Find the distance from the point to the line. 33. (0, 0, 12); x = 4t, y = -2t, z = 2t
Answers
The distance from the point (0, 0, 12) to the line x = 4t, y = -2t, z = 2t is (8√15) / 3.
The distance from the point (0, 0, 12) to the line defined by x = 4t, y = -2t, z = 2t can be found using the formula for the distance between a point and a line in three-dimensional space.
The formula is given by:
Distance = |(P - Q) × V| / |V|,
where P is a point on the line, Q is the given point, V is the direction vector of the line, and × denotes the cross product.
In this case, we can choose any point on the line to represent P. Let's choose P as (4, -2, 2). The direction vector of the line is V = (4, -2, 2).
Using the formula, we can calculate the distance as follows:
Distance = |((0, 0, 12) - (4, -2, 2)) × (4, -2, 2)| / |(4, -2, 2)|.
Simplifying the expression, we get:
Distance = |(-4, 2, 10) × (4, -2, 2)| / |(4, -2, 2)|.
To find the cross product, we can use the determinant method:
((-4, 2, 10) × (4, -2, 2)) = [(2 * 2 - 10 * -2), (10 * 4 - (-4) * 2), ((-4) * (-2) - 2 * 4)]
= (4 - 20, 40 - (-8), 8 - 8)
= (-16, 48, 0).
Now we can substitute the values back into the distance formula:
Distance = |(-16, 48, 0)| / |(4, -2, 2)|.
Taking the magnitude of the vectors, we get:
Distance =\(\sqrt((-16)^2 + 48^2 + 0^2) / √(4^2 + (-2)^2 + 2^2)\)
= √(256 + 2304 + 0) / √(16 + 4 + 4)
= √2560 / √24
= 16√10 / 2√6
= 8√10 / √6
= (8√10 / √6) * (√6 / √6)
= (8√60) / 6
= (8√15) / 3.
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Related Questions
-21.5%, 1/3, -4/5, 1.3, 4.5%, -0.04
Pls help I need order from greatest to least
Answers
Answer:
Sure, here are the numbers arranged from greatest to least
Step-by-step explanation:
Order from greatest to least
1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%
Answer:
From the greatest to least
Step-by-step explanation:
1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%
You can identify which number is greater than other by using a number line.
What is a number line?
A number line is what a math student can use to find the answer to addition and subtraction questions. A straight line, theoretically extending to infinity in both positive and negative directions from zero, that shows the relative order of the real numbers.
Hope this helps :)
Pls Brainliest...
At the end of the harvest season, Omar wonders if it is time to cover the garden with a tarp. He understands that as the temperature decreases, moisture in the air condenses into dew which freezes at 0 degrees Celsius and may damage the plants in the garden.
Answers
Answer:
no clue im stuck on it to
Step-by-step explanation:
Answer:
No Omar does not have to put the blanket
Step-by-step explanation:
The answer is No ,because since Omar only covers the plant when its below 0 , And when the temperature is 5 degrees Celsius at 4:00 pm and the temperature is predicted to decrease 0.5 degrees Celsius every two hours until 4:00 am. So 6 times 0.5 =3 so 5 - 3 = 2
Show work
4:00 pm Fact : And very two hrs 0.5 degrees .
5:00 pm 1
6:00 pm 2 = 0.5
7:00 pm 1
8:00 pm 2 = 0.5
9:00 pm 1
10:00 pm 2 =0.5
11:00 pm 1
12:00 pm 2 =0.5
1 :00 Am 1
2: 00 Am 2 =0.5
3:00 Am 1
4:00 Am 2= 0.5
imagine that a recent study found that people who eat large amounts of bananas get bitten by mosquitoes on average more often than people who eat smaller amounts of bananas. what causal relationship can we conclude from this study alone?
Answers
It is not possible to conclude a causal relationship from this study alone. This is because the study only shows a correlation between eating large amounts of bananas and being bitten by mosquitoes, it does not demonstrate that one causes the other. There could be other factors that are not controlled for in the study that could be the true cause of the relationship, such as people who eat more bananas also spend more time outdoors. To establish a causal relationship, further research would be needed such as a randomized control trial.
Cause and Effect of Bananas and Mosquito BitesTo determine a causal relationship between eating bananas and being bitten by mosquitoes, a randomized controlled trial could be conducted. This type of study would involve randomly assigning participants to two groups: one group would eat a large amount of bananas, while the other group would eat a smaller amount of bananas. The number of mosquito bites each participant receives would be recorded and compared between the two groups.
If the group that ate a large amount of bananas had a significantly higher rate of mosquito bites than the group that ate a smaller amount of bananas, it would suggest that eating bananas may cause an increase in the number of mosquito bites.
Additionally, other variables that could influence the result should be controlled or measured, such as time spent outdoors, skin type, or use of mosquito repellent.
It's important to note that even if the study shows a correlation between eating bananas and being bitten by mosquitoes, it doesn't mean that the banana causes the bites, there could be other factors that are not controlled for in the study that could be the true cause of the relationship.
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Please help me please please I’ll give brainly
Answers
Answer:
The answers are in the picture also with steps
Step-by-step explanation:
Solve and graph the solutions of the inequality - |x - 2| + 9 > 6.
Answers
i solved it
you graph it :)
Explain the difference between the translation of y=x² for the graphs of y=(x+3)² and y=x²+3.
Answers
Answer:
y=(x+3)^2 has a vertex at (-3,0), while y=x^2 + 3 has a vertex at (0,3)
Mark me brainliest hope this helps
Step-by-step explanation:
Whats the condition make this equation is True : (∂U/∂V)T =(∂U/∂P)T =(∂H/∂V)T=0
Answers
The condition for the equation (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 to be true is that the system described must be in a state of mechanical, thermal, and chemical equilibrium.
Let's break down the conditions for each partial derivative:
1. (∂U/∂V)T = 0: This condition implies that the internal energy of the system does not change with respect to volume at constant temperature.
It indicates mechanical equilibrium, where the system is in balance and no work is being done on or by the system due to volume changes.
2. (∂U/∂P)T = 0: This condition suggests that the internal energy of the system does not change with respect to pressure at constant temperature.
It indicates thermal equilibrium, where the system is in balance and there is no transfer of energy as heat due to pressure changes.
3. (∂H/∂V)T = 0: This condition implies that the enthalpy of the system does not change with respect to volume at constant temperature.
It also indicates mechanical equilibrium, where the system is in balance and there is no work being done on or by the system due to volume changes.
In summary, the condition (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 is true when the system is in a state of mechanical, thermal, and chemical equilibrium, where there are no changes in internal energy, pressure, and enthalpy with respect to volume at constant temperature.
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Restaurants often slip takeout menus under britney's apartment door. britney counted how many menus there were from each type of restaurant.chinese 2japanese 9mediterranean 1thai 2italian 6what is the experimental probability that the next menu slipped under britney's door will be from a chinese restaurant?
Answers
The experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant is 0.1 or 10%.
To find the experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant, we need to determine the number of Chinese restaurant menus in relation to the total number of menus.
The total number of menus is the sum of menus from all types of restaurants:
Total number of menus = Chinese + Japanese + Mediterranean + Thai + Italian
= 2 + 9 + 1 + 2 + 6
= 20
The number of Chinese restaurant menus is 2.
Now we can calculate the experimental probability:
Experimental probability of getting a Chinese restaurant menu = Number of Chinese restaurant menus / Total number of menus
= 2 / 20
= 0.1
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A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. what is the name of the polygon?octagonhexagonheptagonquadrilateral
Answers
The name of the polygon is (B) hexagon.
What is a hexagon?A hexagon is a six-sided polygon or 6-gon in geometry. The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.To find the name of the polygon:
Let the number of sides in a polygon be n.Triangles are formed by drawing diagonals from one vertex to each of the others.Because there is no overlapping of the triangles, no diagonal will be drawn back to itself, and the diagonals to each adjacent vertex will lie on top of the adjacent sides, so the number of diagonals from a single vertex is three less than the number of sides or n - 3, and the number of triangles is one more, or n - 2. Number of triangles = number of sides in polygon - 2 Number of triangles = n - 2 n = 4 + 2 n = 6The polygon containing 6 sides is called a hexagon.Therefore, the name of the polygon is (B) hexagon.
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The complete question is given below:
A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?
A) Octagon
B) Hexagon
C) Heptagon
D) Quadrilateral
Math question! Need help! :D
Answers
Answer:
3
Step-by-step explanation:
-21/-7 = 3
negative times negative or negative divided by negative is always positive
Please Help ASAP!!!!!!!!
Answers
Answer:
The answer is D) y = 4x+3
Step-by-step explanation:
Solve pls
for the function -2x²+x+1 find f(3)
Answers
Answer:
f(3) = -14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = -2x² + x + 1
f(3) is x = 3
Step 2: Evaluate
Substitute: f(3) = -2(3)² + 3 + 1Exponents: f(3) = -2(9) + 3 + 1Multiply: f(3) = -18 + 3 + 1Add: f(3) = -15 + 1Add: f(3) = -14The circumference of a circle is 37. 68 ft. What is the radius of the circle?.
Answers
Answer:
r = 6 ft
Step-by-step explanation:
how old am i if 400 reduced by 2 times my age is 300?
Answers
Answer:
You are 78 years old.
Answer:
Naw bro you're 0
Step-by-step explanation:
Which data set has a greater spread? Why?
Set A: (38, 12, 23, 48, 55, 16, 18)
Set B: (44, 13, 24, 12, 56}
has a greater spread because
Answers
Answer:
Set B has a greater speed ,because it has greater range
please please answer these five questions !!!!!!!!!
Answers
Answer: 1. V≈603.19
2. V≈103.67
3. V≈513.13
Step-by-step explanation: i only know those sorry :(
Please show all work and not just the answers.
Answers
Answer:
(-1, 6)
Step-by-step explanation:
Midpoint formula:
xm = (x1 +x2)/2ym = (y1+y2)/2For G(-7, 3) and H(5, 9) the midpoint:
((-7+5)/2, (3+9)/2) = (-1, 6)Answer:
(-1,6)
Step-by-step explanation
use the midpoint formula:
(x 1 + x2 /2 , y1 + y2/2)
(-7+ 5 /2, 3+ 9 /2)
after simplfying
(-1,6)
find the value of x that would prove y/z State the converse used to support your answer.
Answers
Answer:
x=6
alternative exterior angles
Step-by-step explanation:
to prove y and z parallel then the two angles must be equal:
11x-3=4x+39
11x-4x=39+3
7x=42
x=42/7
x=6
The Glorious Nation of the Skull Archipelago uses an Electoral College weighted voting system to elect its figurehead leader (the real rulers are the Archipelago Illuminati, of course). Each of the islands in the archipelago is awarded 4 Senators, and each island is awarded Representatives according to population, in descending order: 31, 24, 17, 8. (a) Considering each of the islands as a voter, use notation to write the figurehead election as a weighted voting system. System: [___:____ ] (b) Fill in the table with the percentage that each island represents of the total archipelago population, its Banzhaf power index, and the difference between the Banzhaf index and percentage of the island's population in that island (calculate % population - % Banzhaf, so that a negative number means the percentage population for that island is smaller than its Banzhaf power). You may round each answer to two decimal places, if necessary. Island % population Banzhaf power index (BI) % % popn - % BI Island 1 (largest) __________ ________________ ________
Island 2 __________ ________________ ________
Island 3 __________ ________________ ________ Island 4 (smallest) __________ ________________ ________
Answers
(a) Considering each of the islands as a voter, the figurehead election as a weighted voting system can be written as follows:
System: [4 : 31, 4 : 24, 4 : 17, 4 : 8]
(b) The percentage that each island represents of the total archipelago population, its Banzhaf power index, and the difference between the Banzhaf index and percentage of the island's population in that island (calculate % population - % Banzhaf) are given below:
Island % population Banzhaf power index (BI) % % popn - % BI Island 1 (largest) 38.44 46.81 -8.37 Island 2 29.62 25.97 3.65 Island 3 21.28 19.51 1.77 Island 4 (smallest) 10.67 7.71 2.96.
Banzhaf power index The Banzhaf power index is used in weighted voting systems to calculate the power of voters or groups of voters to change the result. A voter's Banzhaf power index is determined by calculating the number of ways in which the voter can influence the outcome of the vote. The Banzhaf power index for a group of voters is the sum of the Banzhaf power indices of each voter in the group. The Banzhaf power index for each island is calculated as follows: Island
1: (24 × 17) + (24 × 8) + (31 × 17) + (31 × 8) = 46.81 Island 2: (31 × 17) + (31 × 8) + (4 × 17) + (4 × 8) = 25.97 Island 3: (31 × 24) + (31 × 8) + (4 × 24) + (4 × 8) = 19.51
Island 4: (31 × 24) + (31 × 17) + (4 × 24) + (4 × 17) = 7.71
The percentage of the archipelago population represented by each island is calculated by dividing the population of each island by the total population of the archipelago and multiplying by 100. The total population of the archipelago is 120, so the percentages are as follows: Island 1:
(31 + 24 + 17 + 8) ÷ 120 × 100% = 38.44% Island 2: 24 ÷ 120 × 100% = 20% Island 3: 17 ÷ 120 × 100% = 14.17% Island 4: 8 ÷ 120 × 100% = 6.67%
Difference between Banzhaf index and percentage population The difference between the Banzhaf index and percentage of the island's population in that island is calculated by subtracting the Banzhaf power index from the percentage of the archipelago population represented by each island. A negative number means the percentage population for that island is smaller than its Banzhaf power. The differences for each island are as follows: Island 1:
38.44% - 46.81% = -8.37% Island 2: 20% - 25.97% = -5.97% Island 3: 14.17% - 19.51% = -5.34% Island 4: 6.67% - 7.71% = -1.04%.
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The grocery store was having a sale on apples and oranges. Leo bought 20 apples and oranges
(altogether). If the ratio of apples to oranges is 3 apples: 2 oranges, how many of the 20 total were oranges?
Answers
Answer:
4 ORANGES
Step-by-step explanation:
4 EZ GEOMETRY QUESTIONS FOR 20 POINTS!
Answers
Answer:
1. use the formula
\((n-2)180\)
\((20 - 2)180\\18 * 180 = 3240\)
2. use the formula
\(360/n\\360/12\\n = 30\)
3. There is only one at 360 degrees
4. there are 6 rotational symmetries and the number of reflectional symmetries would be 6 as you can see:
A square is a rhombus.
always
sometimes
never
Answers
Answer:
always, but a rhombus is not always a square
like how all are fruits but not all fruits are
Step-by-step explanation:
If Maria uses 4N of force to lift a box onto a shelf 0.5m high, how much work did she do?
Answers
w = f × distance
w = 4 × 0.5
w=
a particle moves in a straight line with the given velocity ()=6cos() (in m/s).v(t)=6cos(t) (in m/s). find the displacement and distance traveled over the time interval [0,5].[0,5π].
Answers
The displacement and distance traveled depend on the given time interval.
To find the displacement, we need to integrate the velocity function from 0 to 5 or 0 to 5π, depending on the given time interval.
If the time interval is [0,5], we have:
Displacement = ∫[0,5] v(t) dt
Displacement = ∫[0,5] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5
Displacement = 6sin(5) - 6sin(0)
Displacement ≈ 2.785 meters
If the time interval is [0,5π], we have:
Displacement = ∫[0,5π] v(t) dt
Displacement = ∫[0,5π] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5π
Displacement = 0 - 6sin(0)
Displacement = 0 meters
To find the distance traveled, we need to integrate the absolute value of the velocity function over the given time interval.
If the time interval is [0,5], we have:
Distance = ∫[0,5] |v(t)| dt
Distance = ∫[0,5] |6cos(t)| dt
Distance = ∫[0,π/2] 6cos(t) dt + ∫[π/2,5] -6cos(t) dt
Distance = [6sin(t)] from 0 to π/2 + [-6sin(t)] from π/2 to 5
Distance = 6 - 6sin(5) ≈ 2.215 meters
If the time interval is [0,5π], we have:
Distance = ∫[0,5π] |v(t)| dt
Distance = ∫[0,5π] |6cos(t)| dt
Distance = ∫[0,π] 6cos(t) dt + ∫[π,2π] -6cos(t) dt + ∫[2π,3π] 6cos(t) dt + ∫[3π,4π] -6cos(t) dt + ∫[4π,5π] 6cos(t) dt
Distance = [6sin(t)] from 0 to π + [-6sin(t)] from π to 2π + [6sin(t)] from 2π to 3π + [-6sin(t)] from 3π to 4π + [6sin(t)] from 4π to 5π
Distance = 0 meters
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kadeem and quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles an hour. Quinn drives at a constant speed of 75 miles an hour. Who takes longer to drive the 25 miles? How much loner?
Answers
Answer:
I believe it is Kadeem who takes longer by 10 minutes.
Step-by-step explanation:
A person whose speed is slow will take longer to reach so Kadeem takes longer by 0.5 hours.
Given that,
Kadeem and Quinn both drive 25 miles.
Kadeem drives at a constant speed of 50 miles an hour.
Quinn drives at a constant speed of 75 miles an hour.
To determine who takes longer to drive the 25 miles.
Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
Time is taken by Kadeem to reach 25 miles with a speed of 25 miles per hour
= 25 / 50 = 0.5 hour
Time is taken by Quinn to reach 25 miles with a speed of 75 miles per hour,
= 25 / 75 = 0.34 hour
Thus, a person whose speed is slow will take longer to reach so Kadeem takes longer by 0.5 hours.
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a measurable part of a line that consists of two points, called endpoints, and all of the points between them are
Answers
A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.
Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.
\( \bar{AB}\)
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QUESTION OF THE DAY: Judy is recreating a small version of the Statue of Liberty out of clay. The scale for the statue is 3 inches to 100 feet. If the actual height of the statue is 305 feet, what would the height of the model be in inches?
Answers
Answer:
184in
Step-by-step explanation:
Since the scale for the statue is 3 inches to 100 feet, we can say 3:100 as a ratio.
To find approximately 305 feet you must divide 305 by 100.
100 can go into 300 evenly 3 times. Since the ratio is 3:100 you should multiply how many times the 100ft fit into the 300ft and the 3in (3 x 3) which is about 9in.
One way we can do this is to divide the hight of the Statue by the model height:
305ft 20in = 15.25ft 1in or 184in (12in per foot).
And so for every inch of the model, it represents 15.25 feet.
For 305 it would be
Sale! 60% OFF
of the original price!
The original price of an easel is $30. How much will Jamal pay if he buys it during the sale?
Answers
Which is the best approximation of 110
Answers
Step-by-step explanation:
We can find the square root of a number by using scientific notations, specifically the one listed below.\(110 \times 10^{-1}\)
When dealing with negative exponents to base 10, the answer will move left. To our surprise, though, the number does not become negative. Instead, the answer would be 11, because 110 × 10⁻¹ is like saying 110 ÷ 10, which is 11.\(= 11\)
Answer:
Given the answer is 11, we can round that down to 10.5
Hope this helps!
Help me solve the following
Answers
Answer:
C. c = 8
Step-by-step explanation:
Step 1: Write equation
7 - 3c = -17
Step 2: Subtract 7 on both sides
-3c = -24
Step 3: Divide both sides by -3
c = 8
Answer:
C)8
7-3c=-17
-3c= -24
c=8