Lengthh - Heightr - RadiusA - Base area.Now we proceed to determine the surface areas and volumes of the solids:
Case 1
A = 2 · [(5 cm) · (7 cm) + (5 cm) · (2 cm) + (7 cm) · (2 cm)]
A = 2 · (35 cm² + 10 cm² + 14 cm²)
A = 2 · 59 cm²
A = 118 cm²
V = (5 cm) · (7 cm) · (2 cm)
V = 70 cm³
Case 2
A = 6 · (4.5 in)²
A = 121.5 in²
V = (4.5 in)³
V = 91.125 in³
Case 3
A = 2 · 0.5 · (8 m) · (6 m) + (6 m) · (10 m) + (6 m)² + (8 m) · (6 m)
A = 192 m²
V = 0.5 · (8 m) · (6 m)²
V = 144 m²
Case 4
A = 2 · 0.5 · (12 ft) · (8 ft) + 2 · (10 ft) · (12 ft) + (12 ft)²
A = 480 ft²
V = 0.5 · (12 ft) · (8 ft) · (12 ft)
V = 576 ft³
Case 5
A = 2π · (2 yd)² + 2π · (2 yd) · (5 yd)
A = 87.965 yd²
V = π · (2 yd)² · (5 yd)
V = 62.832 yd³
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Which system is equivalent to
O
O
O
[5-x=9x²
y = 5-x
[y=9y²-90y+225
1x=y-5
[5+x=9x²
y = 5+x
y = 3x
x+3x=5
y=9x²?
x+y=5
Answers
The first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
The system that is equivalent to:
O
O
O
[5-x=9x²
y = 5-x
is: x = -2, y = 7
In the given system, the first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
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An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected malpractice suits, a 99% confidence interval was constructed for the true proportion of medical malpractice lawsuits that are dropped or dismissed. The confidence interval was (0.6633, 0.7308) find the Margin of error.
Answers
Answer: I have this same exact question
Step-by-step explanation: So someone please help this person, or animal which ever you perfer
In AABC, AB=32, AC = 23, and BC= 20. What is mZA?
Answers
The measure of m∠A in the triangle is:
m∠A = 38.44°
How to find the measure of m∠A?The cosine rule is used for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula for angles:
cos(A) = (b² + c² − a²)/2bc
cos(B) = (c² + a² − b²)/ 2ac
cos(C) = (a² + b² − c²)/2ab
Where a, b and c are the length of the sides, and A, B, and C are the measures of the angles
We have:
a = BC = 20
b = AC = 23
c = AB = 32
Substituting into:
cos(A) = (b² + c² − a²)/2bc
cos(A) = (23² + 32² − 20²)/(2*23*32)
cos(A) = 0.7833
A = cos⁻¹(0.7833)
A = 38.44°
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what is1+1+1 equal?
this is a not ur typical math problem try to get it right u will get brainliest
Answers
The mathemematical sum of the three numbers 1+1+1 would give 3
Addition of numbersAddition of numbers can involve 2 or more values using the additive sign '+'. For any given sum of values, the result obtained would be greater than any of the individual value in the sum.
Here, 1 + 1 + 1 means that we are adding 1 in three places. The value obtained would be 3.
Therefore, the sum of the 1+1+1 is 3
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Apples cost $1.29 per pound. How much would a bag of apples weighing 4.7 pounds cost? (Round your answer to the nearest cent.)
Answers
Answer:
$6.06
Step-by-step explanation:
$1.29 x 4.7 = 6.063
Round: 6.06
if 4.2 pounds of strawberry sells for an income of $12 what is 24,990 pounds income
Answers
Answer: $71,400
Step-by-step explanation:
We will set up a proportion with income in the numerator and pounds in the denominator.
[tex]\displaystyle \frac{\$12}{4.2\;lbs} =\frac{\$x}{24,990\;lbs}[/tex]
Then we will cross-multiply.
4.2 * x = 12 * 24,990
4.2x = 299,880
Lastly, we will divide both sides of the equation by 4.2.
x = $71,400
The income from 24,990 pounds of strawberries would be approximately $71,690.14.
To find the income from 24,990 pounds of strawberries, we need to use a proportion:
4.2 pounds of strawberries sells for $12, so 1 pound of strawberries sells for $12/4.2 = $2.86 (rounded to two decimal places).
Therefore, 24,990 pounds of strawberries would sell for:
$2.86 x 24,990 = $71,690.14 (rounded to two decimal places).
Consider this equation.
cos(0) = 4/41
If 0 is an angle in quadrant IV, what is the value of sin(0)
Answers
Answer: sin(0) = 40.804/41
Step-by-step explanation:
According to the graph, what is the value of the constant in the equation
below?
Constant/ Width=Height
O A 3
OB. 75
O C. 15
OD. 25
Answers
The calculated value of the constant in the equation is 75
How to determine the value of the constant in the equationFrom the question, we have the following parameters that can be used in our computation:
The graph
Where we have
(3, 25) and (5, 15)
The value of the constant in the equation is calculated as
Constant = Width * Height
So, we have
Constant = 3 * 25
Evaluate
Constant = 75
Hence, the value of the constant in the equation is 75
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Given that ∅ = 12.2° , calculate the area of the triange below
give your answer to 2 d.p.
Answers
Answer:
A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)
A = (1/4)√29√21√7
= about 16.32 mm²
Answer:
16.27 mm² (see comment)
Step-by-step explanation:
You want the area of a triangle with side lengths 11 mm and 14 mm, and the angle between them 12.2°.
AreaThe area is given by the formula ...
A = 1/2ab·sin(C)
A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²
The area of the triangle is about 16.27 square millimeters.
__
Additional comment
If you use Heron's formula for the area from the three side lengths, you find it is about 16.32 mm². That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)
s = (4 +11 +14)/2 = 14.5
A = √(s(s -a)(s -b)(s -c))
A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375
A ≈ 16.32
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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
Karen measures the width of a garden plot and records that it is 40 meters. Its actual width is 42 meters.
What is the percent error in the measurement?
A: 2%
B: 3%
C: 4%
D: 5%
Answers
Explanation:
The error is 42-40 = 2 meters
Divide this over the actual width
2/42 = 0.0476 = 4.76% approximately
This rounds to 5%
Answer:
D. 5%
Step-by-step explanation:
Percent Error = (|40 - 42| / 42) × 100
Percent Error = (2 / 42) × 100
Percent Error ≈ 4.76%
4. The wheels of a bicycle have a
diameter of 22 inches. How many
full revolutions will the wheels need
to make to travel 300 feet? Use 3.14
for .
A 105 revolutions
B 10 revolutions
C164 revolutions
D 53 revolutions
no
Answers
53 revolutions will be needed by the wheels to make it travel 300 feet.
Option D is the correct answer.
We have,
To solve this problem, we can use the formula:
Number of revolutions = Distance / Circumference of the wheel
First, let's convert the distance from feet to inches:
300 feet = 300 x 12 = 3600 inches
Next, we need to calculate the circumference of the wheel using the given diameter:
Circumference = π x diameter
Circumference = 3.14 x 22 inches
Circumference ≈ 69.08 inches
(rounded to two decimal places)
Now we can calculate the number of revolutions:
Number of revolutions = 3600 inches / 69.08 inches
= 52.14 revolutions
Rounding to the nearest whole number.
= 52 revolutions.
Therefore,
53 revolutions will be needed by the wheels to make it travel 300 feet.
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The bicycle wheels will need 53 full revolutions to travel 300 feet.
The circumference of a wheel can be calculated using the formula:
circumference = π x diameter
So, circumference = 3.14 x 22
= 69.08 inches
Now, converting feet to inches
300 feet = 300 x 12 inches
300 feet = 3600 inches
So, number of revolutions:
revolutions = distance / circumference
= 3600 / 69.08
≈ 52.11
Therefore, the bicycle wheels will need 53 full revolutions to travel 300 feet.
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7 in.
12 in.
6 in.
What is the surface area of this rectangular prism?
Answers
The surface area of the rectangular prism is 396 square inches
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
7 in by 12 in by 6 in
The surface area of the rectangular prism is calculated as
Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)
Evaluate
Area = 396
Hence, the area is 396 square inches
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PLEASSE HELP!!! MARKING AS BRAINLIST
Answers
The area of the figure as shown in the diagram is 24 in².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the figure, we use the formula below
Formula:
A = lw+l'w'+l''w''.................. Equation 1Where:
A = Area of the figurel, l', l'' = Length of the first, second and third rectangle respectivelyw, w', w'' = Width of the first second and third rectangle respectiveyFrom the question,
Given:
l = 4 inw = 2 inl' = 2 inw' = 4 inl'' = 4 inw'' = 2 inSubstitute these values into equation 1
A = (4×2)+(2×4)+(2×4)A = 8+8+8A = 24 in²Learn more about area here: https://brainly.com/question/25092270
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What is the mode of the data represented in this line plot?
Enter your answer in the box.
5 - xx
6 - xxxx
7 - xxx
8 - xxxxxx
9 - xx
10 - xxxx
11 - xx
Answers
The mode of the data represented in this line plot will be 8.
Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.
The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.
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Find the value of the unknown variable. -c/6 = -4
Answers
The value of the unknown c in the algebraic fraction equation is equal to -24
How to solve the algebraic fraction equationTo solve the simple algebraic fraction equation, we cross multiply to eliminate the fractions, then simplify by solving for the unknown
Given the algebraic equation:
-c/6 = 4
(-c/6) × 6 = 4 × 6
-c = 4 × 6
-c = 24
multiply both sides by -1
-1 × -c = -1 × 24
c = -24
Therefore, the value of the unknown c in the algebraic fraction equation is equal to -24
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HELP ASAP PHOTO INCLUDED
Answers
The volume of the cylindrical shaped pool with water is V = 75.4 feet³
Given data ,
Let the diameter of the pool be d = 8 feet
So , radius r = 4 feet
And , the height of the cylindrical pool is h = 3 feet
Now , the water is half full
So , Volume of Cylindrical pool is V = ( 1/2 ) πr²h
V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )
On simplifying , we get
V = 75.4 feet³
Hence , the amount of water in pool is V = 75.4 feet³
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Estimate then find the product 34•12
Answers
Answer:
I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408
Step-by-step explanation:
please help! math: find the perimeter of the polygon below. use the correct formula!
the width is 3.8 and the length is 6.3
Answers
The perimeter of the rectangular polygon is given by P = 20.2 units
Given data ,
Let the perimeter of the polygon be represented as P
Now , the value of P is
Perimeter P of rectangle = 2 ( Length + Width )
Now , width is 3.8 and the length is 6.3
On simplifying , we get
P = 2 ( 3.8 + 6.3 )
P = 20.2 units
Hence , the perimeter is P = 20.2 units
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Function
�
gg can be thought of as a scaled version of
�
(
�
)
=
�
2
f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f represents the equation y equals x squared. A parabola labeled g passes through the point negative 1, 4, through the origin, and through the point 1, 4.
Write the equation for
�
(
�
)
g(x)g, left parenthesis, x, right parenthesis.
Answers
The equation for g (x) is,
⇒ g(x) = x² -3
Since, The function is,
⇒ f (x) = x²
when x = 0, f(x) = 0
hence it has vertex at (0,0)
Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),
Then, g(x) must be shifted along y axis.
So, We get;
g(x)= x²+c
when x = - 1, g(x)= 4
4 = (-1)² + c
4 = 1 + c
c = 3
Thus, The equation for g (x) is,
g(x) = x² -3
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Plsss help plsss help
Answers
Answer:
It's B
Step-by-step explanation:
Look at the sides with the number compare them with each other and you will find they are the most similar ones with each other.
Focus: (-5,3); Directrix: y = 1
Answers
The equation of the parabola is: y = (1/4)(x-3)²+ 2
In Parabola mathematics, it is defined as a set of points that are equidistant from a fixed point called the focus and a fixed line called the directrix. In this case, we are given the focus (3,5) and the directrix y=1, y=1, and we need to find the equation of the parabola.
To find the equation of the parabola, we first need to determine the vertex. The vertex is the midpoint between the focus and the directrix, which in this case is (3,3). Since the parabola is symmetric, we know that the axis of symmetry passes through the vertex and is perpendicular to the directrix. Therefore, the equation of the axis of symmetry is x=3.
Next, we need to find the distance between a point on the parabola and the focus, as well as the distance between that same point and the directrix. Let (x,y) be a point on the parabola. The distance between (x,y) and the focus is given by the distance formula: √((x-3)² + (y-5)²)
The distance between (x,y) and the directrix is simply the absolute value of the difference between y and 1: |y-1|
Since the point (x,y) is equidistant from the focus and the directrix, we have: √((x-3)²+ (y-5)²) = |y-1|
Squaring both sides and simplifying, we get: (x-3)²= 4(y-2)
Therefore, the equation of the parabola is: y = (1/4)(x-3)²+ 2
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NOTE : I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.
Complete Question : Find the Parabola with Focus (3,5) and Directrix y=1 (3,5) , y=1
Below are two inequalities and the graphs of their without the shading. By imagining where the shading should be, identify which point would satisfy BOTH
inequalities
Answers
Answer: C
Step-by-step explanation:
Answer:
D. (-2, 10)
Step-by-step explanation:
Given inequalities:
[tex]y > -\dfrac{5}{3}x+2[/tex]
[tex]y > 3x+2[/tex]
Both inequalities have been given in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The first equation has a negative slope, which means that as x increases, y decreases. Therefore, it is the dashed line that begins in quadrant II and ends in quadrant IV.
The second equation has a positive slope, which means that as x increases, y increases. Therefore, it is the dashed line that begins in quadrant III and ends in quadrant I.
When graphing inequalities, the inequality sign ">" indicates a dashed line and shading above the line.
As both inequalities should be shaded above the lines, the region where the shaded regions overlap is the upper "V" of the graph (see attachment).
A point that satisfies both inequalities is any point that is located in the overlapping shaded region, but not found on the dashed lines.
Therefore, the point that satisfies both inequalities is (-2, 10).
The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie?
Answers
This is a linear equation problem with two variables. One way to solve it is by using the substitution method. Let x be the price of the tie and y be the price of the pair of pants. Then we have:
$$
\begin{aligned}
x + y &= 87.18 \\
x &= y - 2.12
\end{aligned}
$$
Substituting x into the first equation, we get:
$$
\begin{aligned}
(y - 2.12) + y &= 87.18 \\
2y - 2.12 &= 87.18 \\
2y &= 89.30 \\
y &= 44.65
\end{aligned}
$$
Therefore, the price of the pair of pants is $44.65. To find the price of the tie, we plug y into the second equation:
$$
\begin{aligned}
x &= y - 2.12 \\
x &= 44.65 - 2.12 \\
x &= 42.53
\end{aligned}
$$
Therefore, the price of the tie is $42.53.
Answer:
42.53
Step-by-step explanation:
write equation
tie + pants = 87.18
since ties cost 2.12 less than pants,
tie = pants -2.12
now substitute back into first equation
pants - 2.12 + pants = 87.18
solve for pants by adding 2.12 to the other side
divide by 2 since there are 2 pants on one side
find pants and then substitute value into the tie equation to find the price of the tie
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
Answer:
B, C, E
Step-by-step explanation:
For a rectangle,
area = length × width
Let length = y.
Then the width is y - 5.
A = LW
750 = y(y - 5)
y(y - 5) = 750
y² - 5y - 750 = 0
All equations that can be put in the form above are correct.
A) y(y + 5) = 750
y² + 5y - 750 = 0
No
B) y² – 5y = 750
y² - 5y - 750 = 0
Yes
C) 750 – y(y – 5) = 0
750 - y² + 5y = 0
y²- 5y - 750 = 0
Yes
D) y(y – 5) + 750 = 0
y² - 5y + 750 = 0
No
E) (y + 25)(y – 30) = 0
y² + 25y - 30y - 750 = 0
y² - 5y - 750 = 0
Yes