Answer:
84
Step-by-step explanation:
How do you find the distance between L1 and L2?
The distance between the lines L1 and L2 given by √293/7.
What is the minimum distance between two lines?The distance is the angular separation between any two points on one line. Eventually, the smallest distance between these lines is zero. The distance between the lines is the same length as the perpendicular between them.
Finding two locations P1 and P2 on L1 and L2 separately will help us determine the shortest path between them. We then need to project P1P2 in the direction n that is perpendicular to both L1 and L2 to arrive at the answer. To put it another way, L1 - L2 distance = COMPN (P1P2).
Let the two points be
[tex]$$\begin{aligned}& \vec{r}=\hat{1}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) \\& \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})\end{aligned}$$[/tex]
These two lines pass through the points having position vectors [tex]$\overrightarrow{a_1}=\hat{i}+2 \hat{j}-4 \hat{k}$[/tex]and [tex]$\overrightarrow{a_2}=3 \hat{i}+3 \hat{j}-5 \hat{k}$[/tex] are parallel to the vector [tex]$\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$[/tex]
Now, [tex]$\overrightarrow{a_2}-\overrightarrow{a_1}=3 \hat{i}+3 \hat{j}-5 \hat{k}-\hat{i}-2 \hat{j}+4 \hat{k}=2 \hat{i}+\hat{j}-\hat{k}$[/tex] and [tex]$\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right) \times \vec{b}=(2 \hat{i}+\hat{j}-\hat{k}) \times(2 \hat{i}+3 \hat{j}+6 \hat{k})$[/tex]
[tex]$$\begin{aligned}& =\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\2 & 1 & -1 \\2 & 3 & 6\end{array}\right| \\& =\hat{i}(6+3)-\hat{j}(12+2)+\hat{k}(6-2) \\& =9 \hat{i}-14 \hat{j}+4 \hat{k}\end{aligned}$$[/tex]
[tex]$$\left|\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right) \times \vec{b}\right|=\sqrt{9^2+(-14)^2+4^2}=\sqrt{81+196+16}=\sqrt{293}$$\pi[/tex]
and [tex]$|\vec{b}|=\sqrt{2^2+3^2+6^2}=\sqrt{4+9+36}=7$[/tex]
The shortest distance between the two lines exists given by [tex]$\frac{\left|\left(\overrightarrow{\mathrm{a}_2}-\overrightarrow{\mathrm{a}_1}\right) \times \overrightarrow{\mathrm{b}}\right|}{|\overrightarrow{\mathrm{b}}|}=\frac{\sqrt{293}}{7}$[/tex]
Therefore, the distance between the lines L1 and L2 given by √293/7.
The complete question is;
Find the distance between the lines L1 and L2 given by
[tex]$$\vec{r}=\hat{1}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) \text { and } \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})$$[/tex]
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What are the 4 main steps of division?
The four main steps of division are dividend, divisor, quotient and remainder.
Dividend: The number that is being divided.
Divisor: The number by which the dividend is being divided.
Quotient: The result of the division, which is the number of times the divisor can "fit into" the dividend.
Remainder: The amount left over after the division is complete. It is the part of the dividend that is not "fit" into the divisor.
For example, when dividing 16 by 3, the dividend is 16, the divisor is 3, the quotient is 5, and the remainder is 1.
It can be written as:
16 ÷ 3 = 5 with a remainder of 1.
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An art gallery has reserved 10 display locations for a show the artist has 10 paintings but is uncertain on how to display them she insists on trying every possible arrangement before making her decision. If she takes one minute to set up and view each arrangement and works 10 hours a day 6 days a week how many years will it take her to decide
It will take her approximately 2.76 years to decide.
The artist has 10 paintings, and there are 10 display locations. So, the total number of possible arrangements is 10! (10 factorial) which is equal to 3,628,800.
If she takes 1 minute to set up and view each arrangement, and she works 10 hours a day 6 days a week, she can work for 60*10=600 minutes in a day.
In a week, she can work for 600*6 = 3600 minutes.
Therefore, in a week, she can view 3600/1 = 3600 arrangements.
So, it will take her to view all possible arrangements is: 3,628,800/3600 = 1008 days
That's approximately 2.76 years.
So, it will take her approximately 2.76 years to decide.
Therefore, It will take her approximately 2.76 years to decide.
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What do I do for this because I don’t think my Equation
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{16}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{16}-\stackrel{y1}{12}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{4}{-4 +6} \implies \cfrac{ 4 }{ 2 } \implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{12}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-6)}) \implies y -12 = 2 ( x +6) \\\\\\ y-12=2x+12\implies {\Large \begin{array}{llll} y=2x+24 \end{array}}[/tex]
6.6 oz for $2.50 or 30 oz for $11.29. Which one is better?
Answer:
30 oz for $11.29
Step-by-step explanation:
We can find the unit cost for each and compare.
We need both in dollars per ounce, so we divide the number of dollars by the number of ounces for each case.
6.6 oz for $2.50
Unit cost = $2.50 / 6 oz = 0.41666... $/oz
30 oz for $11.29
Unit cost = $11.29 / 30 oz = 0.376333... $/oz
At $0.38/oz, 30 oz for $11.29 is a better buy than 6.6 oz for $2.50 which is $0.42/oz.
Answer: 30 oz for $11.29
How do you translate a function left or right?
To translate a function left or right, you need to shift the graph of the function horizontally. To move the graph to the left, you subtract the same amount from each x-coordinate. To move the graph to the right, you add the same amount to each x-coordinate.
To translate a function left or right, you need to shift the graph of the function horizontally. If you want to move the graph to the left, you need to subtract the same amount from each x-coordinate. This means that all the points on the graph will be shifted to the left by the same amount. For example, if the graph of the function is f(x) = x² and you want to move it left by two units, you need to subtract two from each x-coordinate so the new graph would be f(x) = (x-2)². Similarly, if you want to move the graph right, you need to add the same amount to each x-coordinate. For example, if the graph of the function is f(x) = x² and you want to move it right by three units, you need to add three to each x-coordinate so the new graph would be f(x) = (x+3)².
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Pt. 1 write a congruence statement for the above triangles.
The congruence statement for the triangles is SSS
How to determine the congruence statementFrom the question, we have the following parameters that can be used in our computation:
The triangles
On the triangles, we can see that
The corresponding sides have the same mark i.e. I, II and III
This means that The corresponding sides are equal
So, the triangles are congruent by SSS
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Henry has worked for a factor for 31 years and will be retiring. He earned salaries over the past 4 years of $38433, $37776, $39125, and $38782. His employer calculates pension by finding the average of his last 4 years’ salaries and will give him 1. 9% of that average for each year he worked. Calculate his pension
After calculating the average of his last 4 years’ salaries and will give him 1. 9% of that average for each year he worked, the total pension is $2928.204.
In the given question, we have to calculate Henry pension.
Henry has worked for a factor for 31 years and will be retiring.
He earned salaries over the past 4 years of $38433, $37776, $39125, and $38782.
His employer calculates pension by finding the average of his last 4 years’ salaries and will give him 1.9% of that average for each year he worked.
His earning over the past 4 years = $38433, $37776, $39125, $38782
The average of Henry earning = Sum of his earning over 4 years / number of years
The average of Henry earning = ($38433 + $37776 + $39125 + $38782)/4
The average of Henry earning = $154,116/4
The average of Henry earning = $38,529
Hence, the average of Henry last 4 years’ salaries is $38,529.
The pension is 1.9% of the average salary. So,
Pension = $38,529×1.9%
Pension = $38,529×0.019
Pension = $732.051
He worked for total 4 years. So,
Total pension = $732.051×4
Total pension = $2928.204
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Solve the system
xe^y+2e^y= 0
x² − 3x + y² = 19
please help
The solution to the system of equations is x = −2, y = ±√23.
What is equation?Equation is a math statement that expresses two expressions with an equal sign. It is used to find the value of an unknown variable or unknowns. Equations are used in many branches of mathematics and science. For example, equations are used to calculate the force of gravity, the speed of light, the temperature of a gas, and the area of a triangle. Equations are also used to solve problems in physics, chemistry, engineering, and other disciplines. Equations are written in symbols and often involve multiple equations.
This system can be solved by solving the two equations separately.
For the first equation, xe^y+2e^y= 0, we can rearrange it to get xe^y = −2e^y. We can then divide both sides by e^y to get x = −2.
For the second equation, x² − 3x + y² = 19, we can plug in the value of x that we found previously, x = −2, and rearrange the equation to get y² = 23, and then solve for y by taking the square root of both sides, giving y = ±√23.
Therefore, the solution to the system of equations is x = −2, y = ±√23.
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rank the magnitude of each object’s acceleration from greatest to least. disregard the direction of the accelerations.
The rank of object according to acceleration from greatest to least is:
C = B > A
In the given question, we have to rank the magnitude of each object's acceleration from greatest to least: Disregard the direction of the accelerations.
The acceleration is given by:
a = [tex]\frac{dv}{dt}[/tex]
where, dv represents change in velocity and dt represents change in time.
Also, Acceleration = slope of velocity - time graph
For object A acceleration is 0 because velocity is constant.
Now for object B:
[tex]a_{B}=\frac{5-0}{10-0}[/tex]
[tex]a_{B}=\frac{5}{10}[/tex]
[tex]a_{B}=\frac{1}{2}[/tex]
[tex]a_{B}[/tex] = 0.5 m/s square
Now for the object C:
[tex]a_{C}=\frac{-5-0}{10-0}[/tex]
[tex]a_{C}=-\frac{5}{10}[/tex]
[tex]a_{C}=-\frac{1}{2}[/tex]
[tex]a_{C}[/tex] = -0.5 m/s square
As we know that magnitude cannot be negative, so
[tex]a_{C}[/tex] = 0.5 m/s square
As we can see that acceleration of object B and C is same although the acceleration of object A is 0 which is smaller than the acceleration of B and C.
So the rank of object according to acceleration from greatest to least is:
C = B > A
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The complete question is:
The figure below shows velocity versus time graphs for objects. Rank the magnitude of each object's acceleration from greatest to least: Disregard the direction of the accelerations.
The value of t varies directly with w. When t = 32, the value of w = 56. What is the value of w when t = 92
Answer:182 is correct
Step-by-step explanation:
Does the ordered pair (-4, -22) satisfy the function of y=5x-2
Answer:
Yes, the ordered pair (-4, -22) satisfy
Step-by-step explanation:
y=5x-2
To see if it satisfies or not, we need to put the x and y in
-22 = 5(-4) - 2
-22 = -20 -2
-22 = -22
So, the ordered pair (-4, -22) satisfy
How do you find the inverse of a set?
Let f: A→B be a function. The inverse of f, denoted by [tex]f^{-1}[/tex], is the set of ordered pairs {(b, a) ∈ B×A | f(a)=b}. That is, f−1 = {(b,a) ∈ B×A | f(a) = b}.
The inverse of a one-to-one function f: A → B, is the function g: B → A, having the following property
f(x) = y ⇔ g(y) = x
The function f is named invertible if its inverse function g exists.
When is a function from set S to set T then the inverse of f will be a function g from T to S such that each of f and g unties the other: for every s ∈ S we have g(f(s)) = s and for every t ∈ T we have f(g(t)) = t. A function f may or may not carry an inverse. When it does we can represent it as [tex]f^{-1}[/tex].
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How long is the red ribbon if the length or the blue ribbon is
When the blue ribbon measures 10 inches, the red ribbon measures 3 inches, when the blue ribbon measures 27 inches, the red ribbon measures 20 inches, and when the blue ribbon measures 'x' inches, the red ribbon measures (x - 7) inches.
According to craft project instructions, a piece of red ribbon should be 7 inches longer than a piece of blue ribbon.
To find the length of the red ribbon given the length of the blue ribbon, we can subtract 7 inches from the length of the blue ribbon.
a) The length of the blue ribbon is 10 inches.
Red ribbon length = 10 - 7 = 3 inches
b) The length of the blue ribbon is 27 inches.
Red ribbon length = 27 - 7 = 20 inches
c) The length of the blue ribbon is x inches.
Red ribbon length = (x - 7) inches
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The question seems to be incomplete the correct question would be:
Instructions for a craft project say that the length of a piece of red ribbon should be 7 inches than the length of a piece of blue ribbon. How long is the red ribbon the length of the blue ribbon is: 10 inches. 27 inches? x inches?
closure means that whenever you add or subtract two polynomials, you get a ____.
Answer:
Step-by-step explanation:
is this in college?
Given that a = 16 cm and b = 17 cm, work out the height of the triangle.
if a = 16 cm and b = 17 cm then the height of triangle is 15 cm
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that a = 16 cm and b = 17 cm
We have to find the height of the triangle.
The height of the triangle is perpendicular to a.
It forms a right angle triangle.
The base is a/2=8 cm and b is 17 cm. we have to find h.
By pythagoras theorem,
8² + h² = 17²
64+h² =289
h² =225
Square root on both sides
h=15
Hence, if a = 16 cm and b = 17 cm then the height of triangle is 15 cm.
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A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory. Sunglasses Inventory Number of Days Total Amount of Sunglasses 2 52 5 46 7 42 10 36 Which graph shows the relationship given in the table?
A graph that shows relationship between the number of days and total amount of sunglasses is attached.
How to construct and plot the data on a graph?In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).
A linear equation for the line of best fit is given by the scatter plot (see attachment), which models the relationship between the number of days and total quantity of sunglasses:
y = -2x + 62
In conclusion, the scatter plot shows an inverse relationship between the number of days and the total number of sunglasses, which can be reasonably inferred and logically deduced.
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help quick
A student has 4 fifths gallons of popcorn to give away. He wants to split it evenly between his 7 friends. How much popcorn does each friend receive?
1 over 3 gallons
4 over 35 gallons
11 over 5 gallons
28 over 5 gallons
Answer:
2nd option
Step-by-step explanation:
4/5 / 7 = 4/35 or 4 over 35 gallons
how do you graph a linear equation with a fraction in it?
The linear equation with a fraction in it can be solved by using y-intercept form method.
What are linear equations?
A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.
Now,
y-intercept form-
Make sure the linear equation is in the form y = mx + b. This is called the y-intercept form, and it's probably the easiest form to use to graph linear equations. The values in the equation do not need to be whole numbers. Often you'll see an equation that looks like this: y = 1/4x + 5, where 1/4 is m and 5 is b.[1]
m is called the "slope," or sometimes "gradient."[2] Slope is defined as rise over run, or the change in y over the change in x.
b is defined as the "y-intercept." The y-intercept is the point at which the line crosses the Y-axis.[3]
x and y are both variables. You can solve for a specific value of x, for example, if you have a y point and know the m and b values. x, however, is never merely one value: its value changes as you go up or down the line.
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Kendall scored 73 points on her math test her teacher allowed her to retake the test. She scored 98 points on the second test. What was the percentage of the increase
The percentage of the marks scored by Kendall after combining both of her test scores is found out to be as 85.5% .
Her original score = 73 and her score in the second test = 98
Considering that the test is of 100 marks, the percentage can be calculated as follows.
percentage = previous marks + current marks / 2
= 73 + 98 / 2
= 171/2
= 85.5
Therefore, Kendall's average score in both the test is found out to be 85.5% .
The percentage is calculated or is known as the average of a given set of numbers. To find the average we divide the sum of the given numbers by n , where n is the total numbers.
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What expression is equivalent to -5 - (-4)
Answer: The expression -5 - (-4) is equivalent to -5 + 4 = -1.
Step-by-step explanation:
What is the difference between saying two segments have an equal length and two segments are congruent?
Two segments are of equal length indicates its measurable quantity where as when two segments are congruent they are equal in length and shape.
As given in the question,
Difference between two segments are of equal length and the two segments are congruent is given by :
When two segments are of equal length it represents its measurable dimensions.When two shapes are congruent they equal length wise as well as shape wise.Overlapping of shape on each other represents the congruency.In case of line segment when two line segments are of equal length they are said to be congruent to each other.Therefore, the main difference in the segment of equal length and congruent segment is overlapping and only measurable quantity.
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The work done in lifting a forty-pound crate three feet is ?
1. one hundred twenty foot-pounds
2. thirteen foot-pounds
3.thirty-seven foot-pounds
4.forty-three foot-pounds
The work done in lifting a forty-pound crate three feet is forty-three foot-pounds
Lifting a forty-pound crate three feet requires how much effort?The work done in lifting a forty-pound crate three feet is forty-three foot-pounds.Work is the amount of energy transferred when a force is applied over a distance. The equation to calculate work is Work = Force x Distance. In this case, the force is the weight of the crate, which is forty pounds, multiplied by the distance lifted, which is three feet.So, forty pounds multiplied by three feet is equal to forty-three foot-pounds of work.It is important to note that the weight of the crate is the same, no matter how far it is lifted. If the crate were to be lifted only one foot, the work done would still be forty pounds multiplied by one foot, or forty foot-pounds.If the crate were lifted six feet, the work done would be forty pounds multiplied by six feet, or one hundred twenty foot-pounds.In conclusion, the work done in lifting a forty-pound crate three feet is forty-three foot-pounds. It is important to remember that the amount of work done is dependent on both the force applied and the distance over which it is applied.To learn more about a work-energy equation refer to:
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What is the equivalent ratio to 240
Answer:
the equivalent ratio to 240 is 10.
Which linear system is Mcq?
A : y [ n ] = x [ n ] x x [ n - 1]
B : y [ n ] = x [ n ] + x [ n - 10]
C : y [ n ] = x 2 [ n ]
D : (a) and (c)
This is a linear system since it is a linear combination of the inputs x[n] and x[n-1].
A: y[n] = x[n] x x[n-1]
This is a linear system since it is a linear combination of the inputs x[n] and x[n-1]. We can represent this equation as:
y[n] = a * x[n] + b * x[n-1]
where a and b are constants.
For example, if x[n] = 2 and x[n-1] = 3 then y[n] = 2 x 3 = 6.
C: y[n] = x2[n]
This is also a linear system since it is a linear combination of the input x[n] and its squared value x2[n]. We can represent this equation as:
y[n] = c * x[n] + d * x2[n]
where c and d are constants.
For example, if x[n] = 2 then y[n] = c * 2 + d * 2² = c * 2 + d * 4.
Therefore, the correct answer is D: (a) and (c).
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What is the measurement of angle y??
Answer:
y = 154°
Step-by-step explanation:
Because angle z is a straight angle it is 180°.
26° + y = 180°
subtract 26.
y = 154°
Ms. Grove has trays of paint for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction it the colors in 20 trays is purple?
Answer: 1
Step-by-step explanation: Find the total number of colors in the trays. There are 5 colors in each tray. Then Find the number of colors in the purple tray. There is only one color in the purple tray, so the number is 1.
molly wants to buy a skirt. the original price is $29. the skirt is on sale for 30% off. when she goes to pay for it the cashier tells her she can have an additional 20% discount off the sale price. not counting the sales tax, how much will molly pay for the skirt?
The total amount of money molly will pay for the skirt after the total discount is $14.5
How to determine discount?Original price of the skirt = $29
Percentage discount = 30%
Additional percentage discount = 20%
Total percentage discount = 30% + 20%
= 50%
Total amount molly paid for the skirt not counting the sales tax = $29 - (50% of $29)
= 29 - (0.50 × 29)
= 29 - 14.5
= $14.5
Hence, Molly will pay a total of $14.5 after deducting the discount.
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Which of the following fraction is closest to 0? a. 5/12
b. 2/3
c. 5/6
d. 3/4
Answer:
(a) 5/12
Step-by-step explanation:
to solve this problem you can make all fractions equivalent with 12 as the denominator
a) 5/12
b) 2/3 = 8/12 Multiply top and bottom by 4
c) 5/6 = 10/12 Multiply top and bottom by 2
d) 3/4 = 9/12 Multiply top and bottom by 3
if you compare numerators, the smallest one is the closest to zero, which would be (a) 5/12
Answer:
A 5/12
Step-by-step explanation:
first you need to round these all to /12 so a is 5/12
12/3 is 4 so multiply 4 by two which means b is 8/12
12/6 is 2 so multiply 5 by two which gives us c = 10/12
12/4 is 3 and multiply 3 x 3 which is 9 so d is 9/12
5 is the lowest decimal/fraction which makes it the closest to 0
A bedroom door in the house has the same dimensions length and all at the front door. The length is 30 in rather than 63 how much is the value of the front doors in the bedroom door
The front door is twice as long as the bedroom door.
A bedroom door in the house has the same dimensions and length and all at the front door. The length is 30 in rather than 63. If the bedroom door has a length of 30 inches, and the front door has the same dimensions but is longer, we can compare the two lengths using a proportion.
We can write the proportion as 30 inches / x inches = 1/2, where x is the length of the front door. To find the length of the front door, we can cross-multiply and solve for x: x = 30 inches * 2 = 60 inches. So the front door is 60 inches long, which is twice as long as the bedroom door.
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