To find the perpendicular distance between two lines in 3D, you can use the dot product of the vector joining the two lines and the cross product of the direction vectors of the two lines, divided by the length of the cross product vector.
To find the perpendicular distance between two lines in 3D, you can use the following method:
Write the parametric equations of the two lines: Line 1: x = x1 + tv, y = y1 + tw, z = z1 + tu and Line 2: x = x2 + sv, y = y2 + sw, z = z2 + su, where (x1,y1,z1), (x2,y2,z2) are the coordinates of the two lines, (v,w,u) and (s,t,r) is the direction vectors of the two lines respectively.Find the vector joining the two lines: (x2-x1, y2-y1, z2-z1)Find the cross product of the direction vectors of the two lines, this is the vector that is perpendicular to both lines.Take the dot product of the vector joining the two lines and the cross product of the direction vectors, and divide by the length of the cross product vector.The absolute value of the result obtained in step 4 is the perpendicular distance between the two lines.To learn more about 3-D Lines at
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a big water tank contained 200 litres of water. during the day, 88 l 580 ml of water was used and 200 ml leaked. how much water was left in the water tank?
The quantity of water left in the tank as described in the task content is; 111 l 220ml.
What is the amount of water left in the tank?The tank described in the task content initially contains 200 liters, in which case, 1 liter corresponds to 1000ml.
Hence, when 88l 580ml was used, the remaining quantity of water is; 200l - (88l 580ml) = 111 l 420ml.
And finally, since 200 ml leaked, the quantity of water left is; 111l 220ml.
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AABC is an isosceles triangle. AB is the longest side with
length 9x+3, BC = 4x+6 and CA = 3x+9. Find AB.
Answer:
30
Step-by-step explanation:
Since ABC is isosceles, BC = CA.
4x + 6 = 3x + 9x = 3So, AB = 9(3)+3 = 30.
I need help please?
A. {penguin, seagull, crow}
B.{penguin, seagull, crow, bat, mosquito}
C.{seagull, crow}
D.{seagull, crow, bat, mosquito}
The Outcome of event A and B is simply the intersection of both sets written as A ∩ B is; C: {seagull, crow}
How to write sets notation?From the image, we are given the animals namely; Pig, Penguin, Seagull, Tiger, Crow, Bat, Mosquito.
Now, these animals are classified as either a bird or can fly.
Animals that are birds are; Penguin, Seagull, Crow
Animals that can fly are; Seagull, Crow, Bat, Mosquito.
Now, we are told that;
Event A is the animal is a bird. Thus, the set notation that represents this event A is written as;
A = {Penguin, Seagull, Crow}
Event B is that the animal can fly and again the set notation that represents event B is written as;
B = {Seagull, Crow, Bat, Mosquito}
Now, Outcome of event A and B is simply the intersection of both sets. Thus; A ∩ B = {seagull, crow}
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If the ratio of areas of two similar solids is 25:36, what is the linear ratio.
Answer: Hi here go your answer is
25 divides by 36 is 0.69444 or 0.69
Step-by-step explanation:
What is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot
abc =32 ft³ is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.
Calculate a square's area?A rectangle with all equal sides, commonly known as a square. Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,
The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0 we wish to optimize V= abc.
L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)
The four partial derivatives are zero at an ideal position, so:
δLδa=bc−λ(b+2c)=0
δLδb=ac−λ(a+2c)=0
δLδc=ab−λ(2a+2b)=0
Plus the restriction. The first two enlighten:
λ=bcb+2c=aca+2c
Consequently, b(a+2c)=a(b+2c) implies to b=a. The third partial, where b=a, now informs us that a2=4aλ and so λ=a/4 nd by using this information in the second partial, we obtain 4c=a+2c which informs us that c=a/2 .
Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex] which means that a=4 feet, b=4 feet, and c=2 feet.
The maximum volume is therefore, abc=32 ft³
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In a bag of 10 marbles, there are 4 blue, 3 red, 2 green,
and 1 yellow. What is the probability that you draw one
marble that is green, DO NOT replace it, and draw another
marble that is yellow?
1
30
O b. 139
OC. 15
45
a.
O d. 7/19
2
Answer: 1/45
Step-by-step explanation: 10 total marbles. 4 are blue 3 are red 2 are green and 1 is yellow. The chance of drawing a green is 2/10 or 1/5. Then there are only 9 marbles left in the bag. So the chance of a yellow marble is 1/9. 1/5 x 1/9 = 1/45.
What is the value of -3/2÷-7/2?
The value of the given division operation is 3/7
Division operationFrom the question, we are to determine the quotient of the given division operation
The given division operation is
-3/2÷-7/2
[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]
[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]
[tex]=\frac{-3}{-7}[/tex]
[tex]=\frac{3}{7}[/tex]
Hence, the value of the given division operation is 3/7
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Complete the following table:
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
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2x⁴ - 4-7x - 38x²/x - 4
Answer:
2x⁴-45x-8
Step-by-step explanation:
Which equation is the inverse of Y equals 9X Square -4
[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]
[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]
Find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
The least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
A number (A) is divisible by another number (K) when the division of A by K, leaves a remainder of 0.
In the question, we are asked to find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
Now, we need to know that the multiples of 225 end with 00, 25, 50, and 75.
So, to have a multiple with digits 0, 1, and 2, we need the last digits to be 00.
The smallest multiple of 225, ending with 00 is 225*4 = 900.
So, we need to have the least multiple of 900, with digits 0, 1, and 2.
We know that a multiple of 9, has a sum of its digit as 9.
The smallest multiple of 9, with digits 1, and 2, will be 12222.
Adding the last 00 to this, we get the least multiple as 1,222,200.
Thus, the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
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15. If 3x + 10 = 3y - 2(y + 4), what is the value of y in terms of x? (A) x + 18 (B) 3x+6 (C) 3x + 14 (D) 3x + 18
Answer:
3x + 18
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 18 = y
Answer:
D, 3x + 18.
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 10 = y - 8
y = 3x + 10 + 8
y = 3x + 18.
Please help me fast
What is the equation of this graph
Answer-4,5
Step-by-step explanation:
Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function
The function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph of the function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
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what scale factor can be applied to Cone 1 to make Cone 2?
The scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
What are scale factors?This are constants that is used to enlarge of diminish a given figure of sides of a figure
We can determine the scale factor by finding the ratio of the similar sides of two figures, From the given cones, the ratio of their radius can determine the scale factor that is applied to Cone 1 to make Cone 2
From the given figure;
scale factor = radius of cone 2/radius of cone 1
Given the following parameters
radius of cone 2 = 2 ft
radius of cone 1 = 2.5ft
Substitute
scale factor = 2/2.5
scale factor = 0.8
Hence the scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
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Write an equation of the line point(2,-1) and parallel passing through y=3x-5 write in slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Since the lines are parallel, the slopes will be the same. In this case 3. Now we have to find the y-intercept. We will use the slope (3), the x (2) and y (-1) to help us do this. We get the x and the y from the ordered pair given(2,-1).
y = mx + b
-1 = 3(2) + b Plug in what you know
-1 = 6 + b Subtract 6 from both sides
-7 = b
Now we can write the equation
y = 3x -7
La siguiente tabla muestra el saldo de las tres cuentas bancarias de Dmitri.
Ahorros........$573.73
Retiro............$294.43
Cheques --$435.24
Ayuda a Dmitri a ordenar sus cuentas de menor a mayor valor absoluto del saldo.
Las cuentas de Dmitri de menor a mayor se ordenan: retiro, cheques y ahorros.
¿Cómo organizar las cuentas bancarias de Dmitri?Para organizar las cuentas bancarias de Dmitri de menor a mayor debemos observar cuidadosamente los valores de cada una. Adicionalmente para organizarlas por valor absoluto nos fijamos únicamente en el número sin tener en cuenta el símbolo, en ese caso el valor de cheques pierde su símbolo negativo.
Entonces las cuentas quedarían organizadas así:
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Please help and explain how to solve
Answer:
$ 7.52
Step-by-step explanation:
Find charge per minute
59 - 23 min = 36 minutes cost 16.32 - 10.56 = $ 5.76
or $5.76 / 36 min = 16 cents per min
from 59 to 78 = 19 more minutes x .16/min = $ 3.04
so from 59 to 78 will leave 10.56 - 3.04 = $7.52
can someone please help me
answer choices:
A - sin(0°)
B - cos(0°)
C - sin(180°)
D - cos(180°)
E - sin(270°)
F - cos(270°)
Answer:
B
Step-by-step explanation:
Cos(0)=1
since the diagram shows x as (1,0)
20 POINTS
good morning, can you please help me
The area of the paper that remains is 391.04 cm²
Calculating areaFrom the question, we are to calculate the area of the remaining part of the paper
Area of the paper that remains = Area of rectangle - 2×Area of semicircle
Area of the paper that remains = (l×w) - 2(πr²/2)
Area of the paper that remains = (l×w) - (πr²)
Where l is the length of the paper
w is the width if the paper
and r is the radius of the semicircle
From the given information,
l = 37 cm
w = 16 cm
r = w/2 = 16/2 = 8 cm
Putting the parameters into the equation,
Area of the paper that remains = (37×16) - (3.14(8)²)
Area of the paper that remains = 592 - (3.14×64)
Area of the paper that remains = 592 - 200.96
Area of the paper that remains = 391.04 cm²
Hence, the area of the paper that remains is 391.04 cm²
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What is the shape of the graph of the function?
h(t)=0.6\cdot 3.2^th(t)=0.6⋅3.2
t
The graph of a function f exists the set of all points in the plane of the form (x, f(x)).
What is the graph of a function?
The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.
Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]
Substitute the values in the function, we get
t = -2, h(t) = 0.05859375
t = -1, h(t) = 0.1875
t = 0, h(t) = 0.6
t = 1, h(t) = 1.92
t = 2, h(t) = 6.144
t = 3, h(t) = 19.6608
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what is the solution of |2x+3|< 19
Answer:
- 11 < x < 8
Step-by-step explanation:
inequalities of the type | x | < a have solutions of the form
- a < x < a
then
| 2x + 3 | < 19
- 19 < 2x + 3 < 19 ( subtract 3 from each interval )
- 22 < 2x < 16 ( divide each interval by 2 )
- 11 < x < 8
The ratio of boys to girls who play soccer in Mr. Fraser’s class is 14:6. If there were 400students in the school, how many boys would likely play soccer?
Answer:
280
Step-by-step explanation:
Set up a ratio to solve.
Mr. Fraser's class has 20 soccer playing students, and 14 are boys.
14/20 = x/400
Cross multiply. 20x= 5600
Divide by 20 to solve
x= 280
Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer: The function is even because [tex]f(x)=f(-x)[/tex].
Step-by-step explanation:
[tex]f(x)=3x^4 \\\\f(-x)=3(-x)^4 = 3x^4\\\\\therefore f(x)=f(-x)[/tex]
So, the function is even.
Need help in this pls
Answer:
6
Step-by-step explanation:
The arc length is (2)(pi)(27)(40/360)=6pi.
So, k=6.
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school?
Using the mean concept, the average collection for a student in this school was of $16.13.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The number of students is given as follows:
82 + 74 + 96 + 99 = 351.
The sum is:
82 x 26.75 + 74 x 12.25 + 96 x 15.50 + 99 x 10.85 = $5662.15
Hence the mean is:
M = $5662.15/351 = $16.13.
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If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
Answer:
Step-by-step explanation:
If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
PLEASE HELP FAST!
A figure has rotational symmetry if a rotation of 180°
or less produces an image that fits exactly on the original figure. Select each degree of rotation that shows the figure below has rotational symmetry.
30 °
45 °
60 °
90 °
120 °
135 °
150 °
180 °
Answer:180 °
Step-by-step explanation:
Answer:
90 degrees
Step-by-step explanation:
The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.
Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45
45x2= 90
Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.
The answer is 90
If u are 13, and ur birthday is 21 of october, how old will you be in 2050?
Answer:
41 years old
Step-by-step explanation:
2050-2022=28 years
13years old +28years = 41 years old (sorry if wrong)
Answer: Based on today's date of 7/19/2022, you will be 41 until October 21, 2050. On October 21, 2050 you will turn 42. You were born in 2008
Step-by-step explanation: