Use the algebraic properties of vectors to answer the questions below. z a.) -3 + 5 b.) Find a unit vector in the direction of the vector 1
Answers
a. \(3\left[\begin{array}{ccc}2\\-3\\0\end{array}\right]+5\left[\begin{array}{ccc}-1\\0\\1\end{array}\right] = \left[\begin{array}{ccc}1\\-9\\5\end{array}\right]\) by using the algebraic properties of vectors.
b. A unit vector in the direction \(\overline{a} = \left[\begin{array}{ccc}1\frac{5}{\sqrt{34} } \\ \frac{-3}{\sqrt{34} }\\ \frac{0}{\sqrt{34} } \end{array}\right]\) of the vector \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\).
Given that,
Use the algebraic properties of vectors for solving the
a. \(3\left[\begin{array}{ccc}2\\-3\\0\end{array}\right]+5\left[\begin{array}{ccc}-1\\0\\1\end{array}\right]\)
We know that,
By using the algebraic properties of vectors as,
= 3(2i - 3j + 0k) + 5(-i + 0j + k)
= 6i - 9j + 0k -5i + 0j + 5k
= i - 9j + 5k
= \(\left[\begin{array}{ccc}1\\-9\\5\end{array}\right]\)
Therefore, \(3\left[\begin{array}{ccc}2\\-3\\0\end{array}\right]+5\left[\begin{array}{ccc}-1\\0\\1\end{array}\right] = \left[\begin{array}{ccc}1\\-9\\5\end{array}\right]\) by using the algebraic properties of vectors.
b. We have to find a unit vector in the direction of the vector \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\)
The unit vector formula is \(\overline{a}= \frac{\overrightarrow a }{|a|}\)
Let a = \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\)
Determinant of a is |a| = \(\sqrt{5^2 +(-3)^2 + (0)^2}\) = \(\sqrt{25 + 9}\) = \(\sqrt{34}\)
\(\overrightarrow a\) = 5i -3j + 0k
Now, we get
\(\overline{a}= \frac{\overrightarrow a }{|a|}\) = \(\frac{5i -3j + 0k}{\sqrt{34} }\) = \(\frac{5}{\sqrt{34} }i + \frac{-3}{\sqrt{34} }j + \frac{0}{\sqrt{34} } k\)
\(\overline{a} = \left[\begin{array}{ccc}1\frac{5}{\sqrt{34} } \\ \frac{-3}{\sqrt{34} }\\ \frac{0}{\sqrt{34} } \end{array}\right]\)
Therefore, a unit vector in the direction \(\overline{a} = \left[\begin{array}{ccc}1\frac{5}{\sqrt{34} } \\ \frac{-3}{\sqrt{34} }\\ \frac{0}{\sqrt{34} } \end{array}\right]\) of the vector \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\).
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Related Questions
Determine the number of solutions 3x + 1 = 4x - 2
A) One solution
B) Infinitely many solutions
C) No solution
Answers
Answer:
one solution
Step-by-step explanation:
1. 1=4x-2-3x
2. 1=x-2
3. 1+2=x
4. 3=x
From a point 50 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35∘ and 47∘40′ respectively. Find the height of the steeple.
Answers
The height of the steeple is 12.66 feet.
Find the number of heightTo find the height of the steeple, we will use the concept of angle of elevation. Angle of elevation is the angle between the horizontal line and the line of sight when we look up at an object.
Let's denote the height of the church as h1 and the height of the steeple as h2. Then, the total height of the church and the steeple is h1 + h2.
Using the concept of angle of elevation, we can write the following equations:
tan(35°) = h1/50 tan(47°40') = (h1 + h2)/50
Solving the first equation for h1, we get:
h1 = 50 * tan(35°) = 35.08 feet
Substituting the value of h1 into the second equation and solving for h2, we get:
50 * tan(47°40') = 35.08 + h2
h2 = 50 * tan(47°40') - 35.08
= 47.74 - 35.08 = 12.66 feet
Therefore, the height of the steeple is 12.66 feet.
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a company manufactures rice in 10 kg bags with a standard deviation of 1.25 kg per bag. what is the probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs?
Answers
Probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs is 0.0596.
What is probability ? Probability is simply the possibility that something will happen. We may talk about the possibility of one result, or the likelihood of numerous outcomes, when we don't know how an event will turn out. The study of events with a probability distribution is known as statistics.Calculation\(\sigmaT = \sigma / \sqrtn = 1.25 / \sqrt15 = 0.3227\)
\(= P[(9 - 10) / 0.3227 < (T - \muT ) / \sigmaT < (9.5 - 10) / 0.3227)]\)
= P(-3.10 < Z < -1.55)
= P(Z < -1.55) - P(Z < -3.10)
= 0.0606 - 0.001
= 0.0596
Probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs = 0.0596
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Word Bank: Alternate Interior Angles, Alternate Exterior Angles, Vertical Angles, Adjacent Angles, Linear Pair
Corresponding Angles
Use the word bank and fill in the blanks (words will only be used once)
angles.
angles.
angles.
angles.
and
angles.
Answers
The relationship between the angles depend on their relative positions.
∠a and ∠c are Vertical angles
∠a and ∠b are Adjacent angles and linear pair angles
∠b and ∠h are Alternate interior angles
∠f and 55° are Alternate exterior angles
∠a and ∠e are Corresponding angles
How can the different angles formed be identified?The possible drawing in the question created based on the relationship between the angles is attached.
∠a and ∠c =
Vertical angles: Opposite angles formed by intersecting lines
∠a and ∠b =
Adjacent angles: Angles that share a common side
Linear pair angles: Adjacent angles that sum up to 180° or form a straight line
∠b and ∠h =
Alternate interior angles: Angles formed on the opposite side of a transversal intersecting two coplanar lines, and in the interior region between the lines
∠f and 55°
Alternate exterior angles: Angles formed on the exterior region between two lines having a common transversal and on the opposite sides of the transversal
∠a and ∠e
Corresponding angles: Angles formed in similar positions relative to a transversal and the two lines intersected.
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Julietta and mark both have a calculus exam next week. Julietta spends 2 hours studying each night for 7 nights, while mark crams his sessions into 2 blocks of 7 hours. Based on what you know about the spacing effect,you would predict that,.
Answers
For an exam next week, Julietta spends 2 hours studying each night for 7 nights, while Mark crams his sessions into 2 blocks of 7 hours, hence based on spacing effect, it can be predicted that Julietta’s memory would be stronger than Mark.
Spacing effect refers to an observation that repetitions that is spaced in time (spaced learning) can produce stronger long-term memories than repetitions massed closer together in time (massed learning). According to research, spaced learning has demonstrated consistently to offer benefit memory as opposed to massed learning. Spaced learning can lead to enhanced long-term memory and recollection of information learn becomes more easier than in massed learning.
In this case, Julietta opted for spaced learning, spend two hour each night studying for seven nights (the repetition of subject topic spaced over a period of week). Mark opted for massed learning, cram his session in two blocks of seven hours straight (repetition of subject topic contracted over a short period of two blocks). Hence, Julietta will be enabled to remember the material more easily than Mark
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If f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x)
A) 2x-3
B)3x-3
C)4x+1
D)2x-1
Answers
Answer:
C.
Step-by-step explanation:
The mass of a baby boy at birth was 3.6kg. When he was 6 months old and 12 months old, his masses were 7.2 kg and 10.0 kg respectively. What was the percentage increase in his mass at 12 months old when compared with (a) his mass at birth (b) his mass at 6 months old
Answers
Using the concept of fraction and percentage, the percentage increase of the baby at 12 months is 177.7 percent
What is Percentage IncreasePercentage increase is a mathematical concept that refers to the increase in a particular value over its initial amount. It is usually expressed as a percentage and is calculated by dividing the increase in the value by the original amount, then multiplying by 100.
In this problem, the data given are;
Initial mass = 3.6kgmass at 6 months = 7.2kgmass at 12 months = 10kgThe percentage increase at 12 months old can be calculated as
percentage increase = [(mass at 12 months - Initial mass) / Initial mass] * 100
percentage increase = [(10 - 3.6) / 3.6] * 100
percentage increase = 1.7 * 100
Percentage increase = 177.7%
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6) What is the value of x in the figure shown below? (8x) 140° A. 130 C. B. 22.5 D.. 5
Answers
Notice that the angles of 140° and (8x)° are supplementary angles, since they make an angle of 180°. Then:
\(8x+140=180\)Solve for x:
\(\begin{gathered} \Rightarrow8x=180-140 \\ \Rightarrow8x=40 \\ \Rightarrow x=\frac{40}{8} \\ \Rightarrow x=5 \end{gathered}\)Therefore, the value of x is:
\(5\)Consider the vector function given below.
Do the following.
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
(b) Find the curvature.
Answers
(a) The unit tangent and unit normal vectors T(t) and N(t) is ⟨-sin t, 0, -cos t⟩.
(b) The curvature is 3/(9 cos² t + 4 + 9 sin² t)
To find T(t), we first take the derivative of r(t) with respect to t, which gives us the velocity vector v(t) = ⟨3 cos t, 2, -3 sin t⟩. Then, we divide this vector by its magnitude to get the unit tangent vector T(t) = v(t)/||v(t)||, where ||v(t)|| is the magnitude of v(t). This gives us:
T(t) = ⟨(3/√(9 cos² t + 4 + 9 sin² t)), 2/√(9 cos² t + 4 + 9 sin² t), (-3/√(9 cos² t + 4 + 9 sin² t)))⟩
To find N(t), we take the derivative of T(t) with respect to t, and divide by the magnitude of this derivative:
N(t) = T'(t)/||T'(t)||, where T'(t) is the derivative of T(t) with respect to t.
After some algebraic simplification, we find that T'(t) = ⟨-3 sin t, 0, -3 cos t⟩, so
||T'(t)|| = 3, and
N(t) = ⟨-sin t, 0, -cos t⟩.
Now that we have the unit tangent and unit normal vectors, we can move on to finding the curvature, denoted k(t). Specifically, the curvature is given by the formula:
k(t) = ||T'(t)||/||v(t)||²
where ||T'(t)|| is the magnitude of the derivative of the unit tangent vector, and ||v(t)||² is the square of the magnitude of the velocity vector.
We already found ||T'(t)|| and ||v(t)|| in the previous steps, so we can plug these values into the formula to get:
k(t) = 3/(9 cos² t + 4 + 9 sin² t)
This gives us the curvature for every value of t.
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Complete Question:
Consider the vector function given below. r ( t ) = ⟨ 3 sin t , 2 t , 3 cos t ⟩ Do the following:
(a) Find the unit tangent and unit normal vectors, T(t) and N(t).
(b) Find the curvature, k(t).
complete the work to find the length of hd. use the side-splitter theorem to set up a proportion. startfraction e g over g d endfraction
Answers
The measure of HD in the given figure using the side-splitter theorem is 5.5.
We have,
The Side-Splitter Theorem is a geometric theorem that relates the side lengths of two triangles formed when a pair of parallel lines intersects two transversals.
Now,
Applying the side splitter theorem in the given figure,
EG/GD = FH/HD ______(1)
Given,
EG = 4
GD = 11
FH = 2
Substituting in (1).
4/11 = 2/HD
Cross-multiply.
HD = 2/4 x 11
HD = 11/2
HD = 5.5
Thus,
The measure of HD in the given figure using the side-splitter theorem is 5.5.
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The complete question:
complete the work to find the length of HD.
Use the side-splitter theorem to set up a proportion.
EG/GD = FH/HD
Substitute in the known side lengths.
4/11 = 2/HD
Cross multiply and solve for HD.
HD =
Pls help me with this answer
Answers
And angle which would be 90 degrees
Do 52+90 =142
180-142=38
Then you’d do 44+38=82
180-82=98
(This is because angles on straight line add up to 180)
ANSWER = 98
how do i simplify this problem?
Answers
Answer:
\(9x \frac{19}{4}\)
Step-by-step explanation:
Given Expression:
\(\sqrt[4]{(3x^3)^3 times (3x^2)^5}\)
Simplification:
\(9x\frac{19}{4}\)
awnser the questions to describe the transformations of figure ABCD. Is A'B'C'D' a translation rotation or reflection of abcd?
Answers
Answer:
1. Reflection
2. rotation and reflection
3. b', b''
4. 26.3
Step-by-step explanation:
1. It is like looking in a mirror. Its is being reflected across the y axis
2. It is rotated 90 degrees to the right. Then reflected over the x axis.
3. they are the same
4. It is the same as A" B" C" D" so the lengths are the same and you just add them.
Step-by-step explanation:
a nurse is planning care for a client to prevent postoperative atelectasis. which of the following interventions should the nurse include in the plan of care except?
Answers
Answer:
You didn't provide any choices or options to pick from but here are the possible answers is:
- Encourage the use of the incentive spirometer every 2 hours
-Instruct to splint incision when coughing and deep breathing.
-Reposition the client every 2 hours
-Assist with early ambulation.
Step-by-step explanation:
Hope I could help!
In the plan of care to prevent postoperative atelectasis, interventions should not include the use of tobacco products or exposure to secondhand smoke.
The nurse should include several interventions in the plan of care to prevent postoperative atelectasis, but there are specific interventions that should not be included. Atelectasis is the partial or complete collapse of the lung, and preventing it is crucial after surgery. Here are some interventions that should be included:
Incentive Spirometry: The nurse should encourage the client to use an incentive spirometer to promote deep breathing and lung expansion.
Early Ambulation: Encouraging the client to get out of bed and walk as soon as possible after surgery helps improve lung function.
Pain Management: Adequate pain control measures should be in place to ensure the client can take deep breaths without discomfort.
Coughing and Deep Breathing Exercises: The nurse should teach and encourage the client to perform regular coughing and deep breathing exercises to clear the airways and prevent mucus buildup.
Positioning: Proper positioning, such as elevating the head of the bed, can aid lung expansion.
What should not be included in the plan of care is the use of tobacco products or exposure to secondhand smoke, as smoking and smoke exposure are detrimental to lung health and can worsen atelectasis. These should be strictly avoided to prevent postoperative complications.
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please answer quick!!
Answers
Answer: B
Step-by-step explanation:
\(\frac{2}{7k}(k-7)\)
\(\frac{2k-14}{7k}\)
\(\frac{2k}{7k}-\frac{14}{7k}\)
\(\frac{2}{7}-\frac{2}{k}\)
The overnight temperature in Polokwane drops from 11 °C to -2 °C y how many degrees has the
temperature dropped?
Answers
Answer:
13
Step-by-step explanation:
Answer:
13⁰
Step-by-step explanation:
ur answer is 13⁰
11 - (-2)
13
Describe the meaning of the translation (x + 6, y + 10).
All points are moved 6 units right and 10 units up
All points are moved 6 units left and 10 units up
All points are moved 6 units left and 10 units down
All points are moved 6 units right and 10 units down
Answers
Answer:
Step-by-step explanation:
The meaning of the translation (x + 6, y + 10) is that all points in a coordinate plane are moved 6 units to the right and 10 units up.
In other words, for any point (x, y) in the original position, after the translation, the new coordinates would be (x + 6, y + 10). This means that the x-coordinate of each point is increased by 6 units, resulting in a shift to the right, and the y-coordinate is increased by 10 units, resulting in a shift upwards.
Im Not Understanding!
Answers
There are 9, 1/2’s in the equation, since 3/2 + 3/2 + 3/2 = 9/2.
So you would put 9 in the box, since you’re multiplying the numerator.
Hope this helps!
Answer:
3/2 + 3/2 + 3/2 = 3/1
so 3 over 1 times 1 over 2
What animal has the most bones
Answers
Answer:
Pythons is the answer
Plot the points (-3, 4)(−3,4)left parenthesis, minus, 3, comma, 4, right parenthesis and (4, 4)(4,4)left parenthesis, 4, comma, 4, right parenthesis on the coordinate plane below
Answers
Answer:
The image shows the points on a coordinate axis.
Step-by-step explanation:
The first point is \((-3,4)\).
This means that the point on the \(x\) axis is \(-3\) and \(y\) axis is \(4\). The point is in the second quadrant.
The second point is \((4,4)\).
This means that the point on the \(x\) axis is \(4\) and \(y\) axis is \(4\). The point is in the first quadrant.
The image shows the points on a coordinate axis.
Answer:
7 UNITS
Step-by-step explanation:
YW :D
Which of the following best describes the slope of the line below?
Answers
Answer:
I think positive
Step-by-step explanation:
Answer:
zero, D
Step-by-step explanation:
a horizontal line (left to right) would be zero
a verticle line (up and down) would be undifined
Joe's triangle hut is having a sale. All triangles are priced at $0.68
Answers
Joe's Bamboo Hut Kitchen and Seafood, Patong: See 5 unbiased reviews of Joe's Bamboo Hut Kitchen and ... Traditional Thai food with an amazing variety including fresh seafood all at an extremely affordable price and .
36 inch board is to be cut into three pieces so that the second piece is three times as long as the first piece and the third piece is five times as long as the first piece if X represents the length of the first piece find the length of all three pieces
Answers
Answer: the first one would be four then that times 3 would be 12 which is 2 and then 4 times 5 is 20 which would be the third then you could add to check and you would get 36
Step-by-step explanation:
Hope this helped
if something's not clear, write a comment I'll help
Examine the division problem.
StartFraction 15 over 4 EndFraction divided by (negative StartFraction 5 over 8 EndFraction
To solve the problem, you first must find the reciprocal of the second fraction. Which reciprocal fraction should you use?
Negative StartFraction 5 over 1 EndFraction
Negative one-fifth
Negative StartFraction 5 over 8 EndFraction
Negative StartFraction 8 over 5 EndFraction
Answers
Answer:
The answer is -8/5
Step-by-step explanation:
i took the the quiz.
Answer:
-8/5
Step-by-step explanation:
did the assinmant
What is 67 kg in stones and pounds?
Answers
Kilograms (kg) is a unit of mass that is commonly used in the metric system. However, in some countries, such as the United Kingdom and the United States, the customary unit of measurement for weight is stone and pounds.
67 kg in stones is equivalent to approximately 147.71 pounds.
It's important to note that while the conversion from kilograms to stone and pounds is straightforward, the conversion is not exact due to rounding. However, this difference is generally small and can be ignored for most practical purposes.
Overall, understanding the conversion from kilograms to stone and pounds can be useful for students who are studying or traveling between countries that use different units of measurement for weight. Additionally, the process of converting from one unit of measurement to another can help reinforce important mathematical skills, such as division and rounding.
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What Is the solution to the system of equations? Y=-3x-2
5x+2y=15
Answers
Answer:
x,y=-19,55
Step-by-step explanation:
plug in y.
5x+2(-3x-2)=15
5x-6x-4=15
-x=19
x=-19.
Plug in.
y=-3(-19)-2
y=55
correct is B.
Hope this helps :D
in the figure below,two lines are parallel and m < 1 =83°. Find all other angles
Answers
Answer:
angle 3=83(vertically opposite angles are equal)
angle 5=angle 3(alternate interior angles) so = 83
angle 7 =angle 5 ( vertically opposite angles)
angle 2 +angle 1=180 (linear pair ) so angle 1 + 180-83=97
angle 4 = angle 2 (VOA)=97
angle 6 =angle 4 (AIA)=97
angle 8 =angle 6(VOA)=97
hope it helped plz mark me as brailiest
Step-by-step explanation:
The hypotenuse of a right triangle measures 18cm and one of its leg measures 2 cm. find the measure of the other leg
Answers
Using Pythagorean's theorem we can see that the measure of the other leg of the right triangle is 17.89 cm
How to find the measure of the other leg?By Pythagorean's theorem, we know that the sum of the squares of the legs is equal to the square of the hypotenuse.
Then if the other leg has a length x, we can write the equation:
\(x^2 + 2^2 = 18^2\)
Solving for x we get:
\(x = \sqrt{(18^2 - 2^2)}\)
Solving that square root we will get:
x = 17.89 cm
That is the measure of the other leg of the right triangle.
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Find the number that makes the ratio equivalent to 1:7.
Answers
Answer:
So 2:14 and 3:21 are two ratios that are equal to 1:7. Students are also asked to determine whether two given ratios are equal, by first writing each ratio as a fraction, then writing each fraction in lowest terms. If the two fractions are the same when written in lowest terms, then the ratios are equal.
Step-by-step explanation:
Above
Please Mark brainliest if this helped i need 3 more!
Answer:
2:14 or 3:21
Step-by-step explanation:
because u multiply
(refer to figure 26, area 2.) the visibility and cloud clearance requirements to operate vfr during daylight hours over the town of cooperstown between 1,200 feet agl and 10,000 feet msl are
Answers
The visibility requirement is 3 statute miles, and cloud clearance requires maintaining 500 feet below, 1,000 feet above, and 2,000 feet horizontally from clouds during VFR daylight operations over Coopers Town.
Determine how to find the visibility and cloud clearance requirements to operate VFR?The visibility and cloud clearance requirements to operate VFR during daylight hours over the town of Coopers Town between 1,200 feet AGL and 10,000 feet MSL are as follows:
1. Visibility: The minimum visibility required is 3 statute miles.
2. Cloud clearance: Maintain a distance of at least 500 feet below, 1,000 feet above, and 2,000 feet horizontally from clouds.
According to VFR regulations, pilots flying during daylight hours must adhere to certain visibility and cloud clearance requirements for safety. The visibility requirement of 3 statute miles means that the pilot must have a clear horizontal view of at least 3 miles ahead.
This ensures sufficient visual reference to navigate and avoid other aircraft or obstacles.
Regarding cloud clearance, pilots must maintain a safe distance from clouds to ensure visibility and separation from potential hazards. The requirement is to remain at least 500 feet below clouds to avoid inadvertently entering them.
Additionally, pilots must maintain a minimum of 1,000 feet above clouds to prevent the risk of collision or reduced visibility due to cloud turbulence. Lastly, a horizontal separation of 2,000 feet from clouds helps ensure adequate maneuvering space and visual reference in relation to cloud formations.
These visibility and cloud clearance requirements help maintain safety and situational awareness for VFR operations during daylight hours over Coopers Town.
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